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Exercises on Political and Social Divisions in American Society

Edward Nelson

California State University, Fresno

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Table of Contents

Page

Preface 3

Prologue 4

Exercise 1 – Political Divisions 7

Exercise 2 – Gender Divisions 14

Exercise 3 – Socioeconomic Divisions 21

Exercise 4 – Racial Divisions 30

Exercise 5 – Religious Divisions 37

Exercise 6 – Geographical Divisions 47

Exercise 7 – Elaborating Political Divisions 55

Exercise 8 – Elaborating Gender Divisions 62

Exercise 9 – Elaborating Socioeconomic Divisions 69

Exercise 10 – Elaborating Racial Divisions 79

Exercise 11 – Elaborating Religious Divisions 85

Exercise 12 – Elaborating Geographical Divisions 92

Epilogue 99

Appendix – Introduction to Survey Documentation and Analysis (SDA) 109

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Edward Nelson, California State University, FresnoPreface

These exercises could be used in any course that focuses on social structure and divisions between the individuals and groups that make up that social structure. They could also be used in courses that want to introduce students to quantitative data analysis. There are a series of 12 exercises that focus on six different types of divisions – political, gender, socioeconomic, racial, religious, and geographical. The first six exercise focus on two-variable (bivariate) analysis and the last six on three-variable (multivariate) analysis. There is a prologue that introduces the exercises and an epilogue that summarizes the findings of the exercises.

The data set we’ll be using is the 2018 General Social Survey (GSS), a large national probability survey of adults in the U.S. The data are already weighted to make the sample better represent the population from which the same was drawn. The statistical program we're going to use is Survey Documentation and Analysis (SDA) written at UC Berkeley and freely available wherever you have an internet connection. There is a brief introduction to SDA at the end of these exercises.

Since these exercises were written so each exercise was independent of the other exercises, there is considerable duplication from exercise to exercise. If you use several exercises, you are free to remove this duplication and to add material of your own. My suggestion is that you consider using one or more of the paired exercises that focus on particular types of divisions.

Statistical analysis is limited to crosstabulation, Chi Square, and measures of association (Cramer’s V and Tau-c). SDA will carry out the computations for these statistics with the exception of Cramer's V for which I explain how to compute by hand.

You have permission to use these exercises and the data set and to revise the exercises to fit your needs. Feel free to revise them in any way you want. Just recognize the source of the original exercise. I would like to hear from you about your experiences using the exercises.

If you would like to contact me (Edward Nelson), please email me at [email protected]. I’m Professor Emeritus at California State University, Fresno in the Sociology department. I taught research methods, statistics, and critical thinking before retiring and now teach a critical thinking course part time. If you find any errors, please let me know so I can correct them. Please feel free to contact me about any questions or problems you may have when using the exercises.

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mailto:[email protected]


Edward Nelson, California State University, FresnoPrologue

Social structures are made up of individuals and groups and these individuals and groups are often (not always) very different from each other1. We can ask a myriad set of questions about these individuals and groups. Here are some examples.

At the individual level, consider high school seniors who are trying to decide what to do after they graduate. Some will look for a job, others might go into the military, still others decide to go on to college. What are the factors that influence their decision?

At the dyad level, consider friendships. Why do some individuals form friendships and others don't?

At the family level, why are some families more likely to identify with Democrats and other more likely to identify as Republicans?

At both the group and the individual levels, consider political action groups. Some of these groups are liberal and others are conservative. Why are some individuals more politically active than others? Why do some join liberal groups and others conservative groups? Why do some of these political action groups engage in different types of political activities (e.g., voter registration drives, writing their congressional representatives, political protest – both non-violent and violent)?

Consider our country's geographical divisions. Why do some individuals choose to live in different regions of the country? And why do some of these regions vote very differently? Why are some states very Republican (i.e., red states such as Alabama), other very Democrat (i.e., blue states such as California), and others fairly balanced between Republicans and Democrats (i.e., swing state that are sometimes called purple states such as Wisconsin)?

In short, one of the goals of social scientists is to explain why individuals and groups behave differently and why individuals have different attitudes and opinions. Another way to put this is – why aren't we all alike? And still another way to put it is to ask why sometimes there are sharp divisions among us and other times very little division.

Let's consider our nation's response to the pandemic of 2020 caused by the Covid-19 virus. How has our society responded to the spread of this virus?

1 There are two references that you could look at for more discussion of social structure. For a methodological discussion of social structure, see Matilda White Riley, Sociological Research – A Case Approach, Harcourt, Brace & World (1963). For a more conceptual discussion of social structure, see Thomas J. Sullivan, Applied Sociology – Research and Critical Thinking, Macmillan Publishing Company (1992). Both of these books are older treatments of social structure but are well worth reading.

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We could explore this question at the national level or at the state level or at the county level or at the community level? We could also explore this at the individual level. Both individuals, governments, and groups such as colleges and universities have to make decisions about how to respond to the pandemic. Here are just some of the decisions that need to be made.

Should we social distance? That is, should we try to maintain at least a six-foot distance between ourselves and others?

Should we wear a mask when we are around other people? Should we social isolate ourselves from others? Should those who are more at risk (e.g., the elderly or have a compromised immune system)

take more extreme precautions than those at less risk? How should groups (e.g., states and communities) enforce social distancing and mask wearing?

It probably comes as no surprise that individuals and groups make different decisions about the pandemic. Katz, Sanger-Katz, and Quealy provide us with a detailed look at who is wearing masks in the U.S2. Based on a very large survey of about 250,000 individuals they showed that "mask use is high in the Northeast and the West, and lower in the Plains and parts of the South. . . . In many parts of Georgia, seeing unmasked people is common, but mask use is very high in the area around the city of Albany [Georgia], where there was an early and intense outbreak of coronavirus." Nationally, the U.S. ranks below some countries (e.g., Mexico, Spain) in mask wearing but above other countries (e.g., Sweden, Finland, Denmark).

There are large differences in mask wearing among political partisans. Katz et al report that "there is a 20-point split in many surveys, with Republicans substantially less likely to say they wear masks often or always and much more likely to say they never wear a face covering." It's possible that this difference could be accounted for by other variables such as where people live or age but Shana Gadarian "found that your political party is a better predictor of mask use than any other factor they measured. Her team compared people of the same age and living in the same ZIP code and found partisan differences in mask behavior."3 In other words, there are deep divisions between political partisans with respect to mask wearing.

Mark Baldassare, president of the Public Policy Institute of California (PPIC), reports that the "pandemic disproportionately affects the health and wellbeing of Latinos and African Americans."4 In their July 2020 survey, PPIC found that "Latinos (52%) are the most likely to say that their lives have been disrupted a lot by the coronavirus outbreak. . . . Latinos (61%) are also the most likely to be very worried about getting sick from the coronavirus."

These exercises focus on divisions in American society. There are many different ways that divisions can be formed. We're going to look at six such divisions – divisions based on:

politics (Exercises 1 and 7), gender (Exercises 2 and 8),

2 https://www.nytimes.com/interactive/2020/07/17/upshot/coronavirus-face-mask-map.html3 https://www.nytimes.com/interactive/2020/07/17/upshot/coronavirus-face-mask-map.html4 https://www.ppic.org/blog/widespread-worry-racial-ethnic-disparities-as-covid-19-surges/

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https://www.ppic.org/blog/widespread-worry-racial-ethnic-disparities-as-covid-19-surges/

https://www.nytimes.com/interactive/2020/07/17/upshot/coronavirus-face-mask-map.html

https://www.nytimes.com/interactive/2020/07/17/upshot/coronavirus-face-mask-map.html

socioeconomic status (Exercises 3 and 9), race (Exercises 4 and 10), religion (Exercises 5 and 11), and geography (Exercises 6 and 12).

We should expect to find that sometimes these divisions are large and other times they are much smaller. But what are these divisions about? In the example we just considered, it was about mask wearing. We're going to explore several attitudinal and behavioral variables in these exercises such as opinions on abortion and capital punishment, fear of being a victim of a violent crime, how people feel about controlling the distribution of pornography, opinions on the legalization of marijuana, and voting behavior in the 2012 and 2016 presidential elections.

We're going to use some relatively simple statistical tools including frequency distributions and crosstabulation. We're also going to use a statistical test of significance called Chi Square and some commonly used measures of association called Tau-c and Cramer's V. We certainly don't want to get bogged down in computing these statistics by hand so we're going to use a statistical package called Survey Documentation and Analysis (SDA) that is freely available on the internet and can be used anywhere you have an internet connection. We're also going to need a data set that is freely available. The General Social Survey, a large national probability survey conducted biannually, meets this need nicely.

These exercises consist of two sets of six exercises each. The first six exercises explore divisions by looking at two-variable tables (i.e., bivariate analysis). Each exercise will focus on a different division – political, gender, socioeconomic, race, religious, and geographical. The last six exercises explore these same divisions by looking at three-variable tables (i.e., multivariate analysis).

There are several different ways you could use these exercises. You don't have to use all of them. You could select some of these divisions on which to focus. The exercises are written so each exercise is independent of the other exercises. That means there is considerable redundancy across the exercises. If you use several exercises, feel free to skip over these sections. I suggest that you use at least one of the exercises in the two-variable set and at least one of the companion exercises in the three-variable set.

So, let's get started.

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Edward Nelson, California State University, FresnoExercise 1

Political Divisions

It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. A 2019 Gallup report comments:

Partisans on both sides increasingly see institutions in the U.S. not as beneficial and necessary, but as part of an effort by the other side to gain advantage and to perpetuate its power and philosophical positions. Liberals and Democrats today, for example, have lower trust in traditional family institutions, traditional religious institutions and the economic system. Republicans have lower trust in the scientific process, higher education, the mass media, and the role of the state (government).5

Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). There are two critical questions to consider.

Are these groups (e.g., nations, communities, churches) divided? How big are these divisions?

This series of exercises will focus on divisions. The first six exercises will focus on two-variable analysis (i.e., bivariate analysis) and the last six on three-variable analysis (e.g., multivariate analysis). We'll use several statistical tools (i.e., crosstabulation, Chi Square, and measures of association). The data we're going to use is the General Social Survey (GSS), a large national probability survey of adults in the U.S. We'll be using the 2018 GSS. The statistical program we're going to use is Survey Documentation and Analysis (SDA) written at UC Berkeley and freely available wherever you have an internet connection. There is a brief introduction to SDA at the end of these exercises.

Goal of Exercise

The goal of this exercise is to explore political divisions focusing on how respondents said they voted in the 2012 and 2016 presidential elections.

5 Newport, Frank. The impact of Increased Political Polarization. December 5, 2019. https://news.gallup.com/opinion/polling-matters/268982/impact-increased-political-polarization.aspx

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https://news.gallup.com/opinion/polling-matters/268982/impact-increased-political-polarization.aspx

https://news.gallup.com/opinion/polling-matters/268799/public-opinion-role-government-candidates.aspx

https://news.gallup.com/poll/267047/americans-trust-mass-media-edges-down.aspx

https://news.gallup.com/opinion/gallup/223451/political-divide-higher-education-america.aspx

https://www.pewresearch.org/science/2019/08/02/trust-and-mistrust-in-americans-views-of-scientific-experts/?utm_source=link_newsv9&utm_campaign=item_268982&utm_medium=copy

https://news.gallup.com/poll/266960/economic-confidence-drops-lowest-level-shutdown.aspx

https://news.gallup.com/opinion/polling-matters/258032/religious-left-numbers-problem.aspx

https://news.gallup.com/poll/257858/birth-control-tops-list-morally-acceptable-issues.aspx

Part 1 – Measures of Politics

We're going to focus on the political party with which people identify. Here's the question in the GSS that provides us with a way of measuring a person's political identification. The name of the variable is italicized and in parentheses following the question wording.

""Generally speaking, do you usually think of yourself as a Republican, Democrat, Independent, or what?" (partyid)

Let's start by getting frequency distributions for partyid. To access the GSS cumulative data file in SDA format click here. The Introduction to SDA at the end of these exercises will show you how to get frequency distributions for these variables. The variable name is in parentheses above. Your output should look like the following.

Figure 1-1

Notice a few things about this chart.

Some respondents said they didn't know or refused to answer the questions. This is typically referred to as missing data. Cases with missing data are, by default, excluded from the frequency distributions.

Percents appear first and the frequencies or counts appear below the percents. If your results don't look like these figures it might be because you forgot to enter YEAR(2018) in

the SELECTION FILTER box.

Very few people said they belonged to some other party so we're going to exclude these cases from our table. To do that you would enter partyid(0-6) in the SDA dialog box. Rerun the table and convince

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https://sda.berkeley.edu/sdaweb/analysis/?dataset=gss18

yourself that this works. Put the range of values you want to include in your table in parentheses following the variable name.

Part 2 – Statistical Inference

Keep in mind the questions that we're going to focus on in this exercise.

Are Americans divided by their political party identification? How big are these divisions?

It would be nice if we could ask all adults (18 years of age and over) in the U.S. how they felt about these issues but that's clearly impractical. So we're going to use a sample of adults and use the sample data to make inferences about the population of all adults. This is typically referred to as statistical inference. The 2018 GSS is a large national probability sample of adults in the U.S. consisting of a little more than 2,300 adults. As samples go, that's a quite large sample, It might not seem so since 2,300 is a tiny percent of all adults but it turns out that what's important is not the percent of the population in the sample but the absolute size of the sample If you want to learn more about sampling, click on this link and look at Chapter 2. Or just take my word for it. A sample of 2,300 is a large sample regardless whether the population is 100,000 or 1,000,000 or 300,000,000. The nice thing about large probability samples is that the amount of sampling error decreases with sample size (everything else being equal).

Part 3 – Relationships Between Two Variables (Crosstabulation)

We're going to start by comparing Democrats, Independents, and Republicans with respect to how they said they voted in the 2012 presidential election. To make these comparisons we're going to use a statistical technique (or tool) called crosstabulation. The Introduction to SDA at the end of these exercises will show you how to run a crosstabulation in SDA.

Before we look at the relationship between political preference and voting , we need to talk about independent and dependent variables. The dependent variable is whatever you are trying to explain. In our example, that's how people said they voted in a recent presidential election. The independent variable is some variable that you think might help explain how people voted. In our case, that would be political party identification. Normally we put the dependent variable in the row and the independent variable in the column of the crosstabulation. We’ll follow that convention in these exercises.

