1. Chi Square Test Dealing with categorical dependant variable

2. So Far: Continuous DV Categorical DV Categorical IV Continuous IV T-test ANOVA Correlation Regression Categorical IV CHI Square

3. Pearson Chi-Square: Frequencies No mean and SD  2 statistics No assumption of normality Non-parametric test

4. Chi-Square test for goodness of fit 5030 10 Observed Frequencies -Is the frequency of balls with different colors equal in our bag? 25% Expected Frequencies

5. Chi-Square test for goodness of fit 5030 10 Observed Frequencies 25% Expected Frequencies 120 Total  = 30 Expected Frequencies H0

6. Chi-Square test for goodness of fit 5030 10 Observed Frequencies 30 Expected Frequencies Difference Normalize

7. Chi-Square test for goodness of fit 25% ? 100 Total Fixed = 25%

8. Chi-Square test for goodness of fit Critical value = 7.81 26.6  2 (3,n=120) = 26.66, p< 0.001

9. Chi-Square test for Goodness of fit Chi-Square test for goodness of fit is like one sample t-test You can test your sample against any possible expected values 25% 10% 70% H0

10. Chi-Square test for independence When we have tow or more sets of categorical data (IV,DV both categorical) 105035 156040 Male Female NoneObama McCain 95 115 2511075 210 FOFO

11. Chi-Square test for independence Also called contingency table analysis H0: There is no relation between gender and voting preference (like correlation) OR H0: There is no difference between the voting preference of males and females (like t-test) The logic is the same as the goodness of fit test: Comparing observed freq and Expected freq if the two variables were independent

12. Chi-Square test for independence 105035 156040 Male Female NoneObama McCain 95 115 2511075 210 FOFO Male Female NoneObama McCain 12%52%36%100% FEFE

13. Chi-Square test for independence In case of independence: 12%52%36% 12%52%36% Male Female NoneObama McCain 12%52%36%100% FEFE 95 115   Finaly: 11.449.434.2 13.859.841.4 Male Female NoneObama McCain FEFE

14. Chi-Square test for independence Anotehr way: Male Female NoneObama McCain 95 25 210 FEFE 95 x 25 210

15. Chi-Square test for independence Now we can calculate the chi square value : 11.449.434.2 13.859.841.4 FEFE 105035 156040 FOFO

16. Chi-Square test for independence 11.449.4Fixed Male Female NoneObama McCain 95 115 2511075 210 FEFE

17. Chi-Square test for independence  2 (2, n=210) = 0.35, p= 0.83 There is no significant effect of gender on vote preference Or We cannot reject the null hypothesis that gender and vote preference are independent

18. Effect size in Chi square For a 2 x 2 table -> Phi Coefficient For larger tables -> Cramer’s V coeffiecient Correlation between two categorical variables Df* is the smallest of C-1, R-1 Phi of 0.1 small, 0.3 medium, 0.5 large

19. Assumptions of Chi Square Independence of observations each subject in only one category Size of expected frequencies: be cautious with small cell frequencies No assumption of Normality: Nonparametric test

20. Likelihood ratio test: an alternative Instead of using Chi-Square, when dealing with categorical data we can calculate log likelihood ratio: A ration of observed and expected frequencies

21. Likelihood ratio test: an alternative 11.449.434.2 13.859.841.4 FEFE 105035 156040 FOFO Follows a Chi-square distribution with df of (R-1)(C-1)

22. Chi Square test with rank ordered data 105035 156040 Rank order your data for the two variables Get the correlation of the two variables: Spearman r Calculate chi Square as follows: 1 2 123 Anxiety Level 111 232 322 421 511 621 712 S A G