1. CHI-SQUARE TESTS

2. One-Way Chi-Square Test (c2) • Also called Chi-Square “Goodness of Fit” test • Used when dependent variable is counts within categories • Dependent variable has two or more mutually exclusive categories • Compares the “counts” sample (frequencies) to those expected under the null hypothesis • Not a very powerful test

3. Example Question: Which power would you rather have: flight, invisibility, or x-ray vision? Is this difference significant, or is just due to chance?

4. Example Step 1:Write the hypotheses HO: Pfly = Pinvisible = Pxray = 1/3 HA: Not all Powers are equal

5. Example Step 2: Write the observed frequencies, and also the frequencies that would be expected under the null hypothesis N = 42

6. Example Step 3: Calculate the Chi-squared value

7. Example Step 4: Compare to critical value of c2 c2 = 2.286 d.f. = 2 c2crit = 5.991 Retain null hypothesis – There is no significant difference between groups

8. Review Steps: 1) State hypotheses 2) Write observed and expected frequencies 3) Get c2 by summing up relative squared deviations 4) Use Table to get critical c2 and reject or fail to reject null hypothesis

9. Points of interest about c2 • c2 cannot be negative • c2 will be zero only if each observed frequency exactly equals the expected frequency • The larger the discrepancies, the larger the value of c2 • The greater the number of groups, the larger the value of c2

10. Two-factor Chi-Square Test (c2) • Used to test whether two variables are independent or related • Compares the observed frequencies to the frequencies expected if the variables were independent • Called a chi-squared test of independence • Fundamentally testing “do these variables interact”?

11. Example A 1999 poll sampled people’s opinions concerning the use of the death penalty for murder when given the option of life in prison instead. 800 people were polled, and the number of men and women supporting each penalty were tabulated. Are these two variables (gender, penalty preference) independent?

12. Example • H0: Distribution of female preferences matches distribution of male preferences • HA: Female preferences do not match male preferences

13. Example We need to look at the marginal totals to get our expected frequencies

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16. Review Steps: 1) State hypotheses 2) Get expected frequencies3) Get c2 by summing up relative squared deviations 4) Use table to get critical c2 and reject or fail to reject null hypothesis

17. SPSS Chi-Square Tests

18. Chi-Square Test One-way: From the menus choose: Analyze Nonparametric Tests Legacy Dialogs Chi-Square • Select one or more test variables. Each variable produces a separate test • Click Options for descriptive statistics, quartiles, and control of the treatment of missing data

19. Example – One-way • Recall example where people were asked what super power they would rather have: • Enter numerical data, in one column • Either: • enter 42 rows of coded data • OR enter the 3 counts, then go to Data and Weight Cases

20. Chi-Square Test • For the expected values, choose either All Categories Equal (default), or select specific Values

21. Chi-Square Test Two-way: From the menus choose: Analyze Descriptive Statistics Crosstabs • Select a RowVariableand a Column Variable • Choose Chi-Square under Statistics • Tick Display clustered bar charts to get graph

22. Example – Two-way Is there an interaction between flower colour and pollination?

23. Example – Two-way Do you get the same results?