PSYCH 210 Lecture 20 Outline of Last Lecture I. Between-Subjects ANOVAa. Criteriab. Examplei. Fobsii. Hypothesis Testing StepsOutline of Current Lecture I. Finish between-subjects ANOVAa. Hypothesis testingb. Post-hocc. AssumptionsII. New Test: Within-subjects (or repeated-measures) ANOVAa. Why do we need a new test?Current LectureI. SPSS assignment hintsa. Create one single dataset (rather than separate one for each question)b. Save!II. Between-Subjects Hypothesis Testinga. Continue Examplei. Step 3: ‘Omnibus F’ (overall ANOVA)ii. Step 4: Reject H01. If we reject null, what does that mean for ANOVA results?a. Ex) Experimenter Prediction:b. Disease Images>Narrative Danger>Autism Correction>Disease Riski. All we know is that there are significant differences between means SOMEWHERE (but we don’t know what, exactly)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.ii. We need to do a post-hoc test to determine which means are differentIII. Post-hoc test for ANOVAa. Tukey testi. Compares all possible pairs of means to determine whether each pair is significantly differentii. See handout!1. Tukey critical = qt√MS Error/na. For qt use table i. df for denominator F = df for MS withinb. MS error = denominator of F ratioc. n = sampe size for each group 2. Tukey crit = 3.96√11.09/6 = 5.38a. Minimum difference between means that must be met, or exceeded, in order for a particular mean difference to reach significanceb. How are these results interpreted or reported?i. Look back at original hypothesis1. DI > ND > AC > DR2. Compare to Rank order of Meansa. Is general pattern the same? (Not considering significance?)iii. Step 5: Conclusion1. Look at the results form the pairwise comparisons and list which comparisons are significanta. DR is significantly lower than DIb. AC is significantly lower than DI2. Report results in APA Style (more formal, used in research paper)a. State result of overall ANOVA, including F-statementi. Template: say that there were significant differences in the DV according to levels of the IVii. Ex) The ANOVA found significant differences in the rating of how likely parents would give the MMR vaccine to a future child according to the type of informational intervention they received.iii. Template: F (df num.,df denom.) = Fobs, p ___ .1. If significant, p < significance level2. If insignificant, p > significance level3. If value from SPSS, p=output.a. If SPSS says ‘.000’ then p<0.001iv. Ex) F (3,20) = 4.69, p<0.05.b. State result of Tukey test, including means for all conditions, and the ‘significance status’ for all pairwise comparisonsi. See handout for complete example1. Means of all groups (not mean differences)a. Use rank ordering to help ‘flow’3. Recap for Writing Conclusion:a. Include results of omnibus (overall) F - ANOVAb. Include results of post-hoc testc. Describe pattern of MeansIV. Assumptions for between-Subjects ANOVAa. Interval or ratio datab. Independent observationsc. Normal distributiond. Homogeneity of varianceV. Within-Subjects ANOVAa. Why do we need a new test?i. Criteria1. Between-Subjects ANOVAa. More than 2 Tx groupsb. Different Participants in each group2. Within-Subjects ANOVAa. More than 2 Tx groupsb. SAME Participants in each groupii. Review pieces of variance for between-subjects ANOVA1. Partitioning Variancea. Total Variance made up of Between-Groups Variance (Why people in different groups get different scores?) and Within-Groups Variance (Why ppl in same group get different scores?)b. Between-Groups Causesi. Tx effectii. Individual differencesiii. Errorc. Within-Groups Variance Causesi. Individual differencesii. Error2. F = MS Between/MS withiniii. How do the pieces of variance change for within-subjects ANOVA?1. (Differences in) Causes for Variance:a. Individual differences between groups disappears!i. They are the same people now!b. Individual differences within groups still exist but can be measured and mathematically removed2. Within-Subjects a. F=MS Between/MS Errori. Denominator Smaller!1. Relatively speaking, should make F increase2. Larger Fs more likely to be significanta. More