So, let's start with the crosstab of pres12 by partyid. Notice that we describe the crosstab as dependent variable by independent variable. Now we're going to get the crosstab of pres12 by partyid. Before we do this, we need to talk about recoding. We're going to combine strong Democrat (0), not strong Democrat (1), and Independent, leaning toward Democrats (2) into one category and give that category a value of 1. Then we're going to do the same thing for Republicans and combine strong Republican (6), not strong Republican (5), and Independent leaning toward Republicans (4) into another category and give that a value of 3. That leaves us with the Independents who don't lean toward either party. We'll give them a value of 2. So, we'll end up with three categories – Democrats (1), Independents (2), and Republicans (3). Recall that we're going to omit those who indicated a third party (7) from our analysis. If we don't include them in any of our recodes, SDA will omit them.

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http://ssric.org/node/619

We also want to limit our analysis to respondents who voted for either the Democratic or the Republican candidate for president. Since the two major party candidates are coded 1 and 2, all we have to do is to list the variable as pres12(1-2).

The Introduction to SDA at the end of these exercises shows you how to recode. However, it can be a little tricky so I'm going to give you the recode statement and all you have to do is to copy and paste it into the appropriate box in SDA.

For partyid, the recode is:partyid (r:1=0-2"Democrat";2=3-3"Independent";3=4-6"Republican")

Open SDA and enter the following in the dialog box.

In the ROW box, enter: pres12(1-2) In the COLUMN box, enter: partyid (r:1=0-2"Democrat";2=3-3"Independent";3=4-6"Republican") In the SELECTION FILTER box, enter: year(2018). This will tell SDA to use only the data from the

2018 GSS. Notice that the WEIGHT box is already filled in for you. This will weight the data so it better

represents the population of all adults in the U.S. Click on OUTPUT OPTIONS and:

o Uncheck the box for COLOR CODINGo In the SAMPLE DESIGN box, change the selection from COMPLEX to SRSo Check the box for SUMMARY STATISTICS

Click on CHART OPTIONS and then click on the down arrow for TYPE OF CHART and select NO CHART

There's one other option that is sometimes handy. In the OUTPUT OPTIONS, select QUESTION TEXT. This will show you the wording of the question for each variable.

Your SDA dialog box ought to look like the following. Note that the COLUMN box is truncated since the entire command doesn't fit in what is displayed.

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Figure 1-2

Now click on RUN THE TABLE and your crosstab will open in a new window. It should look like the following.

Figure 1-3

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Now we need to interpret the output that SDA gives us. Let's start with the percents. We put our independent variable (partyid) in the column of the table. By default, SDA will compute the column percents which sum down to 100 for each column. That's exactly what we want. If our independent variable is the column variable, then you will always want the column percents which sum down to 100. To interpret these percents, compare the percents straight across. Always compare in the direction opposite to the way the percents sum to 100. If the percents sum down to 100, then compare straight across.

Look at the first row of the table. Approximately 97% of Democrats said they voted for the Democrat (i.e., Obama) compared to 22% of Republicans who said they voted for Obama, a difference of 75 percentage points. As you would expect, Democrats were much more likely to vote for Obama than Romney. Independents lie between Democrats and Republicans but were much closer to the Democrats than to the Republicans. Elections are often determined by the way Independents vote and, in this election, they were more likely to vote for Obama than for Romney. For more information on crosstabulation, click on this link and go to chapter 7.

Now let's look at the second row of the table. Approximately 78% of Republicans voted for the Republican candidate (i.e., Romney) compared to only three percent of Democrats. Again, as you would expect, Republicans were much more likely to vote for Romney than for Obama. But only 30% of Independents voted for Romney. So it was the vote of Independents that partially determined the outcome of this election.

Notice also that 22% of Republicans voted for Obama while only 3% of Democrats voted for Romney. That was a second factor that determined the outcome of this elections. More Republicans defected to Obama than Democrats defected to Romney.

What about the summary statistics? Let's start with Chi Square which is a test of the null hypothesis that the two variables are unrelated to each other or, to put it another way, independent of each other. To test this null hypothesis, we use the observed significance level which is in parentheses to the right of Chisq-P(2) = 738.57. It tells us that the probability that we would be wrong if we rejected the null hypothesis is 0.00. However, this really means less than 0.005 since it's a rounded value. In other words, there very little chance that we would be wrong if we rejected the null hypothesis. The rule that we're going to use is to reject the null hypothesis when the probability of being wrong is less than .05. We often say that this is a statistically significant relationship. This tells that there probably is some relationship between these two variables. It's not just a chance relationship.6 For more information on Chi Square go to this same link and look at chapter 8.

Chi Square is not a measure of the strength of the relationship between two variables. It's just a test of significance to see if there is any relationship present. To measure the strength of the relationship, we need a measure of association. We're going to use Tau-c. This is a measure that is appropriate when both of our variables are ordinal which means they consist of ordered categories.7 Tau-c is .73 which

6 If you're wondering what all these values are here's the answer: the value of the Chi Square statistic is 738.57 and the degrees of freedom is 2. There's more than one Chi Square test. The one we're using is Chisq-P which is the Pearson Chi Square test named after Karl Pearson. 7 An important point to keep in mind is that dichotomies are always considered ordinal. Since pres12 is a dichotomy and partyid is also ordinal, we can use Tau-c. If one of the variables had contained unordered categories, we would have needed to use a different measure of association. For more on this distinction, go to

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tells us that there is an extremely strong relationship between these two variables.8 Measures of association are particularly useful when we want to compare the strength of the relationship between pairs of variables.

So, how would we summarize what we just discovered? There is a statistically significant relationship between political party identification and how people said they voted in the 2012 presidential election. Democrats were considerably more likely to say they voted for Obama and Republicans were far more likely to say they voted for Romney. Independents fell between Democrats and Republicans but were much closer to Democrats than to Republicans. Tau-c indicated that this was a very strong relationship.9

Part 4 – Now it's your turn

Now you get to try your hand at analyzing the relationship between two variables. Repeat the analysis but this time use pres16(1-2) as your dependent variable. Run the crosstab in SDA and then write a paragraph interpreting the relationship. Be sure to recode partyid and make sure that you use the SELECTION FILTER box to select out the 2018 GSS. Write your interpretation of the crosstab using the column percents, Chi Square, and Tau-c. Compare your results with what we found for the 2012 election. How were the findings similar but also different? From the data, why do you think Obama won in 2012 and Trump in 2016?

Part 5 – Summing Up

Now let's go back to the two questions we started with. Are Americans divided by their political identification? How big are these divisions?

For voting in 2012 we found large differences between how Democrats and Republicans said they voted. Chi Square told us that this was probably not a chance relationship and Tau-c indicated that it was a very strong relationship. What did you find for the 2016 presidential election? What does this tell us about political divisions?

Next Exercise

In Exercise 2 were going to consider gender divisions and compare men and women in terms of how they feel about crime and capital punishment.

the same link and look at chapter 1. 8 Tau-c values can also be negative. In those cases, ignore the sign of Tau-c. The sign of Tau-c depends on the way both variables are coded. 9 For more information on measures of association and Tau-c, go to the same link and look at chapter 9.

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Gender Divisions

It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). There are two critical questions to consider.



Goal of Exercise

The goal of this exercise is to explore gender divisions focusing on how respondents feel about crime and capital punishment.

Part 1 – Measures of Gender and Sex

Gender refers to an individual's perception of their own gender while sex refers to biological differences between those born male and female. Most surveys ask respondents to indicate their sex by checking one of two boxes – male and female. But few surveys ask questions to determine a person's gender identity.

Dan Cassino notes that sex is used as a proxy for gender.10 While there are measures of gender identity11 available, they often require many more questions. Since space is limited on surveys, this

10 Cassino, Dan. 2020. "Moving Beyond Sex: Measuring Gender Identity in Telephone Surveys." Survey Practice 13 (1). https://www.surveypractice.org/article/13697-moving-beyond-sex-measuring-gender-identity-in-telephone-surveys11 Bem, Sandra L. 1974. “The Measurement of Psychological Androgyny.” Journal of Consulting and Clinical Psychology 42 (2): 155–62. https://doi.org/10.1037/h0036215.

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https://doi.org/10.1037/h0036215

https://www.surveypractice.org/article/13697-moving-beyond-sex-measuring-gender-identity-in-telephone-surveys

https://www.surveypractice.org/article/13697-moving-beyond-sex-measuring-gender-identity-in-telephone-surveys

typically results in a single question to measure sex being which is then used as a proxy for gender. Cassino proposes a question that could be used to measure gender identity.

"The exact wording of the item was, “The traits that we see as being masculine or feminine are largely determined by society, and have changed dramatically over time. As a result, everyone has some combination of masculine and feminine traits, which may or may not correspond with whether they are male or female. How do you see yourself? Would you say that you see yourself as Completely Masculine, Mostly Masculine, Slightly Masculine, Slightly Feminine, Mostly Feminine, or Completely Feminine?"12

He goes on to observe that the "gender identity placements mostly, but not entirely match up with the respondent's sex. More than 90% of men (identified by interviewers) and more than 80% of women placed themselves on the side of the gender identity scales that matched their sex, but there was tremendous variance within sex groups."13 In other words, sex is a good proxy for gender but definitely not a perfect proxy. The GSS, like many surveys, uses sex as a proxy for gender.

Let's start by getting a frequency distribution for the variable named sex in SDA. To access the GSS cumulative data file in SDA format click here. The Introduction to SDA at the end of these exercises will show you how to get frequency distributions. Your output should look like the following.

Figure 2-1

Notice a few things about these charts.

Some respondents said they didn't know or refused to answer the questions. This is typically referred to as missing data. Cases with missing data are, by default, excluded from the frequency distributions. Sex is one of the few variables in the GSS that does not have any missing data.



12 Cassino, 2020.13 Cassino, 2020.

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Are Americans divided by their gender? How big are these divisions?



We're going to start by comparing men and women about their fear of being a victim of a violent crime. Here's the question in the GSS that asked about fear of crime – "Is there any area right around here--that is, within a mile--where you would be afraid to walk alone at night?" To make these comparisons we're going to use a statistical technique (or tool) called crosstabulation. The Introduction to SDA at the end of these exercises will show you how to run a crosstabulation in SDA.

Before we look at the relationship between gender and fear of crime , we need to talk about independent and dependent variables. The dependent variable is whatever you are trying to explain. In our example, that's respondents' fear of crime. The independent variable is some variable that you think might help explain why some people are more fearful of being a victim of a violent crime than others. In our case, that would be the variable sex. Normally we put the dependent variable in the row and the independent variable in the column of the crosstabulation. We’ll follow that convention in these exercises.

So, let's start with the crosstab of fear by sex. Notice that we describe the crosstab as dependent variable by independent variable. Now we're going to get the crosstab of fear by sex.


In the ROW box, enter: fear In the COLUMN box, enter: sex In the SELECTION FILTER box, enter: year(2018). This will tell SDA to use only the data from the



o Uncheck the box for COLOR CODING

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o In the SAMPLE DESIGN box, change the selection from COMPLEX to SRSo Check the box for SUMMARY STATISTICS



Your SDA dialog box ought to look like the following.

Figure 2-2


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Figure 2-3

Now we need to interpret the output that SDA gives us. Let's start with the percents. We put our independent variable (sex) in the column of the table. By default, SDA will compute the column percents which sum down to 100 for each column. That's exactly what we want. If our independent variable is the column variable, then you will always want the column percents which sum down to 100. To interpret these percents, compare the percents straight across. Always compare in the direction opposite to the way the percents sum to 100. If the percents sum down to 100, then compare straight across.

Look at the first row of the table. The table shows that 21% of men are afraid to walk alone in their neighborhood at night compared to 43% of women, a difference of 22 percentage points. Clearly women are more fearful of becoming a victim of a violent crime. For more information on crosstabulation, click on this link and go to chapter 7.

What about the summary statistics? Let's start with Chi Square which is a test of the null hypothesis that the two variables are unrelated to each other or, to put it another way, independent of each other. To test this null hypothesis, we use the observed significance level which is in parentheses to the right of Chisq-P(1) = 87.17. It tells us that the probability that we would be wrong if we rejected the null hypothesis is 0.00. However, this really means less than 0.005 since it's a rounded value. In other words, there very little chance that we would be wrong if we rejected the null hypothesis. The rule that we're going to use is to reject the null hypothesis when the probability of being wrong is less than .05. We often say that this is a statistically significant relationship. This tells that there probably is some relationship between these two variables. It's not just a chance relationship.14 For more information on Chi Square go to this same link and look at chapter 8.

14 If you're wondering what all these values are here's the answer: the value of the Chi Square statistic is 87.17 and the degrees of freedom is 1. There's more than one Chi Square test. The one we're using is Chisq-P which is the Pearson Chi Square test named after Karl Pearson.

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Chi Square is not a measure of the strength of the relationship between two variables. It's just a test of significance to see if there is any relationship present. To measure the strength of the relationship, we need a measure of association. We're going to use Tau-c. This is a measure that is appropriate when both of our variables are ordinal which means they consist of ordered categories.15 Tau-c is -.22 which tells us that there is a moderate relationship between these two variables.16 Measures of association are particularly useful when we want to compare the strength of the relationship between pairs of variables.

So, how would we summarize what we just discovered? There is a statistically significant relationship between sex and respondents' fear of crime. Women are more fearful than men of being a victim of a violent crime – a difference of 22 percentage points. Tau-c indicate that this is a moderate relationship.17


Now you get to try your hand at analyzing the relationship between two variables. Repeat the analysis but this time use cappun as your dependent variable. Run the crosstab in SDA and then write a paragraph interpreting the relationship. Write your interpretation of the crosstab using the column percents, Chi Square, and Tau-c.


Now let's go back to the two questions we started with. Are Americans divided by their gender? How big are these divisions?

The answer to these questions will vary with the dependent variable we are analyzing. For fear of crime women were more fearful of being a crime victim than men. Chi Square was statistically significant and Tau-c indicated a moderately relationship

What did you find when you repeated the analysis with cappun as your dependent variable? How did it compare with what we found for fear? What does this tell you about gender divisions?

