Chi Square analysis.docx

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Chi Square analysis: dissertation research questions using categorical data

One of the most valuable statistics is a non-parametric procedure called Chi Squareanalysis. It is also called the test of goodness of fit. Its

symbol is x squared (x).Unlike the t-test and ANOVA procedures, the Chi Square analysis is not as powerful to reject the null. It does not use the mean or standard

deviation for computation; it does not rely on an interval or ratio scaling. Because the Chi Square relies on frequency data, its value lays in

the statistics ability to answer questions about data that are nominal. Variables in many settings are measured very often by their categories

- and not exact intervals. Chi Square allows you to answer important questions with variables measured with nominal or ordinal scales.

An example of where a Chi Square analysis would be useful is to see if there are differences between male and female college students on

choice of major field of study- Engineering or English. The null hypothesis would be: There is no difference between male and female college

students on their choice between taking quantitative versus qualitative elective courses. Both variables GENDER and COURSE are categorical.

Perfect for a Chi Square.

Anxious about dissertation statistics? You are notalone!

The dissertation statistics - from the initial research design to writing up statistical results -create anxiety for many graduate students. Most of us have not had math since high school,and it was not our favorite subject.

Plus, professors teach quantitative statistical formulas, and make the research designscomplex. You dont have the confidence to ask questions and when you do, the answers addto your confusion.

I can help. With expertise and care, I have provided dissertation advice to hundreds ofdoctoral students so that they complete their degree in less time, with much less stress and

without breaking the bank. We can do it all online or by mail but you are welcome to visit

my office.

Here are some of the areas where most students have asked for my assistance. I haveprovided each with coaching, tutoring, support, expertise and guidance.

Here are some practical tips on how to pick your dissertationtopic and write a proposal.

1. Select a general dissertation topic before you dive into the library or the Internet anddrown in the resources.There are a few questions you should answer before you begin to

pick your topic.

2. There are several ways that you can determine if your topic is a good one.Here are some

strategies that you can use to assess the value of your dissertation topic.

3. Plan on how you will write the dissertation proposal to get it completed. Allocate days ofthe week, and hours of the day, when you are alert and fresh. Set a schedule and stick to it.
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* Use time management strategies.

* Get a daily calendar and carry it around with you.

* Use the same backpack / briefcase to carry everything related to your dissertation(Laptop,books, notepads, pens, journal articles, etc.)

4. Use multiple library and online resources to establish keywords to get the ball rolling; addkeywords as you move along. Research the research in the literature review process.Here

are several library and online resources that you can use.

5. Take your time in the library and online when reviewing the literature. Avoid costly and

embarrassing mistakes because you were in a hurry.These are the most common errors

students make when doing dissertation literature reviews.

6. Use index cards to take notes and to guide your actual proposal writing for the

dissertation. It seems antiquated but you can shuffle the cards. They are physical and canbe moved in different order.

7. When writing your proposal use an inverted pyramid format (from a broad to a narrowfocus). Have a peer read your proposal to see if it makes sense and to evaluate itsworth.Here are some tips that you can use to write your proposal properly.

8. Market your proposal (i.e., get it approved) by making it appealing to the reader.(Grammar, spelling, appearance) Have someone read what you wrote and use theirfeedback as consultation.

How to state your dissertation research questions and nullhypotheses

Dissertation research begins with your hunches, guesses and questions you want to test

out. The information below will help you to state your dissertation research questions andnull hypothesis in a testable manner.The research hypothesis states your expectations in a positive sense.

The null hypothesis is always stated in the negative. This is because you have to be able toprove something is indeed true. Technically speaking, the word hypothesis is a Greek

word that means an assumption subject to verification.

The null hypothesis is what we test with statistics. This is how we decide whether to acceptor reject the null hypothesis.

*You ACCEPT the null or you fail to reject it. This means that no differences or norelationships were found.
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*You REJECT the null as false. This means that differences or relationships do exist.Furthermore, your research hypothesis is upheld.

There are two types of null hypotheses - directional or non-directional.

Attached to this are one or two tailed tests of statistical significance.

The probability level that we choose influences how liberal or conservative we want to be in

testing our hypothesis. Based on the probability level we choose, there is a chance thateither a Type I or Type II error can be committed.Here is some additional information onprobability levels and errors.

Finally, there are ways to enhance the ability to reject the null.This is called PowerAnalysis.

From start to finish there is a method to the madness.These are the simple steps forhypothesis testing that you will become familiar with as your

Samples and Sample Size

How many times do you wish that you could have a few more hours in the day, even a few

more minutes? This is another advantage of using statistics. Statistics allow you to build afoundation for data driven decisions without spending many, many extra hours.Why is this so? Statistics are based on samples and sample size. We have often heard

these terms batted around in the context of random samples or scientific samples and

the value of a large sample. Yet, few of us really know or understand how valuable theseconcepts are.

