POL 242Introduction to Research Methods

 

Assignment One TutorialDescriptive Statistics

June 2, 2011  

Anthony Sealey anthony.sealey@utoronto.ca

http://individual.utoronto.ca/sealey

Agenda

(1) Introduction • (2) Review

(i) Types of Variables (ii) Principal Descriptives

(iii) Webstats(3) Descriptives in Webstats(4) Exercise in Webstats

Introduction

Please be sure to sign the attendance form.

Research QuestionsReview of Types of Variables

Research QuestionsReview of Principal Descriptives

Research Questions1. Measures of Central Tendency

Research Questions“Pick a number …”

Research Questions“… close counts.”

Research Questions1, 2, 3, 4, 5, 6, 7, 8, 9, 10

n

where ‘n’ denotes the number of elements

S xi _______

n

Mean (x) =

(1+2+3+4+5+6+7+8+9+10)

10

Mean =

Mean = 5.5

i = 1

_

Research Questions1, 2, 3, 4, 5, 6, 7, 8, 9, 100

Research Questions

Median: After arranging the data from highest to

lowest, the median is the

value in the middle.

Research Questions“… close doesn’t count.”

Research Questions1, 2, 2, 3, 4, 5, 6, 7, 8, 9

Research Questions

Mode: The value that occurs with the highest

frequency (i.e. the value that appears most

often).

Research Questions2. Measures of Dispersion

Research Questions1, 2, 3, 4, 5

n where ‘x’ denotes the Mean

S (xi – x)2 _________________

n – 1 (1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2

5 – 1

Mean =

Mean = 2.5

i = 1Variance (s2) =_

_

where ‘s2’ denotes the Variance

Variance(s) =StandardDeviation

√ (s2)

√ 2.5Variance (s) =

1.58114Variance (s) ≈

Research QuestionsDescriptive Statistics

Measures of Central Tendency Measures of Dispersion

Mean Median Mode Variance Standard

(m)     (s2) Deviation (s)

  Nominal     ü    

Data TypeOrdinal   ü ü    

Interval ü ü ü ü ü

  Ratio ü ü ü ü ü

When to use key descriptive statistics:

Research QuestionsReview of Webstats

• There are four basic steps to the • analysis of a variable in Webstats: • (1) Select a dataset. • (2) Run a ‘frequency’ to understand

how the variable is coded. • (3) Refine the variable. • (4) Perform the analysis.

• In today’s tutorial we’ll use the 2006 • CES to consider three variables: • (1) A citizen’s province. • (2) Citizen’s preferences for or

against income redistribution. • (3) Citizen’s evaluations of the

competence of political leaders.

Research Questions

I strongly recommend going to my site, downloading the ‘code’ file and following along:

http://individual.utoronto.ca/sealey

Research Questions

Step One: Select the dataset

• Go to the course website located at: http://groups.chass.utoronto.ca/pol242/ • Go to: Webstats > Start Webstats.• In section 1, select ‘CES 2006’.• In section 3, select ‘Syntax Method’.• Hit <PROCEED>.

Research Questions

Step Two: Run a Frequency

• Let’s begin with the ‘province’ variable. • To run a frequency, use this code:

fre VAR = province.• Given that this variable has no missing

values and does not require a recode, we can skip the third step (‘refine the variable’) and go to the fourth (‘perform the analysis’).

Research QuestionsMoving on to the next variable …

Research Questions

The question wording for ‘cps_f6’ in the 2006 iteration of the Canadian Elections Study:

Research Questions

Step Two: Run a Frequency

• Since we’ve already selected the dataset, we don’t need to repeat step one. • To run a frequency, use this code:

fre VAR = cps_f6.

Research Questions

Step Three: Refine the Variable

• Notice the ‘don’t know’ and ‘refused’ responses. These responses take on the values of ‘8’ and ‘9’ respectively. We’ll want to code them as missing, and then rerun the frequency: missing values cps_f6 (8,9). fre VAR = cps_f6.

Research QuestionsAnd finally …

Research Questions

The ‘cps_h2b0’ and ‘cps_h2d0’ variables in the 2006 iteration of the Canadian Elections Study asks about respondent’s perceptions of levels of political leaders’ competence. In today’s tutorial, we’ll focus on the two most successful political leaders in the 2011 election.

Smiling Jack

Smiling Stephen

Research Questions

Step Two: Run a Frequency

• Since we’ve already selected the dataset, we don’t need to repeat step one. • To run frequencies, use this code:

fre VAR = cps_h2b0. fre VAR = cps_h2d0.

Research Questions

Step Three: Refine the Variables

• Notice the ‘don’t knows’ are coded as ‘98’. To code them as missing, use this code: missing values cps_h2b0 (98). fre VAR = cps_h2b0.

missing values cps_h2d0 (98). fre VAR = cps_h2d0.

Research QuestionsDescriptives in Webstats

Research Questions

Once we’ve refined our variables, the final step is to perform the analysis. To obtain descriptive statistics, we do this by simply adding some extra code at the end of our frequency command.

Research Questions

Step Four: Perform the Analysis

• Suppose we want to find the mode of the ‘province’ variable; in order to do this, we simply add ‘/statistics=mode’ at the end of our frequency command: fre VAR = province/statistics=mode.

Research Questions

• If we want other descriptive statistics, simply include the appropriate code at the end of the frequency command.• For example, if we want to know the

median, mean, variance and standard devation, simply add ‘/statistics=median mean variance stddev’ at the end of our frequency command.

Research Questions

Use appropriate descriptives for each level of measurement. • For nominal variables, find the mode: fre VAR = province/statistics=mode.

• For ordinal variables, find the mode and median: missing values cps_f6 (8,9). fre VAR = cps_f6/statistics=mode median.

Research Questions

• For interval/ratio variables, find the mode, median, mean, variance and standard deviation: missing values cps_h2b0 (98). fre VAR = cps_h2b0/statistics = mode median mean variance stddev.

Research Questions

We can use the means and standard deviations of similar variables to compare them. • For example, if we want to compare

perceptions of Jack’s and Stephen’s competence, use this code: missing values cps_h2b0 (98). fre VAR = cps_h2b0/statistics = mean stddev.

missing values cps_h2d0 (98). fre VAR = cps_h2d0/statistics = mean stddev.

Research Questions

Once we’ve completed our analysis, we’ll be prepared to ‘tell the story’. In other words, what have we learned from our analysis? When doing this, use the information we’ve gathered from the frequency distribution as well as from the appropriate descriptive statistics.

Research QuestionsExercise in Webstats

Research Questions

Exercise

Choose a public opinion dataset that you are interested in. Find a variable for each of the nominal, ordinal and (interval or ratio) levels of measurement. Run frequency distributions, refine the variables by declaring missing values and performing necessary recodes and calculate appropriate descriptive statistics for each of the identified variables. What’s the ‘story’ of your analysis? What have you learned?