If you worked through Exercise 1, you recall that you found a large difference of 75 percentage points between Democrats and Republicans with respect to how they voted the 2012 presidential election. In other words, there are fairly wide divisions based on political party identification but a smaller division based on gender. This, of course, will vary depending on the dependent variable we're analyzing.

15 An important point to keep in mind is that dichotomies are always considered ordinal. Since fear and sex are both dichotomies, we can use Tau-c. If one of the variables had contained unordered categories, we would have needed to use a different measure of association. For more on this distinction, go to the same link and look at chapter 1. 16 Notice that in this table Tau-c is negative. When Tau-c is negative, it's best to ignore the sign of Tau-c. The sign of Tau-c depends on the way both variables are coded. 17 For more information on measures of association and Tau-c, go to the same link and look at chapter 9.

19



Next Exercise

In Exercise 3 were going to compare different socioeconomic group in terms of how they feel about abortion.

20



Socioeconomic Divisions

It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). There are two critical questions to consider.



Goal of Exercise

The goal of this exercise is to explore socioeconomic divisions focusing on how respondents feel about abortion.

Part 1 – Measures of Socioeconomic Status

One definition of socioeconomic status refers to "the position or standing of a person or group in a society as determined by a combination of social and economic factors that affect access to education and other resources crucial to an individual’s upward mobility."18 There are various ways we could measure socioeconomic status including a person's education, income, and subjective assessment of their own status. Here are some of the questions in the GSS that we can use. The names of the variables are italicized and in parentheses following the question wording.

Respondent's highest educational degree (degree) Total family income in 2017 (income16) Social class in which respondent places self (class)

18 https://www.dictionary.com/browse/socioeconomic-status?s=t

21

https://www.dictionary.com/browse/socioeconomic-status?s=t

Let's start by getting frequency distributions for these three variables. To access the GSS cumulative data file in SDA format click here. The Introduction to SDA at the end of these exercises will show you how to get frequency distributions for these variables. The variable names are in parentheses above. Your output should look like the following.

Figure 3-1

22


Figure 3-2

Figure 3-3



23


the SELECTION FILTER box. You'll also notice that the frequency distribution for family income is very large (26 categories).

We'll going to reduce the number of categories to make it more manageable by recoding it. In fact, we're going to recode all three variables.



Are Americans divided by their socioeconomic status? How big are these divisions?

Also keep in mind that people could be divided on some issues but not others.

It would be nice if we could ask all adults (18 years of age and over) in the U.S. how they felt about these issues but that's clearly impractical. So we're going to use a sample of adults and use that sample data to make inferences about the population of all adults. This is typically referred to as statistical inference. The 2018 GSS is a large national probability sample of adults in the U.S. consisting of a little more than 2,300 adults. As samples go, that's a quite large sample, It might not seem so since 2,300 is a tiny percent of all adults but it turns out that what's important is not the percent of the population in the sample but the absolute size of the sample If you want to learn more about sampling, click on this link and look at Chapter 2. Or just take my word for it. A sample of 2,300 is a large sample regardless whether the population is 100,000 or 1,000,000 or 300,000,000. The nice thing about large probability samples is that the amount of sampling error decreases with sample size (everything else being equal).


We're going to start by comparing respondents with different levels of education. Then we'll compare those with different family incomes and finally we'll compare those who have different subjective class identifications. To make these comparisons we're going to use a statistical technique (or tool) called crosstabulation. The Introduction to SDA at the end of these exercises will show you how to run a crosstabulation in SDA.

Before we start, we need to talk about independent and dependent variables. The dependent variable is whatever you are trying to explain. In our example, we're going to try to explain why respondents have different views about abortion. The independent variable is some variable that you think might help explain why some people think abortion should be legal and others think it shouldn’t be legal. In our case, that would be the three measures of socioeconomic status. Normally we put the dependent variable in the row and the independent variable in the column of the crosstabulation. We’ll follow that convention in these exercises.

The GSS includes seven questions about abortion. Each question asks if the respondent thinks that "it should be possible for a pregnant woman to obtain a legal abortion" in different scenarios:

For any reason (abany)

24


Where there is a strong chance of a serious birth defect (abdefect) When the mother's health is seriously endangered (abhlth) If the woman is married and doesn't want more children (abnomore) If the woman is poor and can't afford more children (abpoor) If the woman is pregnant as a result of rape (abrape) When the woman is unmarried (absingle)

Respondents are more likely to think that abortion should be legal in the case of a serious birth defect, the mother's health is endangered, and the woman is pregnant as a result of rape. We're going to focus on abortion for any reason (abany) in this exercise.

So, let's start with the crosstab of abany by degree. Notice that we describe the crosstab as dependent variable by independent variable. Now we're going to get the crosstab of abany by degree. Before we do this, we need to talk about recoding. We're going to combine those with less than a high school degree (0) and those with a high school degree (1) into one category and give that category a value of 1. Then we're going to do the same thing for those with a junior college degree (2), a bachelor's degree (3), and a graduate degree (4) and combine them into another category and give that a value of 2. So, we'll end up with two categories – high school or less (1) and at least some college (2).

The Introduction to SDA at the end of these exercises shows you how to recode. However, it can be a little tricky so I'm going to give you the recode statements for all three measures of socioeconomic status. All you have to do is to copy and paste them into the appropriate box in SDA.

For degree, the recode is:degree (r:1=0-1"high school or less"; 2=2-4"some college or degree")

For income16, the recode is:income16(r:1=1-15"under $30K";2=16-19"$30K to under $60K";3=20-22"60K to under $110K";4=23-26"$110K+")

For class, the recode is:class (r:1=1-2"lower, working class";2=3-4"middle, upper class")


In the ROW box, enter: abany In the COLUMN box, enter: degree(r:1=0-1"high school or less"; 2=2-4"some college or degree") In the SELECTION FILTER box, enter: year(2018). This will tell SDA to use only the data from the






25


Figure 3-4


26

Figure 3-5

Now we need to interpret the output that SDA gives us. Let's start with the percents. We put our independent variable (degree) in the column of the table. By default, SDA will compute the column percents which sum down to 100 for each column. That's exactly what we want. If our independent variable is the column variable, then you will always want the column percents which sum down to 100. To interpret these percents, compare the percents straight across. Always compare in the direction opposite to the way the percents sum to 100. If the percents sum down to 100, then compare straight across.

Look at the first row of the table. Approximately 60% of those with at least some college think abortion should be legal for any reason compared to 43% of those with a high school or less education, a difference of 17 percentage points. Clearly those with some college are more likely than those with a high school or less education to think that abortion should be legal for any reason. For more information on crosstabulation, click on this link and go to chapter 7.

What about the summary statistics? Let's start with Chi Square which is a test of the null hypothesis that the two variables are unrelated to each other or, to put it another way, independent of each other. To test this null hypothesis, we use the observed significance level which is in parentheses to the right of Chisq-P(1) = 40.67. It tells us that the probability that we would be wrong if we rejected the null hypothesis is 0.00. However, this really means less than 0.005 since it's a rounded value. In other words, there very little chance that we would be wrong if we rejected the null hypothesis. The rule that we're going to use is to reject the null hypothesis when the probability of being wrong is less than .05. We often say that this is a statistically significant relationship. This tells that there is probably some

27


relationship between these two variables. It's not just a chance relationship.19 For more information on Chi Square go to this same link and look at chapter 8.

Chi Square is not a measure of the strength of the relationship between two variables. It's just a test of significance to see if there is any relationship present. To measure the strength of the relationship, we need a measure of association. We're going to use Tau-c. This is a measure that is appropriate when both of our variables are ordinal which means they consist of ordered categories.20 Tau-c is -.16 which tells us that there is a weak relationship between these two variables.21 Measures of association are particularly useful when we want to compare the strength of the relationship between pairs of variables. We'll come back to this shortly.

So, how would we summarize what we just discovered? There is a statistically significant relationship between education and how people feel about abortion for any reason. Those with more education are more likely to think that abortion should be legal for any reason – a difference of about 17 percentage points – than those with less education.22


Now you get to try your hand at analyzing the relationship between two variables. Run the crosstabs for the other two measures of socioeconomic status – family income and subjective class identification – and abany. Then write several paragraphs interpreting the relationships using the percents, Chi Square, and Tau-c. Use the following recodes for income16 and class:

income16(r:1=1-15"under $30K";2=16-19"$30K to under $60K";3=20-22"60K to under $110K";4=23-26"$110K+")class (r:1=1-2"lower, working class";2=3-4"middle, upper class")

Was the relationship stronger for degree or income16 or class? How did you decide?


Now let's go back to the two questions we started with. Are Americans divided by their socioeconomic status? How big are these divisions?

The answer to these questions will vary with the dependent variable we are analyzing. For abortion for any reason the difference between those with more education and those with less education was about 17 percentage points. Chi Square told us that this was probably not a chance relationship. However,

19 If you're wondering what all these values are here's the answer: the value of the Chi Square statistic is 40.67 and the degrees of freedom is 1. There's more than one Chi Square test. The one we're using is Chisq-P which is the Pearson Chi Square test named after Karl Pearson. 20 An important point to keep in mind is that dichotomies are always considered ordinal. Since both abany and recoded degree are dichotomies, we can use Tau-c. If one of the variables had contained unordered categories, we would have needed to use a different measure of association. For more on this distinction, go to the same link and look at chapter 1. 21 Ignore the fact that Tau-c is negative. The sign of Tau-c depends on the way both variables are coded. 22 For more information on measures of association and Tau-c, go to the same link and look at chapter 9.

28




Tau-c indicated that it was a moderate relationship. So while we found a moderately large difference between those with more and less education, it wasn't a strong relationship.

What did you find when you used income16 and class as measures of socioeconomic status? Were the differences larger or smaller for some of our measures of socioeconomic status? What does this tell you about socioeconomic divisions?

Next Exercise

In Exercise 4 were going to compare whites and blacks in terms of how they voted in the 2012 and 2016 presidential elections.

29



Racial Divisions

It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. The Pew Research Center reports that blacks are more likely than whites to say that race relations in the United States are generally bad and that blacks and whites "differ widely in views of how blacks are treated."23

Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). There are two critical questions to consider.



Goal of Exercise

The goal of this exercise is to explore racial divisions focusing on how respondents said they voted in the 2012 and 2016 presidential elections.

Part 1 – Measures of Race

It's not a simple task to measure race. The decennial U.S. Census has never asked the same question in more than one census. The GSS asks respondents, "What race do you consider yourself?" and codes their responses into three categories – white, black, and other.

The GSS also asks respondents, "Are you Spanish, Hispanic, or Latino/Latina?" They combined these two questions into a single variable which classifies respondents as white, black, Hispanic, and other. They indicate that "White does not include those who said they were Hispanic. And Hispanic does not include

23 https://www.pewresearch.org/fact-tank/2019/04/09/key-findings-on-americans-views-of-race-in-2019/

30

https://www.pewresearch.org/fact-tank/2019/04/09/key-findings-on-americans-views-of-race-in-2019/

those who said they were black."

Let's start by getting a frequency distribution for these two variables which are named race and racehisp in SDA. To access the GSS cumulative data file in SDA format click here. The Introduction to SDA at the end of these exercises will show you how to get frequency distributions. Your output should look like the following.

Figure 4-1

Figure 4-2


31







Are Americans divided by their race? How big are these divisions?

We're going to focus on how respondents said they voted in the 2012 and 2016 presidential elections. The variable names are pres12 and pres16. We're only going to consider respondents who said they voted for either of the two major candidates who are coded 1 and 2. To accomplish this, enter the variable names as pres12(1-2) and pres16(1-2).



We're going to start by comparing whites, blacks, and others with respect to how they said they voted in the 2012 and 2016 presidential elections. To make these comparisons we're going to use a statistical technique (or tool) called crosstabulation. The Introduction to SDA at the end of these exercises will show you how to run a crosstabulation in SDA.

Before we look at the relationship between our political variables and voting, we need to talk about independent and dependent variables. The dependent variable is whatever you are trying to explain. In our example, that's how people said they voted. The independent variable is some variable that you think might help explain why some people voted Democrat and others voted Republican. In our case, that would be the variables race and racehisp. Normally we put the dependent variable in the row and the independent variable in the column of the crosstabulation. We’ll follow that convention in these exercises.

Let's start with the crosstab of pres12 by race. Notice that we describe the crosstab as dependent variable by independent variable. Open SDA and enter the following in the dialog box.

32


In the ROW box, enter: pres12(1-2) In the COLUMN box, enter: race In the SELECTION FILTER box, enter: year(2018). This will tell SDA to use only the data from the






Your SDA dialog box ought to look like the following.

Figure 4-3


33

Figure 4-4

Now we need to interpret the output that SDA gives us. Let's start with the percents. We put our independent variable (race) in the column of the table. By default, SDA will compute the column percents which sum down to 100 for each column. That's exactly what we want. If our independent variable is the column variable, then you will always want the column percents which sum down to 100. To interpret these percents, compare the percents straight across. Always compare in the direction opposite to the way the percents sum to 100. If the percents sum down to 100, then compare straight across.

Look at the first row of the table. The table shows that 56% of whites said they voted for Obama compared to 97% of blacks who said they voted for Obama -- a difference of 41 percentage points. Blacks are much more likely to say than voted for Obama than whites. Respondents in the other category fall between blacks and whites. For more information on crosstabulation, click on this link and go to chapter 7.

What about the summary statistics? Let's start with Chi Square which is a test of the null hypothesis that the two variables are unrelated to each other or, to put it another way, independent of each other. To test this null hypothesis, we use the observed significance level which is in parentheses to the right of Chisq-P(2) = 154.17 It tells us that the probability that we would be wrong if we rejected the null hypothesis is 0.00. However, this really means less than 0.005 since it's a rounded value. In other words, there very little chance that we would be wrong if we rejected the null hypothesis. The rule that we're going to use is to reject the null hypothesis when the probability of being wrong is less than .05. We often say that this is a statistically significant relationship. This tells that there probably is some relationship between these two variables. It's not just a chance relationship.24 For more information on Chi Square go to this same link and look at chapter 8

Chi Square is not a measure of the strength of the relationship between two variables. It's just a test of significance to see if there is any relationship present. To measure the strength of the relationship, we

24 If you're wondering what all these values are here's the answer: the value of the Chi Square statistic is 154.17 and the degrees of freedom is 2. There's more than one Chi Square test. The one we're using is Chisq-P which is the Pearson Chi Square test named after Karl Pearson.

