1. Lab Chapter 14: Analysis of Variance 1

2. Lab Topics: One-way ANOVA – the F ratio – post hoc multiple comparisons Two-way ANOVA – main effects – interaction effects

3. One-Way ANOVA To test hypotheses about the mean on one variable for three or more groups Sample hypotheses: – “There are differences in the average income of sociology, social work, and criminology majors.” – “There are differences in the recidivism rate of persons convicted of burglary, larceny, forgery, and robbery.”

4. One-Way ANOVA (cont.) The hypotheses: – research hypothesis: at least one group has a different mean – null hypothesis: all groups have the same mean inferential statistic: F ratio – non-directional hypotheses – degrees of freedom:

5. One-Way ANOVA (cont.) Post hoc multiple comparison tests Tukey, Tukey’s b, and Bonferonni most common tests – One-way ANOVA can only tell you if F ratio is significant but not which groups are significantly different form one another – Post hoc tests can identify pairs of groups that significantly differ – If F ratio for model not significant, post hoc test not needed

6. One-Way ANOVA Example Were there significant differences by region in the average willingness to allow legal abortion among 1980 GSS young adults? DV: Willingness to allow abortion (I-R level) IV: Region (nominal level – 4 groups) 1.State the research and the null hypothesis. research hypothesis: There were regional differences in average willingness to allow legal abortion. null hypothesis: There were no regional differences in average willingness to allow legal abortion.

7. One-Way ANOVA Example (cont.) 2.Are the sample results consistent with the null hypothesis or the research hypothesis? Analyze | Compare Means | One-Way ANOVA (Use Post-Hoc to request Multiple Comparison Test)

8. Requesting Sample Means and Post Hoc Multiple Comparisons

9. Sample Means for Each Region

10. 3.What is the probability of getting the sample results if the null hypothesis is true? 4.Reject or do not reject null hypothesis. p =.000 < α =.05, Reject null hypothesis, there is a significant difference. Which groups are different? 5.See post-hoc multiple test (next slide) One-Way ANOVA Example (cont.)

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12. Two-Way ANOVA Tests hypotheses about the mean on one dependent variable for groups created by two or more independent variables (or factors) Nominal or ordinal level variables entered as “fixed factors” Tests for significant… – interaction effects – main effects

13. More on Two-way ANOVA “Fixed Factors” are at the nominal or ordinal level of measurement and have a limited number of discrete categories Note: Two-way ANOVA can also employ IV’s at the I-R level as covariates – In this case the process is known as ANCOVA (Analysis of Covariance) and the I-R variable is entered into the dialogue box as a covariate. – However, this is a much more complex analysis and we will be using multiple regression for models that have both nominal/ordinal and I-R level variables

14. Two-Way ANOVA Example questions: – Was there a significant interaction effect of marital status and gender on hours worked among 1980 GSS young adults? – If the interaction wasn’t significant, did marital status and gender have significant individual net effects? Analyze | General Linear Model | Univariate (Use Plots and Post-Hoc to request Subgroup Means and a Plot of Subgroup Means)

15. Producing a Two-Way ANOVA

16. Requesting Subgroup Means and a Plot of Subgroup Means 16

17. Significance Tests 1.overall model: significant 2.interaction effect: significant 3.main effect: not needed Answering Questions with Statistics Chapter 14 1 2

18. Subgroup Means and Plot 18

19. More on Two-Way ANOVA If interaction is significant, then interpret it along with means and plot. – This indicates that the IV’s are not acting separately from one another in their effect on the DV. Main effect becomes irrelevant. If interaction is not significant, interpret main effects. – This indicates that IV effects on DV are independent of one another and that there is no significant interaction of the two IV’s in the population. 19

20. Example: Effects of Married and Sex on Number of Children (DV) 1.overall model: significant 2.interaction effect: not significant 3.main effects – MARRIED: significant – SEX: significant 1 2 3