1. Sociology 601 Class 29: December 10, 2009 REVIEW Homework 10 Review –Chart reviewing which tests when –5 steps in hypothesis testing –Chi-Square (maybe work out a sample) –Measures of association (e.g., gamma, Pearson correlation) –Regression assumptions esp. Heteroscedasticity –Sum of Squares Total and Sum of Squares Error –the formulas from the second half –Interpreting quadratic regression equations –Interpreting coefficients for dummy variables –Interaction effects and STATA outputs 1

2. Chapter 6: Significance Tests for Single Sample  or  sample sizebest test meanlarge z-test for Y bar -  0 proportionlarge z-test for  hat -  1 meansmall t-test for Y bar -  0 proportionsmallFisher’s exact test 2

3. Comparing scores for two groups  or  sample sizesample schemebest test meanlargeindependent z-test for  2 -  1 proportionlargeindependent z-test for  2 -  1 meansmallindependent t-test for  2 -  1 proportionsmallindependentFisher’s exact test meanlargedependentz-test for D proportionlargedependentMcNemar test meansmalldependentt-test for D proportionsmalldependentBinomial test 3

4. Formal steps in a significance test Class 6, slide 4+: 1.) List assumptions 2.) State a hypothesis (or two) 3.) Calculate a test statistic 4.) Look up a p - value 5.) State a formal conclusion 4

5. Chi-squared Test Test statistic: –  2 =  ((f o – f e ) 2 / f e ); df = (r-1)*(c-1) –where f o is the observed count in each cell –and where f e is the expected count for each cell. Assumptions: –two categorical variables (for this course) –random sample or stratified random sample –fe  5 for all cells Hypothesis: Ho: the two variables are statistically independent. Example: GSS 1996: married/not married X in lf or not for women 25-54. 5

6. Measuring ordinal associations with gamma Class 13, Slide 18 Gamma (γ): A measure for concordant and discordant patterns. gamma = (C –D) / (C+D), where C = number of concordant pairs. D = number of discordant pairs. If gamma is between 0 and +1, the ordinal variables are positively associated. If gamma is between 0 and –1, the ordinal variables are negatively associated. The magnitude of gamma indicates the strength of the association. If gamma = 0, the variables may still be statistically dependent because Chi-squared could still be large. However, the categories may not be dependent in an ordinal sequence. 6