34



need a measure of association. We're going to use Cramer's V. This is a measure that is appropriate when one or both of our variables are nominal which means they consist of unordered categories.25 Unfortunately, SDA does not compute Cramer's V. Fortunately, it easy to compute V.

Here's how to compute V. All you have to do is follow these simple steps. V equals the square root of the following: Chi Square divided by the product of the number of cases in the table and the smaller of two values – the number of rows minus 1 and the number of columns minus 1.

The Pearson Chi Square is 154.17, the number of cases in the table is 1,328, the number of rows minus 1 is 2-1 or 1, the number of columns minus 1 is 3 – 1 or 2.

The smaller of the number of rows minus 1 and the number of columns minus 1 is 1 since 2 -1 is smaller than 3 – 1.

So divide 154.17 by the product of 1,328 and 1. This equals 154.17 divided by 1,328 or .116092. Now take the square root of .116092 which equals 0.341.

V suggests a fairly strong relationship between race and pres12. Measures of association are particularly useful when we want to compare the strength of the relationship between pairs of variables.26

So, how would we summarize what we just discovered? There is a statistically significant relationship between race and how people said they voted in the 2012 election. Blacks are considerably more likely than whites to have voted for Obama – a difference of about 41 percentage points. Respondents of other races fall between blacks and whites.

Now you can practice by running the crosstab for pres12 by racehisp. Here's what your table should look like.

Figure 4-5

Write an interpretation of the crosstab using what we did above as your guide.

25 For more on this distinction, go to the same link and look at chapter 1. 26 For more information on measures of association and Tau-c, go to the same link and look at chapter 9.

35




Now you get to try your hand at analyzing the relationship between two variables. Run the crosstabs that we ran above but this time use pres16(1-2) as your dependent variable. Be sure to use the SELECTION FILTER box to select the 2018 GSS. Write your interpretant of the tables using the percents, Chi Square, and Cramer's V to help you make sense out of the tables.


Now let's go back to the two questions we started with. Are Americans divided by their race? How big are these divisions?

For the 2012 presidential election we found a very large difference between how blacks and whites said they voted. Chi Square was statistically significant and Cramer's V showed a strong relationship.

What did you find for the 2016 election? Was there a large difference between blacks and whites? What about respondents of other races? How did this compare to the 2012 election?

If you worked through the previous exercises, you recall that we found a difference of 75 percentage points between Democrats and Republicans with respect to how said they voted in the 2012 presidential election, a smaller but still substantial difference of 41 percentage points between blacks and whites in terms of how they voted in the 2012 election, and smaller differences between men and women in their fear of crime (22 percentage points) and between those with some college and those with a high school education in terms of how they felt about abortion (17 percentage points).

Next Exercise

In Exercise 5 were going to compare different religious groups in terms of how they feel about controlling the distribution of pornography and the legalization of marijuana.

36



Religious Divisions

It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). For example, views on the Supreme Court vary both by religious affiliation and political party identification.27 There are two critical questions to consider when focusing on divisions.



Goal of Exercise

The goal of this exercise is to explore religious divisions focusing on how respondents feel about controlling the distribution of pornography and the legalization of marijuana.

Part 1 – Measures of Religion

We’re going to focus on two dimensions of religion – religious preference or identification and religiosity. There Here are three questions in the GSS that provide us with a way of measuring religious identification and religiosity. The names of the variables are italicized and in parentheses following the question wording.

"What is your religious preference? Is it Protestant, Catholic, Jewish, some other religion, or no religion?" (reliten)

"How often do you attend religious services?" (attend)

27 https://www.pewresearch.org/fact-tank/2020/03/03/with-religion-related-rulings-on-the-horizon-u-s-christians-see-supreme-court-favorably/

37

https://www.pewresearch.org/fact-tank/2020/03/03/with-religion-related-rulings-on-the-horizon-u-s-christians-see-supreme-court-favorably/

https://www.pewresearch.org/fact-tank/2020/03/03/with-religion-related-rulings-on-the-horizon-u-s-christians-see-supreme-court-favorably/

"Would you call yourself a strong (PREFERENCE NAMED IN RELIG) or a not very strong (PREFERENCE NAMED IN RELIG)?" Note that some respondents volunteered "somewhat strong." That was added as a response category. (reliten)

Let's start by getting frequency distributions for these three variables. To access the GSS cumulative data file in SDA format click here. The Introduction to SDA at the end of these exercises will show you how to get frequency distributions for these variables. The variable names are in parentheses above. Your output should look like the following.

Figure 5-1

38


Figure 5-2

Figure 5-3





39



Are Americans divided by their religious preference and their religiosity? How big are these divisions?

It would be nice if we could ask all adults (18 years of age and over) in the U.S. how they felt about these issues but that's clearly impractical. So we're going to use a sample of adults and use the sample data to make inferences about the population of all adults. This is typically referred to as statistical inference. The 2018 GSS is a large national probability sample of adults in the U.S. consisting of a little more than 2,300 adults. As samples go, that's a quite large sample, It might not seem so since 2,300 is a tiny percent of all adults but it turns out that what's important is not the percent of the population in the sample but the absolute size of the sample If you want to learn more about sampling, click on this link and look at Chapter 2. Or just take my word for it. A sample of 2,300 is a large sample regardless whether the population is 100,000 or 1,000,000 or 300,000,000. The nice thing about large samples is that the amount of sampling error decreases with sample size (everything else being equal).


We're going to start by comparing respondents who identify with different religious traditions. To make these comparisons we're going to use a statistical technique (or tool) called crosstabulation. The Introduction to SDA at the end of these exercises will show you how to run a crosstabulation in SDA.

Before we look at the relationship between our religious variables and abortion , we need to talk about independent and dependent variables. The dependent variable is whatever you are trying to explain. In our example, that's how people feel about pornography. The independent variable is some variable that you think might help explain why some people think pornography should be illegal to everyone regardless of age and others think it should only be illegal to those under 18. In our case, that would be our three religious variables. Normally we put the dependent variable in the row and the independent variable in the column of the crosstabulation. We’ll follow that convention in these exercises.

So, let's start with the crosstab of pornlaw by relig. Notice that we describe the crosstab as dependent variable by independent variable. Now we're going to get the crosstab of pornlaw by relig. Before we do this, we need to talk about recoding. You'll notice that some of the religious groups don't have very many cases so we’re going to combine these smaller categories. To do this we'll combine values 3 and 5 through 13 into one category and give that a value of 3. So, we'll end up with four categories – Protestants (1), Catholics (2), Other (3), and None (4).

We're also going to recode attend into three categories by combining values 0 through 3 into one category and giving it a value of 1, combining values 4 and 5 into a second category and giving it a value of 2, and combining values 6 through 8 into a third category and giving it a value of 3. We'll end up with three categories – seldom or never (1), sometimes (2), and often (3).

Finally, we're going to recode reliten into two categories by combining values 2 through 4 into one category and giving it a value of 2 and leaving 1 as a category by itself and giving it a value of 1. So, we'll have two categories – strong (1) and not strong (2).

40


The Introduction to SDA at the end of these exercises shows you how to recode. However, it can be a little tricky so I'm going to give you the recode statements and all you have to do is to copy and paste it into the appropriate box in SDA.

For relig, the recode is: relig (r:1=1-1"Protestant";2=2-2"Catholic"; 3=3,5,6,7,8,9,10,11,12,13"Other"; 4=4-4"None")

For attend, the recode is:attend (r:1=0-3"seldom or none";2=4-5"sometimes"; 3=6-8"often")

For reliten, the recode is:reliten (r:1=1-1"strong";2=2-4"not strong")


In the ROW box, enter: pornlaw In the COLUMN box, enter: relig (r:1=1-1"Protestant";2=2-2"Catholic";

3=3,5,6,7,8,9,10,11,12,13"Other"; 4=4-4"None") In the SELECTION FILTER box, enter: year(2018). This will tell SDA to use only the data from the







41

Figure 5-4


Figure 5-5

42

Now we need to interpret the output that SDA gives us. Let's start with the percents. We put our independent variable (relig) in the column of the table. By default, SDA will compute the column percents which sum down to 100 for each column. That's exactly what we want. If our independent variable is the column variable, then you will always want the column percents which sum down to 100. To interpret these percents, compare the percents straight across. Always compare in the direction opposite to the way the percents sum to 100. If the percents sum down to 100, then compare straight across.

Look at the first row of the table. We'll focus on Protestants, Catholics, and those who have no religious preference (i.e., nones).28 Approximately 39% of Protestants and 35% of Catholics think that pornography should be illegal in everyone regardless of age. Only 14% of Nones (i.e., those with no religious preference) think that pornography should be illegal to everyone. Clearly those with no religious preference are less likely than Christians to want stricter control by age over the distribution of pornography. For more information on crosstabulation, click on this link and go to chapter 7.

What about the summary statistics? Let's start with Chi Square which is a test of the null hypothesis that the two variables are unrelated to each other or, to put it another way, independent of each other. To test this null hypothesis, we use the observed significance level which is in parentheses to the right of Chisq-P(6) = 87.84. It tells us that the probability that we would be wrong if we rejected the null hypothesis is 0.00. However, this really means less than 0.005 since it's a rounded value. In other words, there very little chance that we would be wrong if we rejected the null hypothesis. The rule that we're going to use is to reject the null hypothesis when the probability of being wrong is less than .05. We often say that this is a statistically significant relationship. This tells us that there probably is some relationship between these two variables. It's not just a chance relationship.29 For more information on Chi Square go to this same link and look at chapter 8.

Chi Square is not a measure of the strength of the relationship between two variables. It's just a test of significance to see if there is any relationship present. To measure the strength of the relationship, we need a measure of association. We're going to use Cramer's V. This is a measure that is appropriate when one or both of our variables are nominal which means they consist of unordered categories.30 Unfortunately, SDA does not compute Cramer's V. Fortunately, it easy to compute V.




28 The other category is very heterogenous making it less useful. The other category consists primarily of non—Christian groups and they are more similar to the nones than they are to Christians in terms of how they answered this question.29 If you're wondering what all these values are here's the answer: the value of the Chi Square statistic is 87.84 and the degrees of freedom is 6. There's more than one Chi Square test. The one we're using is Chisq-P which is the Pearson Chi Square test named after Karl Pearson. 30 For more on this distinction, go to the same link and look at chapter 1.

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So divide 87.84 by the product of 1,560 and 2. This equals 87.84 divided by 3,120 or .0282. Now take the square root of .0282 which equals 0.17.

So, how would we summarize what we just discovered? There is a statistically significant relationship between religious preference and how people feel about controlling the distribution of pornography. Those with no religious preference are considerably less likely to think that pornography should be illegal for everyone regardless of age. Cramer's V tells us that we have a moderate relationship31

Now run the crosstab of pornlaw by reliten recoded. Here's what your table should look like.

Figure 5-6

How would you describe the relationship between pornlaw and attend? Since both of our variables are ordinal, we can use a measure of association that takes into account the order of the categories. We'll use Tau-c which equals .22 and this means we have a moderate relationship. By the way, don't compare Cramer's V coefficients with Tau-c coefficients. Only compare values of Cramer's V with other values of Cramer's V and the same for Tau-c.

Now run our third crosstab – pornlaw by attend. Be sure to use the recoded version of attend described earlier in this exercise. Here's what your table should look like. How would you interpret this table?

31 For more information on measures of association and Cramer's V, go to the same link and look at chapter 9.

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Figure 5-7


Now you get to try your hand at analyzing the relationship between pairs of variables. Repeat the analysis we just did but this time use grass as your dependent variable. Grass is the name of the variable in the GSS that records how respondents answered the following question: "Do you think the use of marijuana should be made legal or not?"

Run the table with reliten (recoded) as your independent variable and then write a paragraph interpreting the relationship. When you have finished doing this, repeat the analysis but this time use attend as your independent variable. Use the following recodes for attend and reliten:attend (r:1=0-3"seldom or none";2=4-5"sometimes"; 3=6-8"often")reliten (r:1=1-1"strong";2=2-4"not strong")

Was the relationship stronger for attend or for reliten? How did you decide?


Now let's go back to the two questions we started with: Are Americans divided by their religious preference and religiosity? How big are these divisions?

The answer to these questions will vary with the dependent variable we are analyzing. Democrats were much more likely to have voted for Obama in 2012 than were Republicans – a difference of 75 percentage points. Blacks were more likely to have voted for Obama – a difference of 41 percentage points. Women were 22 percentage points more likely than men to say they were afraid to walk alone

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at night in their neighborhood and those with some college were 17 percentage points more likely than those with a high school or less education to think abortion for any reason should be legal. All these relationships were statistically significant but there was considerable variation in the strength of the relationships. Divisions were much stronger when looking at voting behavior.

What did you find when you used grass as your dependent variable? How did it compare to what we found for pornlaw?

Next Exercise

In Exercise 6 were going to compare respondents' geographical location in terms of how they said they voted in the 2012 president and 2016 presidential elections.

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Geographical Divisions

It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). For example, there are certain states that almost always vote Republican and others that typically vote Democratic in presidential elections. There are two critical questions to consider when focusing on divisions.



Goal of Exercise

The goal of this exercise is to explore geographic divisions focusing on how respondents said they voted in the 2012 and 2016 presidential elections.

Part 1 – Measures of Geography

We’re going to focus on two dimensions of geography – region of country and size of the community in which respondents live. The names of these variables are region and size.

Let's start by getting frequency distributions for these two variables. To access the GSS cumulative data file in SDA format click here. The Introduction to SDA at the end of these exercises will show you how to get frequency distributions for these variables. The variable names are listed above. I'm not going to show the frequency distribution for size because it's very long but run it for yourself. Your output for region should look like the following.

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Figure 6-1


Some respondents said they didn't know or refused to answer the questions. This is typically referred to as missing data. Cases with missing data are, by default, excluded from the frequency distributions. However, for these two variables there are no missing data.





Are Americans divided by their geography? How big are these divisions?

It would be nice if we could ask all adults (18 years of age and over) in the U.S. how they felt about these issues but that's clearly impractical. So we're going to use a sample of adults and use the sample data to make inferences about the population of all adults. This is typically referred to as statistical inference.

