Making Comparisons All hypothesis testing follows a common logic of comparison Null hypothesis and alternative hypothesis mutually exclusive exhaustive Experimental design and control group “Republicans have higher income than Democrats”?

Methods of Making Comparisons Independent Variable Categorical measures (nominal or ordinal) Continuous measures (interval or ratio) Dependent Variable Cross-Tabulation & (Chapter 7) Chi-square (Chapter 10) Logistic Regression Compare Means & (Chapter 9) Dummy Variables (Chapter 8) Correlation & Linear Regression

Cross-tabulation Relationship between two (or more) variables Joint frequency distribution Contingency table Observations should be independent of each other One person’s response should tell us nothing about another person’s response Mutually exclusive and exhaustive categories

Cross-tabulation If the null hypothesis is true, the independent variable has no effect on the dependent variable The expected frequency for each cell Male Female Total Pro- ? 20 Anti- 80 50 100

Expected Frequency of Each Cell Expected frequency in the ith row and the jth column ……… (Eij) Total counts in the ith row ……… (Ti) Total counts in the jth column ……… (Tj) Total counts in the table ……… (N)

Inferences about Sample Means Hypothesis testing is an inferential process Using limited information to reach a general conclusion Observable evidence from the sample data Unobservable fact about the population Formulate a specific, testable research hypothesis about the population

Null Hypothesis no effect, no difference, no change, no relationship, no pattern, no … any pattern in the sample data is due to random sampling error

Errors in Hypothesis Testing Type I Error A researcher finds evidence for a significant result when, in fact, there is no effect (no relationship) in the population. The researcher has, by chance, selected an extreme sample that appears to show the existence of an effect when there is none. The p-value identifies the probability of a Type I error.

Cross-Tabulation Lambda Cramer’s V gamma Kendall’s tau-b Independent Variable Nominal measures Ordinal measures Dependent Variable Lambda Cramer’s V gamma Kendall’s tau-b Kendall’s tau-c Somer’s d

Measures of Association Symmetrical measures of association e.g. Kendall’s tau-b and tau-c Asymmetrical measures of association e.g. lambda and Somer’s d Directional measures of association e.g. Somer’s d PRE measures of association