Transcript Ch. 14 Lab
Lab Chapter 14: Analysis of Variance 1 Lab Topics: • One-way ANOVA – the F ratio – post hoc multiple comparisons • Two-way ANOVA – main effects – interaction effects 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.” 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 one-way ANOVA: df = (K – 1 and N - K) – degrees of freedom: 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 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. 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) Requesting Sample Means and Post Hoc Multiple Comparisons Sample Means for Each Region One-Way ANOVA Example (cont.) 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) duplicate duplicate duplicate duplicate 11 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 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 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) Producing a Two-Way ANOVA Requesting Subgroup Means and a Plot of Subgroup Means 16 Significance Tests 1. overall model: significant 2. interaction effect: significant 3. main effect: not needed 1 2 Answering Questions with Statistics Chapter 14 Subgroup Means and Plot 18 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 Example: 1. overall model: significant Effects of Married 2. interaction effect: not significant and Sex on 3. main effects Number of – MARRIED: significant Children (DV) – SEX: significant 1 3 2