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The 2018 GSS is a large national probability sample of adults in the U.S. consisting of a little more than 2,300 adults. As samples go, that's a quite large sample, It might not seem so since 2,300 is a tiny percent of all adults but it turns out that what's important is not the percent of the population in the sample but the absolute size of the sample If you want to learn more about sampling, click on this link and look at Chapter 2. Or just take my word for it. A sample of 2,300 is a large sample regardless whether the population is 100,000 or 1,000,000 or 300,000,000. The nice thing about large samples is that the amount of sampling error decreases with sample size (everything else being equal).


We're going to start by comparing respondents who live in different areas of the country . To make these comparisons we're going to use a statistical technique (or tool) called crosstabulation. The Introduction to SDA at the end of these exercises will show you how to run a crosstabulation in SDA.

Before we look at the relationship between our geographic variables and voting, we need to talk about independent and dependent variables. The dependent variable is whatever you are trying to explain. In our example, that's how people said they voted in the 2012 and 2016 presidential elections. The independent variable is some variable that you think might help explain why some people voted for the Democratic candidate and others voted for the Republican candidate. In our case, that would be where they live. Normally we put the dependent variable in the row and the independent variable in the column of the crosstabulation. We’ll follow that convention in these exercises.

So, let's start with the crosstab of pres12 by region. Notice that we describe the crosstab as dependent variable by independent variable. Now we're going to get the crosstab of pres12 by region. Before we do this, we need to talk about recoding. We can group these nine regions into four categories using the Census classification. To do this we'll combine values 1 and 2 into one category and give that a value of 1. Then we'll combine values 3 and 4 into a second category and give it a value of 2. We'll group values 5 through 7 into a third category and give it a value of 3. Finally, we'll combine values 8 and 9 into a fourth category and give it a value of 4. So, we'll end up with four categories – Northeast (1), Midwest (2), South (3), and West (4).

Size is measured by the number of residents of the place (in thousands) where respondents live. We're also going to recode size into four categories by combining values 0 through 9 into one category and giving it a value of 1, combining values 10 through 34 into a second category and giving it a value of 2, combining values 36 through 144 into a third category and giving it a value of 3, and combining values of 153 through 8175 into a fourth category and giving it a value of 4. We'll end up with four categories – small (1), small medium (2), large medium (3), and large (4).32

The Introduction to SDA at the end of these exercises shows you how to recode. However, it can be a little tricky so I'm going to give you the recode statement and all you have to do is to copy and paste it into the appropriate box in SDA.

For region, the recode is: region (r:1=1-2"Northeast";2=3-4"Midwest"; 3=5-7"South"; 4=8-9"West")

32 The gaps in the values are because there are categories that don't have any respondents in them.

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For size, the recode is:size (r:1=0-9"small";2=10-34"small medium"; 3=36-144"large medium";4=153-8175"large")


In the ROW box, enter: pres12(1-2). Note that the addition of (1-2) following the variable name tells SDA that we only want to look at respondents who said they voted for one of the two major presidential candidates who are coded 1 and 2.

In the COLUMN box, enter: region (r:1=1-2"Northeast";2=3-4"Midwest"; 3=5-7"South"; 4=8-9"West")

In the SELECTION FILTER box, enter: year(2018). This will tell SDA to use only the data from the 2018 GSS.

Notice that the WEIGHT box is already filled in for you. This will weight the data so it better represents the population of all adults in the U.S.

Click on OUTPUT OPTIONS and:o Uncheck the box for COLOR CODINGo In the SAMPLE DESIGN box, change the selection from COMPLEX to SRSo Check the box for SUMMARY STATISTICS




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Figure 6-2


Figure 6-3

Now we need to interpret the output that SDA gives us. Let's start with the percents. We put our independent variable (region) in the column of the table. By default, SDA will compute the column percents which sum down to 100 for each column. That's exactly what we want. If our independent variable is the column variable, then you will always want the column percents which sum down to 100. To interpret these percents, compare the percents straight across. Always compare in the direction opposite to the way the percents sum to 100. If the percents sum down to 100, then compare straight across.

Look at the first row of the table. Approximately 72% of respondents who live in the Northeast said they voted for Obama. This decreased slightly to 69% of those in the West and 65% of those in the Midwest. It decreased even further to 58% of those living in the South. In other words, those who live in Northeast were most likely to vote for Obama and those in the South were least likely. Those in the Midwest and West fell between those in the Northeast and the South. For more information on crosstabulation, click on this link and go to chapter 7.

What about the summary statistics? Let's start with Chi Square which is a test of the null hypothesis that the two variables are unrelated to each other or, to put it another way, independent of each other. To test this null hypothesis, we use the observed significance level which is in parentheses to the right of Chisq-P(3) = 17.52. It tells us that the probability that we would be wrong if we rejected the null

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hypothesis is 0.00. However, this really means less than 0.005 since it's a rounded value. In other words, there very little chance that we would be wrong if we rejected the null hypothesis. The rule that we're going to use is to reject the null hypothesis when the probability of being wrong is less than .05. We often say that this is a statistically significant relationship. This tells us that there probably is some relationship between these two variables. It's not just a chance relationship.33 For more information on Chi Square go to this same link and look at chapter 8.

Chi Square is not a measure of the strength of the relationship between two variables. It's just a test of significance to see if there is any relationship present. To measure the strength of the relationship, we need a measure of association. We're going to use Cramer's V. This is a measure that is appropriate when one or both of our variables are nominal which means they consist of unordered categories.34 Unfortunately, SDA does not compute Cramer's V. Fortunately, it easy to compute V.




So divide 17.52 by the product of 1,328 and 1. This equals 17.52 divided by 1,328 or .0132 Now take the square root of .0132 which equals 0.115.

So, how would we summarize what we just discovered? There is a statistically significant relationship between region of the country and how people said they voted in the 2012 presidential election. Those who live in the South were less likely to vote for Obama while those in the Northeast were most likely. Cramer's V tells us that we have a weak relationship35

Now run the crosstab of pres12(1-2) by size recoded. Here's what your table should look like.

33 If you're wondering what all these values are here's the answer: the value of the Chi Square statistic is 17.52 and the degrees of freedom is 3. There's more than one Chi Square test. The one we're using is Chisq-P which is the Pearson Chi Square test named after Karl Pearson. 34 For more on this distinction, go to the same link and look at chapter 1. 35 For more information on measures of association and Cramer's V, go to the same link and look at chapter 9.

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Figure 6-4

How would you describe the relationship between pres12 and size? One thing to keep in mind – dichotomies are considered ordinal variables. So this time both our variables have ordered categories. We call these ordinal variables. When both of our variables are ordinal, we can use a measure of association that takes into account the order of the categories. We'll use Tau-c which equals -.1936 This means that we have a weak to moderate relationship. By the way, don't compare Cramer's V coefficients with Tau-c coefficients. Only compare values of Cramer's V with other values of Cramer's V.


Now you get to try your hand at analyzing the relationship between pairs of variables. Run the appropriate table with region (recoded) as your independent variable. This time use pres16(1-2) as your dependent variable. Write a paragraph interpreting the relationship using the column percents, Chi Square, and Cramer's V. When you have finished doing this, repeat the analysis but this time use size (recoded) as your independent variable.

Were the relationships similar to what we found for the 2012 presidential election? In what ways were they similar and different?


Now let's go back to the two questions we started with: Are Americans divided by their geographical location? How big are these divisions?

36 Tau-c can be positive or negative. However, it's best to ignore the sign which depends on the way the variable is coded.

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The answer to these questions will vary with the dependent variable we are analyzing. Democrats were much more likely to say they voted for Obama in 2012 – a difference of 75 percentage points. Blacks were 41 percentage points more likely than whites to have voted for Obama in 2012. Those who attended worship services were 33 percentage points more likely to feel that pornography should be illegal for everyone regardless of age. Women were 22 percentage points more likely to be afraid of walking alone in their neighborhoods at night. And those with at least some college were more likely to think that abortion for any reason should be legal – a difference of 17 percentage points.

When we compare these findings with the other exercises, we can see that sometimes there are large divisions and other times the division are smaller. But keep in mind that you will have different results for different dependent variables.

What were the divisions you found for voting in the 2016 presidential election when you compared respondents by the region where they lived and the size of their community?

Next Exercise

In Exercise 7 through 12 were going to move from two-variable analysis (bivariate analysis) to three-variable analysis (multivariate analysis). Exercise 7 will elaborate our analysis of political divisions by adding gender into the analysis.

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Elaborating Political Divisions

These exercises focus on divisions in American Society. It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). There are two critical questions to consider when focusing on divisions.


In this exercise and the ones following, we'll elaborate the analysis we carried out in the first six exercises. Each of the last six exercises in this series is paired with one of the first six exercises. Exercise 1 focused on the relationship between political party preference and how respondents said they voted in the 2012 and 2016 presidential elections. This exercise will add another variable – what we will call our control variable – into the analysis.

We'll use several statistical tools (i.e., crosstabulation, Chi Square, and measures of association). The data we're going to use is the General Social Survey (GSS), a large national probability survey of adults in the U.S. We'll be using the 2018 GSS. The statistical program we're going to use is Survey Documentation and Analysis (SDA) written at UC Berkeley and freely available wherever you have an internet connection. There is a brief introduction to SDA at the end of these exercises.

Goal of Exercise

The goal of this exercise is to explore how gender affects the relationship between political party preference and who respondents said they voted for in the 2012 and 2016 presidential elections. Our focus will continue to be on political divisions.

Part 1 – Political Party Identification and Voting in the 2012 Presidential election

Let's start by rerunning the crosstabulation of political party preference and how respondents voted in the 2012 presidential election. To access the GSS cumulative data file in SDA format click here. Remember to use the recode for partyid.

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For partyid, the recode is:partyid (r:1=0-2"Democrat";2=3-3"Independent";3=4-6"Republican")

If you need to review how to get two-variable tables, look back at Exercise 1 and the Introduction to SDA at the end of these exercises.

Part 2 – Adding Another Variable into the Analysis

Behavior is usually too complicated to be studied with only two variables (i.e., bivariate analysis). Often we want to consider sets of three or more variables (i.e., multivariate analysis) in order to find out (1) if a relationship might be due to some other factor, (2) how or why these variables are related, (3) if the relationship is the same for different types of individuals, and (4) which of a set of variables is more strongly related to our dependent variable.

In each situation, we identify a third variable that we want to consider. This is called the control variable. (Although it is possible to use several control variables simultaneously, we will limit ourselves to one control variable at a time in these exercises.) To introduce a third variable, we identify the control variable and separate the cases in our sample by the categories of the control variable. For example, if the control variable is age divided into two categories--younger and older, we would separate the cases into two groups. One group would consist of individuals who are younger and the other group would be those who are older. We would then obtain the crosstabulation of the independent and dependent variables for each of these age groups separately. Since there are two categories in this control variable, we obtain two partial tables, each containing part of the original sample. (If there were three categories in our control variable, for example, younger, middle aged, and older, we would have three partial tables.) We compare the partial tables with the original two-variable table to see the effect of holding the control variable constant.

The process of adding a control variable into the analysis is called elaboration and was developed at Columbia University by Paul Lazarsfeld, Patricia Kendall, and their associates.

We would want to introduce a control variable into the analysis in the following scenarios.

You found a relationship between two variables and you want to check to see if that relationship might be due to some other variable. In other words, you want to know if your two-variable relationship could be explained away by this third variable.37

You found a relationship between two variables and you want to try to discover why or how these variables are related.38

You found a relationship between two variables and you want to determine if this relationship varies for different categories of respondents.39

37 When the control variable has explained away the relationship between the independent and dependent variable, we refer to this as explanation. The control variable has explained away the original relationship. Typically we say that the original relationship was spurious.38 When the control variable helps us understand why or how the two variables are related, we refer to this as interpretation because you are interpreting why your independent variable is related to the dependent variable.39 When the relationship varies by the category of your control variable, we refer to this as specification because it specifies the conditions under which the relationship between the independent variable and the dependent variable varies.

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You want to determine which of a set of variables is more strongly related to the dependent variable.

Part 3 – Adding in a Control Variable

In Exercise 1 we found that Democrats were considerably more likely to vote for the Democratic presidential candidate than Republicans and Republicans were much more likely to vote for the Republican candidate. Independents fell between Democrats and Republicans but were closer to Democrats. Chi Square was statically significant and our measure of association, Tau-c, suggested a very strong relationship.

Let's think about gender as a possible control variable. Research in this area indicates that females are more likely to identify as Democrats and also more likely to vote for the Democratic presidential candidate. Males are more likely to identify as Republican and more likely to vote Republican. Here's a diagram of these relationships.

Figure 7-1

To check to see if these findings also occur in the 2018 GSS, run two crosstabs.

partyid by sex pres12(1-2) by sex

You should find that females are about 6 percentage points more likely to say they are Democrats and males approximately 8 percentage points more likely to be Republicans. Females were 6 percentage points more likely to vote for Obama and males 6 percentage points more likely to vote for Romney. That confirms what other studies have found.

It also raises the possibility that some part of the relationship between political party preference and voting might be due to gender. It's highly doubtful that gender can explain away all of the relationship between party identification and voting but it might explain away part of that relationship. There's a simple way to test this possibility. Divide your sample into two groups – males and females – and then rerun the crosstab of pres12 by partyid for each subgroup. That's what a three-variable crosstab does and SDA can do it for you. It's easy to do. Here's what you SDA dialog box ought to look like.

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Figure 7-2

The only difference between this and the two-variable table that you ran earlier is that you add sex as your control variable. Everything else remains the same.

When you run this table, you'll notice that SDA gives you three tables – one partial table for the males, another partial table for the females, and a third table that contains both males and females. It also gives you the summary statistics for each table. Here's the table for males.

Figure 7-3

Look at this table and note what it tells you.

The difference between Democrats and Republicans if 74 percentage points (98-24). Chi square is statistically significant. Tau-c equals .73.

Here's the table for females.

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Figure 7-4

Look at the same summary statistics.


And here's the table including both males and females. You might be asking how this table differs from the table you ran in Exercise 1. Recall that cases with missing data for any variable are excluded from the table. So in Exercise 1, SDA excluded cases with missing data for partyid and pres12 while in the table you just ran it excluded cases with missing data for partyid, pres12, and sex. It turns out that there aren't any cases with missing data for sex so the two tables are the same but that won't be the case for most three-variable tables that you run.