Sample is a smaller version of the entire population that your dissertation research is about.

Sample size is the number of subjects in your study. Although these two terms can besimply and easily defined, there are many important sampling questions that you will haveto consider as you plan your dissertation research.

What is the difference between a population and a sample?

When we think of the term population, we usually think of people in our town, region,

state or country and their respective characteristics such as gender, age, marital status,ethnic membership, religion and so forth. In statistics the termpopulation takes on a

slightly different meaning. The population in statistics includes all members of a definedgroup that we are studying or collecting information on for data driven decisions.
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Apartof the population is called a sample. It is a proportion of the population, a slice of it,

a part of it and all its characteristics. A sample is a scientifically drawn group that

actuallypossesses the same characteristicsas the population if it is drawn randomly.(Thismay be hard for you to believe, but it is true!)

Randomly drawn samples must have two characteristics:

*Every person has an equal opportunity to be selected for your sample; and,

*Selection of one person is independent of the selection of another person.

What is great about random samples is that you can generalize to the population that you

are interested in. So if you sample 500 households in your community, you can generalize

to the 50,000 households that live there. If you match some of the demographiccharacteristics of the 500 with the 50,000, you will see that they are surprisingly similar.

Sampling question #1: Why should I sample instead of usingthe entire population?

Why not use the entire population to draw our conclusions? This is a very good question

that a smart researcher would ask. But when dollars are tight, human resources are limited,

and time is of the essence, sampling is a wonderful option. And the reason is that for most

purposes we can obtain suitable accuracy quickly and inexpensively on information gainedfrom a sample.The bottom line is it would be wasteful and foolish to use the entire population when asample, drawn scientifically, provides accuracy in representing your population of interest.Assessing all individuals may be impossible, impractical, expensive or even inaccurate.

Here are some reasons why doctoral students should not even try to use the entirepopulation in their dissertation research.

*We hardly ever know who makes up the entire population.

*It is too costly in terms of human resources and other expenses.

*It is time consuming and costly.

*There is alot of error to control and monitor.

*Lists are rarely up to date.

Sampling question #2: How do I determine sample size?


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Many students wonder about their sample size. How large should it be? Some of thedecision is based on practical aspects. What population do you have access to? How much

time and money are you willing or able to spend on sample acquisition. Here are some realworld sampling suggestions to help you out!*Ask experts what they would suggest for sample size.

*See what the literature recommends.

*Must have at least 10 per cell for statistical analysis.

*Rule of thumb- larger is better.

If you would like to get a feeling for the size of samples that represent entire populations,

please refer to Krejcie (1970). The chart below suggests the great benefit that randomly-selected samples afford. (Population size is noted by uppercase N and sample size by

lower case n.)

Random Sample Sizes (n) Required for Population (N) Representation

Population Size (N) ------ Sample Size(n)

50 ------------------ 44

100 ----------------- 80

500 ----------------- 217

1,000 ---------------- 278

1,500 ---------------- 306

3,000 ---------------- 341

5,000 ---------------- 357

10,000 --------------- 375

50,000 --------------- 381

100,000 -------------- 384


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Source: Krejcie, R.V. & Morgan, D.W. (1970) Determining sample size for researchactivities. Educational and Psychological Measurements, 30, 607-610.

Sampling question #4: Are there other useful samplingstrategies?

Yes!

Systematic sampling is an often-used sampling strategy and cost effective. Again, youmust have a population sampling frame list that is in random order and non-overlapping.

Determine both the size of the population and the size of the sample you want to work with.Then, divide the sample size (n) into the population (N) size to get your key number,symbolized as k.

Cluster sampling is exactly what its title implies. You randomly select clusters or groups ina population instead of individuals.

Quota sampling is used if a stratum is small in the population but important to theresearch questions being presented. So we may over sample, or establish a quota, so thatwe get the subjects needed to address our research.

Stratified sampling is used when the population is heterogeneous and it is important to

represent the different strata or sub-populations. There is a proportional representation ofstrata in the sample - proportional to the population strata. We divide the entire population

into strata (groups) to obtain groups of people that are more or less equal in some respect.Then, select a random sample from each stratum.

Convenience samples, exactly what the name suggests, are oftentimes what we have to

use because of reality. We cannot draw a sample, but we have a group that is accessible, isrepresentative of our target population and just available to us. Instead of becoming puristsand throwing out the chance for collecting data for decisions, use what you have with the

honest acknowledgement that there are limitations.

