Chi Square Test Dealing with categorical dependant variable

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

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

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

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

Chi-Square test for goodness of fit Observed Frequencies 30 Expected Frequencies Difference Normalize

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

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

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

Chi-Square test for independence When we have tow or more sets of categorical data (IV,DV both categorical) Male Female NoneObama McCain FOFO

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

Chi-Square test for independence Male Female NoneObama McCain FOFO Male Female NoneObama McCain 12%52%36%100% FEFE

Chi-Square test for independence In case of independence: 12%52%36% 12%52%36% Male Female NoneObama McCain 12%52%36%100% FEFE   Finaly: Male Female NoneObama McCain FEFE

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

Chi-Square test for independence Now we can calculate the chi square value : FEFE FOFO

Chi-Square test for independence Fixed Male Female NoneObama McCain FEFE

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

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

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

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

Likelihood ratio test: an alternative FEFE FOFO Follows a Chi-square distribution with df of (R-1)(C-1)

Chi Square test with rank ordered data Rank order your data for the two variables Get the correlation of the two variables: Spearman r Calculate chi Square as follows: Anxiety Level S A G