Question

Learning Objectives

1. Understand when and how Chi-square testing is used.
2. Become proficient with the Chi-square analysis in SPSS.
3. Gain more experience with customizing statistical calculations in Excel.
4. Perform a basic interpretation of a Chi-Square analysis.

Using Chi Square

Using a statistical test without having a good idea of what it can and cannot do means that you may misuse the test. This also means that you won't have a clear grasp of what your results really mean. We know that there are basically two types of random variables and they yield two types of data: numerical and categorical. Up to this point in class, we've focused mostly on numerical data. A Chi-square (X²) analysis is used to investigate whether distributions of categorical variables differ from one another. We do this by comparing observed frequencies in different categories of one or more independent variables. Then, we compare these observed frequencies with expected frequencies and determine if there is a significant, proportional difference in the frequency counts of the different categories.

About Your Data

A Psychologist is interested in looking at the personality traits of Business majors. She administers the Big Five personality inventory to 258 Business majors at her university. For each participant, their strongest personality trait was determined and tallied in the corresponding category. The results she obtained are reported below. The psychologist has brought you in to analyze her data. You will need to perform a Chi-square test of goodness of fit.

	Open	Conscientious	Extrovert	Agreeable	Neurotic
Participants	41	52	46	61	58

Instructions

In this lab, you will be completing a Chi-square test in both SPSS and Excel. You will interpret your results. You will submit screenshots and your interpretations.

Chi-Square In SPSS

1. Open SPSS.

2. Enter the personality data in SPSS as per the instructions in the video tutorial.
3. Perform a Chi-square, goodness of fit analysis, as per the instructions in the video tutorial.
4. Assess your output from the analysis. You should see three tables: Descriptives, Frequencies, and Test Statistics. By this point in the semester, you should be able to quickly determine whether you will reject or fail to reject the null hypothesis for this study.
5. Take a screenshot showing your output. I'm most interested in seeing the Test Statistics table.
6. Near the end of the SPSS tutorial, you will see Todd offer conclusions that look a lot like the ones we have practiced in other labs. Use these conclusions as a template to write up your own. Please make sure that your conclusions are clear, correct and free of grammatical mistakes.

Chi-Square In Excel

1. Open Microsoft Excel.

2. Open the Chi-Square in Excel video above. Using the personality data listed in the previous section, follow the steps in the video exactly. Perform all of the same steps. This will be more like a computer-assisted walkthrough of Chi-square. The only thing you don't need to worry about is highlighting rows and columns with color, though I would encourage you to do so. If you run into problems, you might try searching YouTube for other videos providing similar tutoring.

3. When you have completed the Excel analysis, check your Chi-square statistic with the one calculated in SPSS. Do they match? They should.
4. Take a Screenshot of your Excel spreadsheet with the completed work. It should look like the one in the Excel video.

Answer 1

Excel output is:

SPSS output is:

The hypothesis being tested is:

H₀: There is no significant, proportional difference in the frequency counts of the different categories.

H_a: There is a significant, proportional difference in the frequency counts of the different categories.

Since the p-value (0.258) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a significant, proportional difference in the frequency counts of the different categories.