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Figure 7-5

Here are the summary statistics for this third table that includes both males and females.


Now compare the summary statistics for the two partial tables with the summary statistics for the table with all the cases. They're virtually the same. So, what does that tell you about the effect of controlling for gender on the relationship between party identification and voting in the 2012 presidential election? Gender had no effect at all on this relationship. We often call this replication because the partial tables replicate (or repeat) the original two-variable relationship. In other words, gender doesn't explain any of the relationship between party and voting in 2012. The original two-variable relationship is not spurious.

Part 4 – Now It's Your Turn

Now you get to try your hand at analyzing the relationships for these three variables. Repeat the analysis but this time use pres16(1-2) as your dependent variable. Run the three-variable crosstab in SDA and then write a paragraph interpreting the relationships. Be sure to recode partyid and make sure that you use the SELECTION FILTER box to select out the 2018 GSS. Indicate that you want to include only those who voted for either of the two major presidential candidates by entering pres16(1-2) in the row box. Write your interpretation of the crosstabs using the column percents, Chi Square, and Tau-c. Compare your results with what we found for the 2012 election. What was the effect of controlling for gender for the 2016 presidential election? Did gender explain any of the original two-variable relationship? Were the findings different in any way from the 2012 analysis? Does this give you any clues as to why Trump won in 2016?

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Now let's go back to the two questions we started with. Are Americans divided by their political identification? How big are these divisions?

Did controlling for gender change our interpretation from Exercise 1? Did it add anything to the analysis in Exercise 1? What does this tell us about political divisions in the U.S.?

Next Exercise

In Exercise 8 were going to elaborate our analysis of gender divisions by adding education into the analysis.

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Elaborating Gender Divisions



In this exercise and the ones following, we'll elaborate the analysis we carried out in the first six exercises. Each of the last six exercises in this series is paired with one of the first six exercises. Exercise 2 focused on the relationship between gender and how respondents felt about crime and capital punishment. This exercise will add another variable – what we will call our control variable – into the analysis.


Goal of Exercise

The goal of this exercise is to explore how other variables affect the relationship between gender and how respondents felt about crime and capital punishment. More specifically, we're going to explore how gender, education, and subjective class identification are jointly related to fear of crime and capital punishment. Our focus will continue to be on gender divisions.

Part 1 – Gender and its Relationship to Fear of Crime

Let's start by rerunning the crosstabulation of gender and respondents' fear of crime. To access the GSS cumulative data file in SDA format click here. If you need to review how to get two-variable tables, look back at Exercise 2 and the Introduction to SDA at the end of these exercises.

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In Exercise 2 we found that women were more likely than men to report that they were afraid to walk


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alone in their neighborhood at night – a difference of 22 percentage points. Chi Square was statistically significant and our measure of association, Tau-c, suggested a moderate relationship.

Let's think about some other variables we might want to add into the analysis. The GSS has two possible measures of socioeconomic status – education and subjective class identification.43 It's easy to imagine how socioeconomic status might be related to respondents' fear of crime. Those with higher socioeconomic status tend to have greater access to resources to deal with their lives. For example, they have greater access to medical care and heightened economic opportunities.

Here are these two variables in the GSS.

Highest educational degree (degree) Subjective class identification (class)44

We're going to use recodes of both these variables. Here are the recode statements that you should copy and paste into SDA.

Here's the recode for degree.degree (r:1=0-1"high school or less"; 2=2-4"some college or degree")

And here's the recode for class.class (r:1=1-2"lower, working class";2=3-4"middle, upper class")

So, we have two variables – sex and degree – that might be related to respondent's fear of being a victim of a violent crime. How can we determine how these three variables are interrelated? The answer is to run a three-variable table that includes all three of these variables.

Let's start by comparing men and women while holding constant education. Here's what you SDA dialog box ought to look like.

Figure 8-1

The only difference between this and the two-variable table that you ran earlier is that you add recoded degree as your control variable. Everything else remains the same.

When you run this table, you'll notice that SDA gives you three tables – one partial table for those with a high school or less education and another partial table for those with at least some college. It also gives

43 There actually are other possible measures of socioeconomic status such as family income but we're going to limit our analysis to education and subjective class identification. 44 The question in the GSS reads, "If you were asked to use one of four names for your social class, which would you say you belong in: the lower class, the working class, the middle class, or the upper class?"

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you a third table that contains everyone regardless of their education. And it gives you the summary statistics for each table. Here's the table for those with less education.

Figure 8-2


The difference between men and women is 25 percentage points (47-22). Chi square is statistically significant. Tau-c equals - 25.45

Here's the table for those with more education.

45 We're going to ignore the sign of the percentage difference and Tac-c and simply look at the crosstab to see that women are more fearful of being a victim of a violent crime than are men.

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Figure 8-3


The difference between men and women is 19 percentage points (39-20). Chi square is statistically significant. Tau-c equals -.18.

And here's the table including both educational groups. You might be asking how this table differs from the table you ran in Exercise 2. Recall that cases with missing data for any variable are excluded from the table. So in Exercise 2, SDA excluded cases with missing data for sex and fear while in the table you just ran it excluded cases with missing data for sex, fear, and degree.

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Figure 8-4

Here are the summary statistics for this third table that includes both educational levels.

The difference between men and women is 22 percentage points (43-21). Chi square is statistically significant. Tau-c equals -.22.

Now compare the summary statistics for the two partial tables with the summary statistics for the table with all the cases. The difference between men and women is slightly bigger for those with less education. But the difference between men and women is statistically significant for both educational groups.

Now run the three-variable table again but this time control for gender and use education as your independent variable. Run that table for yourself and work though the analysis of the tables as we did above.

There's another way of presenting the findings that is more visually appealing and shows the interrelationships of these three variables. Consider this table.

High school or less At least some college Percent differenceacross

Male 21.8% 19.7% 2.1Female 46.9% 38.6% 8.3Percent differencedown

-25.1 -18.9

Figure 8-5

This table has the same data but arranges the percentages in a single table making it easier to see the interrelationships. What can we learn from this table?

Females are more fearful than males and the difference is a little bigger for those with less education.

There's really no difference between educational groups for males but for females those with less education are somewhat more fearful

The most fearful group is females with less education and the least fearful group is males regardless of their education.

In other words, education makes a difference for females but not for males. This is what we typically refer to as statistical interaction. Gender and education interact in such a way that females with less education are the most fearful.


Now you get to try your hand at multivariate analysis. Repeat the analysis but this time use cappun as your dependent variable. Run the three-variable crosstab in SDA and then write a paragraph

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interpreting the relationships. Be sure to recode degree and to use the SELECTION FILTER box to select out the 2018 GSS. Write your interpretation of the crosstabs using the column percents, Chi Square, and Tau-c. Create a table similar to Figure 8-5 to help you see how gender and education interact.


Now let's go back to the two questions we started with. Are Americans divided by their gender? How big are these divisions?

What did we learn by adding education into the analysis? What does this tell you about gender divisions in the U.S. and how education influences those divisions?

Next Exercise

In Exercise 9 were going to elaborate our analysis of socioeconomic divisions in terms of how respondents feel about abortion.

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Elaborating Socioeconomic Divisions



In this exercise and the ones following, we'll elaborate the analysis we carried out in the first six exercises. Each of the last six exercises in this series is paired with one of the first six exercises. Exercise 3 focused on the relationship between several measures of socioeconomic status and how respondents feel about abortion. This exercise will further explore these relationships by adding control variables into the analysis.


Goal of Exercise

The goal of this exercise is to explore the interrelationships of education, family income, subjective class identification and how respondents feel about abortion. Our focus will continue to be on socioeconomic divisions.

Part 1 – Socioeconomic Status and Abortion

In Exercise 3 we saw that there are several possible measures of socioeconomic status in the 2018 GSS – education, family income, and subjective class identification. Our analysis in this exercise will focus on these measures of socioeconomic status and how respondents feel about abortion. To access the GSS cumulative data file in SDA format click here. If you need to review how to get two-variable tables, look back at Exercise 3 and the Introduction to SDA at the end of these exercises.

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In Exercise 3 we found that those with at least some college were more likely to think that abortion for


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any reason should be legal than those with a high school or less education – a difference of approximately 17 percentage points. Other indicants of socioeconomic status are family income and subjective class identification. As you would expect, these three measures of socioeconomic status are strongly related to each other. You can check this out for yourself by running two crosstabs – degree by income16 and degree by class. When your run the tables, be sure to use the recodes.

For degree, the recode is:degree (r:1=0-1"high school or less"; 2=2-4"some college or degree")

For income16, the recode is:income16(r:1=1-15"under $30K";2=16-19"$30K to under $60K";3=20-22"60K to under $110K";4=23-26"$110K+")

For class, the recode is:class (r:1=1-2"lower, working class";2=3-4"middle, upper class")

While they are highly interrelated to each other, these measures are certainly not perfectly correlated. In other words, there are respondents who have high education and low income as well as those with low education and high income. And subjective class identification is not perfectly correlated with degree and income as well. There are respondents with high education and high income who see themselves as lower or working class.

In this exercise we want to address the question -- are some of these indicants of socioeconomic status more strongly related to abortion that others and do these variables interact with each other such that particular combinations of these variables produce greater or lesser support for abortion?

Let's explore this question by running the three-variable crosstab for abany by income16 by degree to see how these measures interact with abortion. Be sure to use the recodes.

Here's what your SDA dialog box ought to look like for this crosstab.

Figure 9-1

When you run this table, you'll notice that SDA gives you three tables – one partial table for the those with a high school or less education , another partial table for those with at least some college, and a third table that contains both educational groups. It also gives you the summary statistics for each table. Here's the table for those with a high school or less education.

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Figure 9-2


The difference between the lowest income level and the highest income level is 8 percentage points (49-41).

Chi square is not statistically significant. Tau-c equals - 05.49

Here's the table for those with at least some college.

49 We're going to ignore the sign of Tau-c. The sign depends on how the variables are coded. We can look at the percents to see whether support for abortion increases or decreases with income.

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Figure 9-3


The difference between those with the lowest income and those with the highest income is 12 percentage points (65-53).

Chi square is not statistically significant. Tau-c equals -.07.

And here's the table including both those with less and those with more education. You might be asking how this table differs from the table you ran in Exercise 3. Recall that cases with missing data for any variable are excluded from the table. So the two-variable table would have excluded cases with missing data for income16 and abany while in the table you just ran it excluded cases with missing data for income16, abany, and degree.

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Figure 9-4

Here are the summary statistics for this third table that includes both educational levels.

The difference between those with the lowest income and those with the highest income is 16 percentage points (59-43).

Chi square is statistically significant. Tau-c equals -.12.

Now compare the summary statistics for the two partial tables with the summary statistics for the table with all the cases. There are some important differences.

The percentage differences for all the valid cases is 16 which decreases to 8 and 12 in the two partial tables.

The Chi Square tests are not statistically significant for either partial table but Chi Square is significant for the table that includes all the valid cases.

Tau-c decreases from .12 for the table with all the valid cases to .05 and .07 for the two partial tables.

The relationship appears to have pretty much gone away when you controlled for education. There still another way to look at the percents which might make it easier to see what is happening.

We could also have run the crosstab for abany by degree by income. Go ahead and run that three-variable table being sure to use the recodes. Here's what your tables should look like. This time the control variable has four categories so you'll have four partial tables. Here's the table for those with family incomes less than $30,000.

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Figure 9-5

Here's the table for those with family incomes between $30,000 and under $60,000.

Figure 9-6

Here's the table for those with family incomes of $60,000 and under $110,000.

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Figure 9-7

Here's the table for those family incomes of $110,000 and more.

Figure 9-8

And here's the table for all respondents regardless of their family income.

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Figure 9-9

That's a lot of tables. Work through the analysis of these tables as we did for the previous set of tables. There still another way that we can visually present the data. In the table below, I entered the percent that think abortion for any reason should be legal.

Under $30K $30K to Under $60K

$60K to Under $110K

$110K or More Percentage point difference

Less education 40.8% 45.3% 43.7% 49.4% 8.6

More education

53.2% 59.7% 58.9% 64.5% 11.3

Percentage point difference

12.4 14.4 15.2 15.1

Figure 9-10

When the data are laid out in this format, some patterns become obvious.

The educational differences (i.e., 12.4, 14.4, 15.2, 15.1) are all larger than the income differences (8.6, 11.3) indicating that education makes more of a difference than does income. When we looked at the summary statistics, we found that the educational differences were statistically significant while the income difference were not significant.

The educational differences increase with income so the group that is most likely to think that abortion for any reason should be legal is those with at least some college with an income of

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$110,000 or more and the group least likely to think abortion should be legal is those with a high school education who make under $30,000 a year.

This is an example of specification because our analysis specifies the conditions under which the relationship varies. Education and income interact such that the group most likely to think that abortion for any reason should be legal is those with high education and high income.


Now you get to try your hand at analyzing the interrelationships of these three variables. Repeat the analysis but this time use degree and class as your independent variable with abany as your dependent variable. Run the three-variable crosstab in SDA and interpret the tables as we did in the previous examples. Be sure to recode degree and class and make sure that you use the SELECTION FILTER box to select out the 2018 GSS.


Now let's go back to the two questions we started with. Are Americans divided by their socioeconomic status? How big are these divisions?

What did we discover about the interaction of the various ways of measuring socioeconomic status? Based on your analysis, would you say that socioeconomic divisions are small, moderate, or large?

Next Exercise

In Exercise 10 were going to elaborate our analysis of racial divisions by adding education into the analysis.

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Elaborating Racial Divisions



In this exercise and the ones following, we'll elaborate the analysis we carried out in the first six exercises. Each of the last six exercises in this series is paired with one of the first six exercises. Exercise 4 focused on the relationship between race and how respondents said they voted in the 2012 and 2016 presidential elections. This exercise will add other variables – what we will call our control variable – into the analysis.


Goal of Exercise

The goal of this exercise is to explore how race affects voting behavior by adding education and subjective class identification into the analysis. Our focus will continue to be on racial divisions.

Part 1 – Race and Voting in the 2012 Presidential election

Let's start by rerunning the crosstabulation of race and how respondents voted in the 2012 presidential election. The variable names are race and pres12(1-2). To access the GSS cumulative data file in SDA format click her. If you need to review how to get two-variable tables, look back at Exercise 4 and the Introduction to SDA at the end of these exercises.

