Making Comparisons

1. 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”?

2. Methods of Making Comparisons

3. 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

4. Cross-tabulation • If the null hypothesis is true, the independent variable has no effect on the dependent variable • The expected frequency for each cell

5. 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)

6. 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

7. 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

8. 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.