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
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

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
Male
Female
Total
Pro- ? 20
Anti- 80 50
100

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.

9. 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

10. 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