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80


In Exercise 4 we found that blacks were considerably more likely than whites to say they voted for Obama in the 2012 presidential election. Independents fell between blacks and whites. Chi Square was statistically significant and our measure of association, Cramer's V, suggested a strong relationship.

If you run a frequency distribution for race, you'll notice that the other category is much smaller than the other categories. When we add more variables into our analysis, each of these categories gets subdivided which means that small categories such as other get even smaller. So we're going to omit the other category. We can do this entering race(1-2) into the appropriate SDA box.

Now we're going to divide our sample into two groups – those with a high school or less education and those with at least some college – and then rerun the crosstab of pres12 by race for each subgroup. That's what a three-variable crosstab does and SDA can do it for you. It's easy to do. Here's what your SDA dialog box ought to look like.

Figure 10-1

The only difference between this and the two-variable table that you ran earlier is that you add degree as your control variable. Everything else remains the same. Remember to tell SDA that we only want to consider those who voted for either of the two major presidential candidates by entering pres12(1-2) in the row box and to enter year(2018) in the SELECTION FILTER box to indicate that we want to use the 2018 GSS. Be sure to use the recode for degree. Here's the recode: degree (r:1=0-1"high school or less"; 2=2-4"some college or degree")

When you run this table, you'll notice that SDA gives you three tables – one partial table for those with a high school or less education, another partial table for those with at least some college, and a third table that contains both educational levels. It also gives you the summary statistics for each table. Here's the table for those with a high school education or less.

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Figure 10-2


The difference between blacks and whites is 46 percentage points (98-52). Chi square is statistically significant. Tau-c equals -.34.


Figure 10-3


The difference between whites and blacks is 35 percentage points (94-59). Chi square is statistically significant. Tau-c equals -.17.

And here's the table that includes both educational levels. You might be asking how this table differs from the table you ran in Exercise 4. Recall that cases with missing data for any variable are excluded from the table. So in Exercise 4, SDA excluded cases with missing data for race and pres12 while in the table you just ran it excluded cases with missing data for race, pres12, and degree.

Figure 10-4

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Here are the summary statistics for this third table that includes both educational categories.

The difference between whites and blacks is 41 percentage points (97-56) Chi square is statistically significant. Tau-c equals -.25.

Now compare the summary statistics for the two partial tables with the summary statistics for the table with all the cases. The relationship between race and voting is stronger for those with less education. The percentage point difference is larger (46 versus 35) and the Tau-c values are larger (.34 versus .17). This is usually referred to as specification. We have specified the conditions under which the relationship is stronger or weaker.

Here's another way to present the data visually which is helpful in making sense of our analysis. In this table, I have entered the percent vote for Obama. You could have entered the percent vote for Romney. I created the percentage point difference by subtracting the percent vote for whites from the percent vote for blacks and I subtracted the percent vote for those with a high school education from the percent vote for those with some college. You could have chosen to subtract in the other direction. What's important is that you are consistent.

White Black Percentage Point Difference

High school or less 51.8 98.4 46.6At least some college 59.0 93.8 34.8Percentage Point Difference

7.2 -4.6

Figure 10-5

This table makes it easy to see patterns.

Racial differences are much larger than educational differences. Racial differences are larger for those with less education. Educational differences are much smaller than racial differences and are actually in opposite

directions for whites and blacks. Blacks with less education are the most likely to vote for Obama and whites with less education

are the least likely.


Now you get to try your hand at analyzing the relationships for these three variables. Repeat the analysis but this time use pres16(1-2) as your dependent variable. Run the three-variable crosstab in SDA and then write a paragraph interpreting the relationships. Be sure to recode degree and make sure that you use the SELECTION FILTER box to select out the 2018 GSS. Indicate that you want to include only those who voted for either of the two major presidential candidates by entering pres16(1-2) in the row box. Limit the categories for race to 1 (whites) and 2 (blacks) meaning that you are omitting others (3) from the analysis.

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Write your interpretation of the crosstabs using the column percents, Chi Square, and Tau-c. Compare your results with what we found for the 2012 election. What was the effect of controlling for education for the 2016 presidential election? Did education explain any of the original two-variable relationship? Were the findings different in any way from the 2012 analysis? Does this give you clues as to why Obama won in 2012 and Trump won in 2016?


Now let's go back to the two questions we started with. Are Americans divided by their political party identification? How big are these divisions?

Did controlling for education change our interpretation from Exercise 4? Did it add anything to the analysis in Exercise 4? What does this tell us about political divisions in the U.S.?

Next Exercise

In Exercise 11 were going to elaborate our analysis of religious divisions by adding gender and age into the analysis.

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Elaborating Religious Divisions



In this exercise and the ones following, we'll elaborate the analysis we carried out in the first six exercises. Each of the last six exercises in this series is paired with one of the first six exercises. Exercise 5 focused on the relationship between religion and how respondents felt about pornography. This exercise will add another variable – what we will call our control variable – into the analysis.


Goal of Exercise

The goal of this exercise is to explore how other variables affect the relationship between religion and how respondents felt about pornography. More specifically, we're going to explore how religion and gender are jointly related to opinions on controlling the distribution of pornography. Our focus will continue to be on religious divisions.

Part 1 – Gender and its Relationship to Fear of Crime

Let's start by rerunning the crosstabulation of religiosity and how respondents felt about controlling the distribution of pornography. We'll use reliten as our measure of religiosity. To access the GSS cumulative data file in SDA format click here. If you need to review how to get two-variable tables, look back at Exercise 5 and the Introduction to SDA at the end of these exercises.

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In Exercise 5 we found that respondents who are more religious were more likely than those who are

53 When the control variable has explained away the relationship between the independent and dependent variables, we refer to this as explanation. The control variable has explained away the original relationship. Typically we say that the original relationship was spurious.54 When the control variable helps us understand why or how the two variables are related, we refer to this as interpretation because you are interpreting why your independent variable is related to the dependent variable.55 When the relationship varies by the category of your control variable, we refer to this as specification because it specifies the conditions under which the relationship between the independent variable and the dependent variable varies.

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less religious to want stricter controls over pornography. They were more likely to want pornography to be illegal to everyone regardless of age. Those who were less religious were more likely to want pornography to be illegal only for those under the age of 18. Chi Square was statistically significant and our measure of association, Tau-c, suggested a relationship, although a weak relationship.

Could this relationship be due to some other variable such that when we controlled or held constant that variable (i.e., our control variable) the original relationship either disappeared or, as is more likely, weakened. For this to occur our control variable would need to be related to both religiosity and how respondents felt about controlling the distribution of pornography.

One possible control variable could be gender. Gender is related to both religiosity and control of pornography. We know from previous research that women are more religious than men. They go to worship services more often; they pray more often; they tell us they are more religious. And we have good reasons to suspect that women are more concerned about pornography than are men. Women are usually the objects of pornography; pornography demeans women.

We can use the 2018 GSS to check on these assertions. But first we need to decide how we're going to measure these variables.

We'll use sex as a proxy for gender. The variable name is sex. Religiosity can be measured in several ways. We can ask respondents how often they attend

worship services and we can ask them how important their religion is to them. These variables are named attend and reliten.

How respondents feel about controlling the distribution of pornography is measured by the following question: "Which of these statements comes closest to your feelings about pornography laws – illegal to all, illegal under 18, legal?" This variable is named pornlaw.

We're going to recode attend and reliten using the following recodes.

For attend, the recode is:attend (r:1=0-3"seldom or none";2=4-5"sometimes"; 3=6-8"often")

For reliten, the recode is:reliten (r:1=1-1"strong";2=2-4"not strong")

Now we're ready to check on our assumptions. Run two crosstabs.

pornlaw by sex attend (recoded) by sex reliten (recoded) by sex

Now were ready to run our three-variable crosstab. Your SDA dialog box ought to look like this.

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Figure 11-1

The only difference between this and the two-variable table that you ran earlier is that you added sex as your control variable. Everything else remains the same.

When you run this table, you'll notice that SDA gives you three tables – one partial table for men and another partial table for women It also gives you a third table that contains both men and women. And it gives you the summary statistics for each table. Here's the table for men.

Figure 11-2


The difference between those who are more religious (i.e., strong) and those who are less strong (i.e., not strong) is 19 percentage points (35-16)

Chi square is statistically significant.

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Tau-c equals .1556

Here's the table for females.

Figure 11-3


The difference between those who are more religious (i.e., strong) and those who are less strong (i.e., not strong) is 26 percentage points (55-29)

Chi square is statistically significant. Tau-c equals .26.

Here's the table including both men and women. You might be asking how this table differs from the table you ran in Exercise 5. Recall that cases with missing data for any variable are excluded from the table. So in Exercise 5, SDA excluded cases with missing data for reliten and pornlaw while in the table you just ran it excluded cases with missing data for reliten, pornlaw, and sex.

56 We're going to ignore the sign of the percentage difference and Tac-c and simply look at the crosstab to see that those who are more religious are more likely to want pornography to be illegal to everyone regardless of age.

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Figure 11-4

Here are the summary statistics for this third table that includes both men and women.

The difference between those who are more religious (i.e., strong) and those who are less religious (i.e., not strong) is 24 percentage points (46-22)

Chi square is statistically significant. Tau-c equals .22.

If the original relationship was spurious, then it either ought to go away or decrease substantially for both males and females. So look carefully at the two tables – one for males and the other for females. But how can we tell if the relationship goes away or decreases markedly for both males and females? One clue will be the percent differences. Compare the percent differences between those who are more religious (i.e., strong) and those who are less religious (i.e., not strong) for males and then for females with the percent differences in the original two-variable table. Did the percent differences stay about the same or did they decrease substantially? Another clue is your measure of association. Did the measures or association for males and females stay about the same or did they decrease substantially from that in the original two-variable table?

If the relationship had been due to gender, then the relationship between strength of religion and opinion on pornography laws would have disappeared or decreased substantially for both males and females when we took out the effect of gender by holding it constant. In other words, the relationship would be spurious. Spurious means that there is a statistical relationship, but not a causal relationship.

In our case, the relationship between reliten and pornlaw was about the same for males and for females. So it's not spurious due to gender. It important to note that just because a relationship is not spurious due to gender doesn’t mean that it is not spurious at all. It might be spurious due to some other variable such as age.

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Recall that we have two different measures of religiosity – reliten and attend. The nice thing about having multiple measures is that you can repeat your analysis using an alternative measure. If you discover the same relationships, you can have more confidence in your findings. So, repeat the analysis we just did using attend as your measure of religiosity. Interpret your findings and decide if you found basically the same relationships.


Now you get to try your hand at multivariate analysis. Repeat the analysis but this time use age as your control variable. Run the three-variable crosstab in SDA and then write a paragraph interpreting the relationships. Be sure to use the SELECTION FILTER box to select out the 2018 GSS. Use the following recode for age: age(r:1=18-34 "under 35"; 2=35-64 "35 to 64"; 3=65-89 "65 and older")

Write your interpretation of the crosstabs using the column percents, Chi Square, and Tau-c. What did you find with age as your control variable? Was the relationship spurious due to age? How did you decide?


Now let's go back to the two questions we started with. Are Americans divided by their religiosity ? How big are these divisions?

What did we learn by adding age into the analysis? What does this tell you about religious divisions in the U.S. and how age influences those divisions?

Next Exercise

In Exercise 12 were going to elaborate our analysis of geographical divisions by adding education into the analysis.

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Exercises on Political and Social Divisions in American Edward Nelson, California State University, Fresno

Exercise 12Elaborating Geographic Divisions



In this exercise and the ones following, we'll elaborate the analysis we carried out in the first six exercises. Each of the last six exercises in this series is paired with one of the first six exercises. Exercise 6 focused on the relationship between the region of the country in which the respondent lived and the size of their community on the one hand and how respondents said they voted in the 2012 and 2016 presidential elections on the other hand. This exercise will add other variables – what we will call our control variable – into the analysis.


Goal of Exercise

The goal of this exercise is to explore how geography affects voting behavior by adding education into the analysis. Our focus will continue to be on geographic divisions.

Part 1 – Geography and Voting in the 2012 Presidential election

Let's start by rerunning the crosstabulation of the region of the country in which respondents lived and how respondents voted in the 2012 presidential election. The variable names are region and pres12(1-2). To access the GSS cumulative data file in SDA format click here. Be sure to use following recode for region: region (r:1=1-2"Northeast";2=3-4"Midwest"; 3=5-7"South"; 4=8-9"West") and to tell SDA that you want to use the 2018 GSS.

If you need to review how to get two-variable tables, look back at Exercise 6 and the Introduction to SDA at the end of these exercises.

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In Exercise 6 we found that those who lived in the Northeast were more likely to vote for Obama in the 2012 presidential election while those in the South were least likely to vote for Obama. Those in the Midwest and West fell between these two geographical groups. Chi Square was statistically significant and our measure of association, Cramer's V, suggested a weak relationship.

Now we're going to divide our sample into two groups – those with a high school or less education and those with at least some college – and then rerun the crosstab of pres12 by region for each subgroup. That's what a three-variable crosstab does and SDA can do it for you. It's easy to do. Here's what you SDA dialog box ought to look like.

Figure 12-1

The only difference between this and the two-variable table that you ran earlier is that you add degree as your control variable. Everything else remains the same. Remember to tell SDA that we only want to consider those who voted for either of the two major presidential candidates by entering pres12(1-2) in the row box and to enter year(2018) in the SELECTION FILTER box to indicate that we want to use the 2018 GSS. Be sure to use the recode for degree. Here's the recode: degree (r:1=0-1"high school or less"; 2=2-4"some college or degree")

When you run this table, you'll notice that SDA gives you three tables – one partial table for those with a high school or less education, another partial table for those with at least some college, and a third table that contains both educational levels. It also gives you the summary statistics for each table. Here's the table for those with a high school education or less.

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Figure 12-2


The difference between those living in the Northeast and South is 11 percentage points (72-61). Chi square is not statistically significant. Cramer's V equals .08. SDA doesn't compute Cramer's V for you. Look back to Exercise 6 to see

how to compute it.


Figure 12-3


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The difference between those living in the Northeast and South is 17 percentage points (72-55). Chi square is statistically significant. Cramer's V equals .15.