Sampling question #3: How do I draw a simple randomsample?

There is a method to the madness of drawing a random sample. You must abide by the

rules of the game in sampling in order for your sample to be representative of thepopulation.


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1. The first step is to identify all of the members in your population. You must be able to

list them in what is called a sampling frame. The frame should have the names without

order to them and non-overlapping (no duplicates). Alphabetizing the list by surname is away to insure a random order in the sampling frame.

2. Second, you must give each name an identification number. Start with 1 and continue.

3. Third, you must decide what the size will be for your sample. You can use the tablesuggested in the Krejcie (1970) article, or whatever feels right for you to believe in theresults you obtain. As a rule of thumb, use as large a sample size as possible.

4. Fourth, you need to get a Table of Random Numbers. Many are located at the end of

statistical or mathematical textbooks. The Table of Random Numbers consists of rows and

columns of numbers arranged at random so that they can be used as any point by readingin any direction left or right, up or down. We are now ready to draw our random sample.

A Really Simple Example

Sampling FrameID Name

1. Alex

2. Allen

3. Allison

4. Amelia

5. Brett

6. Deanna

7. Ellen

8. Emily

9. Felice

10. Juan

11. Julia

12. Kara

13. Krista

14. Mark


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15. Miguel

16. Maura

17. Olivia

18. Rachael

19. Rebecca

20. Seth

Fifth, we know that our largest ID number has two digits (20). So we are going to need a

two-digit column in the Table of Random Numbers. We close our eyes and put our finger

down anyplace in the Table of Random numbers. This is our starting point. We have decided

in advance whether we would use two digits going up, down, left or right. So we begin.

Sixth, Number #6 is the first ID number that is within our band of between 1 and 20. This

is the first member of our random sample and it is Deanna. We continue 82, 56, 96, 66, 46until we and come up with the next is ID #13Krista. Our three last members of the sample

are ID #8 (Emily), ID #5 (Brett) and ID #4 (Amelia). We have five randomly selectedmembers: Deanna, Krista, Emily, BrettandAmelia.

Choices for your research design and dissertationmethodology

"The best statistics cannot save an inferior design! This is the foundation of a good

dissertation. "

Research design and dissertation methodology are plans that promote systematicmanagement of data collection. Design and methodology dictate what you need to answeryour research questions.There are manytypes of research designs for dissertation research. Here are the most

common with a simple example to illustrate.

Historical Research Design -The Evolution of the Laptop Computer

Case and Field Research Design -Observations of Autistic Children in the AmericanClassroom
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Descriptive or Survey Research Design - The Public View of American and EuropeanLeaders

Correlational or Prospective Research - Breastfeeding's Impact on NewbornDevelopment

Causal Comparative or Ex Post Facto Research Design - Maternity Satisfaction withtheir Hospital Stay

Developmental or Time Series Research Design - Monthly Peer Counseling and theJuvenile Delinquency

Experimental Research Quasi Experimental Research Design - Water with Fluorideand Dental Health

Types of research designs you can use for yourdissertation

Listed below is the whole range of research designs that you could use for your dissertation.Historical Research Design - The purpose is to collect, verify, synthesize evidence to

establish facts that defend or refute your hypothesis. It uses primary sources, secondary

sources, and lots of qualitative data sources such as logs, diaries, official records, reports,etc. The limitation is that the sources must be both authentic and valid.

Case and Field Research Design - Also called ethnographicresearch, it uses directobservation to give a complete snapshot of a case that is being studied. It is useful whennot much is known about a phenomenon. Uses few subjects.

Descriptive or Survey Research Design - It attempts to describe and explain conditionsof the present by using many subjects and questionnaires to fully describe a

phenomenon. Survey research design /survey methodology is one of the mostpopular for dissertation research.There are many advantages.

Correlational or Prospective Research Design - It attempts to explore relationships tomake predictions. It uses one set of subjects with two or more variables for each.

Causal Comparative or Ex Post Facto Research Design - This research design attemptsto explore cause and affect relationships where causes already exist and cannot bemanipulated. It uses what already exists and looks backward to explain why.

Developmental or Time Series Research Design - Data are collected at certain points in

time going forward. There is an emphasis on time patterns and longitudinal growth orchange.


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Experimental Research Design - This design is most appropriate in controlled settings

such as laboratories. The design assumes random assignmentof subjects and random

assignment to groups (E and C). It attempts to explore cause and affect relationships wherecauses can be manipulated to produce different kinds of effects. Because of the requirement

of random assignment, this design can be difficult to execute in the real world (nonlaboratory) setting.

Quasi Experimental Research Design - This research design approximates the

experimental design but does not have a control group. There is more error possible in theresults.

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