And here's the table that includes both educational levels. You might be asking how this table differs from the table you ran in Exercise 6. Recall that cases with missing data for any variable are excluded from the table. So in Exercise 6, SDA excluded cases with missing data for region and pres12 while in the table you just ran it excluded cases with missing data for region, pres12, and degree.

Figure 12-4

Here are the summary statistics for this third table that includes both educational categories.

The difference between those living in the Northeast and South is 14 percentage points (72-58). Chi square is statistically significant. Cramer's V equals .11.

Now compare the summary statistics for the two partial tables with the summary statistics for the table with all the cases. The relationship between race and voting is slightly stronger for those with more education. The percentage point difference is larger (17 versus 11) and the Cramer V values are larger (.15 versus .08). It's also important to note that the pattern of the percents is similar for both educational groups. Those in the Northeast are the most likely to vote for Obama while those in the South are least likely. In other words, the relationship between region and pres12 really didn't change much when degree was introduced into the analysis.

Here's another way to present the data visually which is helpful in making sense of our analysis. In this table, I have entered the percent vote for Obama. You could have entered the percent vote for Romney. I created the percentage point difference by subtracting the percent vote for those in the South from the percent vote for those in the Northeast and I subtracted the percent vote for those with a high school education from the percent vote for those with some college. What's important is that

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you are consistent. You could have chosen to subtract in the other direction. Notice that I did not include those in the Midwest and the West in order to simplify the table.

Northeast

South Percentage Point Difference

High school or less 71.8 60.7 11.1At least some college 72.1 55.2 16.9Percentage Point Difference

0.3 -5.5

Figure 12-5

This table makes it easier to see the patterns.

Regional differences are larger than educational differences. Educational differences are somewhat larger for those living in the South. Those in the Northeast are the most likely to vote for Obama and respondents in the South with

more education are the least likely.


Now you get to try your hand at analyzing the relationships for these three variables. Repeat the analysis but this time use pres16(1-2) as your dependent variable. Run the three-variable crosstab in SDA and then write a paragraph interpreting the relationships. Be sure to recode degree and region and make sure that you use the SELECTION FILTER box to select out the 2018 GSS. Indicate that you want to include only those who voted for either of the two major presidential candidates by entering pres16(1-2) in the row box.

Write your interpretation of the crosstabs using the column percents, Chi Square, and Cramer's V. Compare your results with what we found for the 2012 election. What was the effect of controlling for education for the 2016 presidential election?

Were the findings different in any way from the 2012 analysis? Does this give you clues as to why Obama won in 2012 and Trump won in 2016?


Now let's go back to the two questions we started with. Are Americans divided by their geographical identification? How big are these divisions?

Did controlling for education change our interpretation from Exercise 6? Did it add anything to the analysis in Exercise 6? What does this tell us about political divisions in the U.S.?

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Next Exercise

This concludes this series of 12 exercises. A brief epilogue follows which attempts to pull together our findings across these exercises.

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Edward Nelson, California State University, FresnoEpilogue

It is often said that the United States is a very divided nation. Some refer to this divide as polarization; others refer to it as partisanship; others use different terms. Groups (e.g., nations, communities, churches) can be divided along many lines: political, gender, socioeconomic, race, religion, and geography (among others). We consider two critical questions.


The first six exercises focused on two-variable analysis (i.e., bivariate analysis) and the last six on three-variable analysis (e.g., multivariate analysis). We used several statistical tools (i.e., crosstabulation, Chi Square, and measures of association). The data we used was the 2018 General Social Survey (GSS), a large national probability survey of adults in the U.S. The statistical program used was Survey Documentation and Analysis (SDA) written at UC Berkeley.

The purpose of this epilogue is to briefly summarize the findings of these exercises and to address the two questions listed above. We considered the six possible divisions mentioned above and a number of variables were used to measure these divisions. These variables are listed at the end of this epilogue.

Groups and individuals can be divided on a large number of different issues. We focused on seven of these issues – who respondents voted for in the 2012 and 2106 presidential elections, fear of walking alone in their neighborhood at night, whether they favored or opposed capital punishment, whether they thought abortion for any reason should be legal, how they felt about controlling the distribution of pornography, and their opinion on the legalization of marijuana.

Here's a brief summary of what we found in these exercises. I included information that we didn't cover in the exercises.

Divisions Based on Political Party Identification

Dependent variable: Party Identification – % of Democrats minus % of Republicans:

Who voted for Democratic presidential candidate in 2012

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83

Were afraid of walking alone in neighborhood at night

5

Who favored capital punishment -34

99

Who thought abortion for any reason should be legal

29

Who thought pornography should be illegal for everyone regardless of age

-13

Who thought marijuana should be legalized 23

Average absolute percentage point difference 37.4

Range of absolute percentage point differences 83-5=78

Figure 1

These percent differences refer to the percent of Democrats minus the percent of Republicans who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was quite a large range to these percent differences. As you would expect, they were largest for voting and they were smallest for fear of crime. The average absolute percent difference was 37.4 percentage points which is a quite large difference.

Divisions Based on Gender

Dependent variable:Gender – % of Females minus % of Males:


6


15


22



1


17

Who thought marijuana should be legalized -3



These percent differences refer to the percent of females minus the percent of males who, for example,

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voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a moderate-sized range for these percent differences. They were largest for the fear of walking alone at night in their neighborhood and they were smallest for abortion. The average absolute percent difference was 10.1 percentage points which is fairly small.

Division Based on Highest Educational Degree

Dependent variable: Education – % of those with at least some college minus % of those with a high school or less education:


0


7


-4



17


-2




These percent differences refer to the percent of those with at least some college minus the percent of those with a high school or less education who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was fairly small range for these percent differences. They were largest for abortion and they were smallest for those voting in the 2016 presidential election. The average absolute percent difference was 6.3 percentage points which is quite small.

Division Based on Family Income

Dependent variable: Family Income – % of those with high income minus % of those with low income:


-25

101


-17


-14

Who favored capital punishment 4


16


-3




These percent differences refer to the percent of those with high family income minus the percent of those with low family income who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a moderate-sized range for these percent differences. They were largest for voting in the 2012 presidential election and smallest for those who thought pornography ought to be illegal for everyone regardless of age. The average absolute percent difference was 11.9 percentage points which is fairly small.

Division Based on Subjective Class Identification

Dependent variable: Subjective Class Identification – % of those who were upper or middle class minus % of those who were working or lower class:


-14


-1


-7



7


-3

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These percent differences refer to the percent of those who identified with the middle or upper class minus the percent of those who identified with the working or lower class who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a fairly small range for these percent differences. They were largest for voting in the 2012 presidential election and smallest for those who favored the legalization of marijuana and those voting in the 2016 election. The average absolute percent difference was 5.4 percentage points which is very small.

Division Based on Race

Dependent variable: Race – % of blacks minus % of whites:


41


54


10



-4


-6




These percent differences refer to the percent of blacks minus the percent of whites who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a quite large range for these percent differences. They were largest for voting in the presidential elections and smallest for those who favored the legalization of marijuana. The average absolute percent difference was 20.1 percentage points which is a moderate-sized difference.

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Divisions Based on Religious Preference

Dependent variable:Religious Preference – % of those who had no religious preference minus % of Protestants:


33


34


-4



31


-25




These percent differences refer to the percent of those who have no religious preference minus the percent of Protestants who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a moderate-sized range for these percent differences. They were largest for voting in the presidential elections and smallest for those who were afraid of walking alone at night in their neighborhood. The average absolute percent difference was 21.9 percentage points which is a moderate-sized difference.

Divisions Based on Subjective Religiosity

Dependent variable:Subjective Religiosity – % of those who were less religious minus % of those who were more religious:


20


16


-4

Who favored capital punishment 7

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29


-24



Range of absolute percentage point differences 29-4 = 25

These percent differences refer to the percent of those who defined themselves as more religious minus the percent of those who thought they were less religious who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a moderate-sized range for these percent differences. They were largest for abortion and smallest for those who were afraid of walking alone at night in their neighborhood. The average absolute percent difference was 17.9 percentage points which is a moderate-sized difference.

Division Based on Attendance at Worship Services

Dependent variable:Attendance at Worship Services – % of those who were frequent attenders minus % of those who rarely attended:


-24


-15


9



-33


34




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These percent differences refer to the percent of those who attended worship services frequently minus those who rarely attended who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a moderate-sized range for these percent differences. They were largest for abortion, those who thought marijuana should be legalized, and those who thought pornography should not be legal regardless of age and smallest for those who favored capital punishment. The average absolute percent difference was 21.9 percentage points which is a moderate-sized difference.

Divisions Based on Region of Country Where Lived

Dependent variable:Region of Country – % of those who lived in the Northeast minus % of those who lived in South:


14


8


-3



20


-9




These percent differences refer to the percent of those who lived in the Northeast minus the percent of those who lived in the South who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a small range for these percent differences. They were largest for abortion and smallest for fear of walking alone at night in their neighborhood. The average absolute percent difference was 11.0 percentage points which is a fairly small difference.

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Divisions Based on Size of Community

Dependent variable:Size of Community – % of those who lived in large communities minus % of those who lived in small communities:


25


36


18



17


-5




These percent differences refer to the percent of those who lived in large communities minus the percent of those who lived small communities who, for example, voted for the Democratic presidential candidate in 2012 (i.e., Obama) and 2016 (i.e., Clinton). Notice that there was a moderate-sized range for these percent differences. They were largest for voting and smallest for legalization of marijuana. The average absolute percent difference was 17.4 percentage points which is a moderate-sized difference.

Summary

What can we conclude from all this? There were sizeable political divisions, more moderate-sized divisions based on race, religion, and geography (i.e., size of community), and smaller divisions based on region, gender, and socioeconomic status. In other words, we are divided on some issues and not as much on other issues.

Are we a divided nation? People are going to differ on what they view as large, moderate, and small divisions but it seems clear that we are politically divided and not as divided by region, gender, and socioeconomic status.

Variables Used in These Exercises Political divisions

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o Party identification Gender divisions

o Sex as a proxy for gender Socioeconomic divisions

o Highest educational degreeo Family income in previous year (2017)o Subjective class identification

Racial divisionso Subjective racial identification

Religious divisionso Religious preference or identificationo Attendance at worship serviceso Subjective importance of religion

Geographical divisionso Region of country where respondents liveo Size of community where respondents live

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AppendixIntroduction to Survey Documentation and Analysis (SDA)

Selecting the Data Set to be AnalyzedWe’re going to use the General Social Survey (GSS) for these exercises. The GSS is a national probability sample of adults in the United States conducted by the National Opinion Research Center (NORC). The GSS started in 1972 and has been an annual or biannual survey ever since. For this exercise we’re going to use the 2018 GSS. To access the GSS cumulative data file in SDA format click here. SDA stands for Survey Documentation and Analysis. This introduction will tell you most of what you need know to run SDA. The GSS cumulative data file contains all the data from each GSS survey conducted from 1972 through 2018. We want to use only the data that was collected in the most recent survey in 2018. To select out the 2018 data, enter year(2018) in the SELECTION FILTER(S) box. Your screen should look like Figure 1.

Figure 1

Notice that a weight variable has automatically been entered in the WEIGHT box. This will weight the data so the sample better represents the population from which the sample was selected.

The GSS is an example of a social survey. The investigators selected a sample from the population of all adults in the United States. This particular survey was conducted in 2018 and is a relatively large sample of adults. In a survey we ask respondents questions and use their answers as data for our analysis. The answers to these questions are used as measures of various concepts. In the language of survey research these measures are typically referred to as variables.

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Getting a Frequency DistributionOne of the variables in the GSS is the respondent's educational level. Each variable has a name which is degree60 for this variable. (Variable names will in lower case and will be italicized.) To get a frequency distribution for degree, enter the variable name in the ROW box. Your screen should look like Figure 2.

Figure 2

Notice that we have entered year(2018) in the SELECTION FILTER box. SDA will automatically enter the weight variable in the WEIGHT BOX. Click on RUN THE TABLE and your screen should look like Figure 3.

TFigure 3

60 Degree is the respondent's highest educational degree.

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Getting a CrosstabNow let's get the crosstabulation of degree and grass. Grass is the respondent's answer to the following question: "Do you think the use of marijuana should be made legal or not?"

We'll talk about crosstabulation in these exercises. The purpose of this introduction to SDA is to show you how to use SDA. Look back at Figure 1. Your dependent variable goes in the ROW box and your independent variable in the COLUMN box. You'll want the column percents which is the default in SDA so you don't have to do anything else to get them. Your screen should look like Figure 4.

Figure 4

Click on RUN THE TABLE and your screen should look like Figure 5.

Figure 5

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There are several options that you will want to change.

SDA uses something called "color coding" which we won't be using in these exercises. You can turn it off if you wish by clicking on OUTPUT OPTIONS and then unchecking the box for COLOR CODING.

On OUTPUT OPTIONS locate the SAMPLE DESIGN options and click on the box for SRS. Under CHART OPTIONS, change the TYPE OF CHART to NO CHART.

RecodingOften we want to combine categories of a variable. Run a frequency distribution for the variable partyid. Your output ought to look like this.

Figure 6

Let's say we want to combine categories 0 through 2 into one category and assign it a value of 1 and give it the label "Democrat." Then we'll combine categories 4 through 6 into another category and give it a value of 3 and the label "Republican." We'll change category 3 to the value of 2 and give it the label "Independent." Additionally, we want to omit category 7 from our analysis. Here's the way you will accomplish this.

First you enter r: after the variable name. The r stands for recode.

Then you indicate the new value you want to assign to the first category which is 1.

Then you put the values that you are combining which are 0-2 for the first category. These values must be separated by a dash (i.e., hyphen). The hyphen must always be used even if there is only one value for that category.

This is followed by the label you want to assign to this category enclosed in double quotation marks which is “Democrat” for the first category. This is free form meaning you can put what you want for the label.

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This is separated from another recode category by a semi-colon.

Finally, the entire recode specification is in parentheses.

To omit the value 7, just leave it out of the recode statement.

So your recode statement will be the following:

partyid (r:1=0-2"Democrat";2=3-3"independent";3=4-6"Republican")

It can be tricky to write these recode statements properly, so in these exercises I'll give you the recode statement and all you have to do is to copy and paste it into the appropriate box in SDA.

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