PSYCH 210 Lecture 21 Outline of Last 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?Outline of Current Lecture I. Within-Subjects ANOVAa. Calculations for F observedb. Hypothesis testing stepsCurrent LectureII. Within-Subjects ANOVAa. Why do we need a new test?i. Between-Subjects: F=MS Between/MS Withinii. Within-Subjects: F= MS Between/MS Error1. MS Error= MS Within-Groups Variance without individual differencesa. Size of denominator is decreasing for within-Ssb. Relative to a between-Ss ANOVA, within Ss is thus more powerfuli. (Same Relationship as Independent vs. Related-Samples t-test)ii. Doesn’t work for all experimental set-upsb. Calculations for F observedi. See handoutii. Ex) Counterconditioning of phobias (systematic desensitization)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.1. Use of classical conditioning2. See template for sample data3. CER: Conditioned Emotional Responseiii. Independent Variable: Time of Measurement1. Common for Within-Subjects Design2. Note: ANOVA can measure any # of groups3. n = number of participants total and N = total number of observationsa. Compare to Between-Subjects: n = Number of Participants per conditions, N = total number of participantsc. Hypothesis testing stepsi. Calculate Step 3 of Hypothesis Test first (Fobs)1. Find:a. SSb. dfc. MS2. Five pieces of varianceVarianceBetween-Groups Within-GroupIndv. Diffs Error3. Fobs= MS between/MS error4. SStotal = Σx2-G2/N = 3495 – 2952/32 = 775.475. SSwithin= Σ SS for each level = 157.88 + 60 + 90 + 132 = 439.886. SSbtwn= ΣT2/n – G2/N = 1152/8 + 762/8 + 482/8 + 562/8 – 2952/32 = 335.597. SSindv diffs= ΣP2/k – G2/N = 342/4 + 352/4 + … + 582/4 – 2952/32 = 245.22a. No short-hand way to do this; a lot of work!8. SSerror= SSwithin – SSindv diffs = 439.88 – 245.22 = 194.66a. Accounts for variability we can’t attribute to any given source (“Leftover variability)9. dftotal= N – 1 = 32 – 1 = 3110. dfbtwn= k – 1 = 4 – 1 = 311. dfwithin= N – k = 32 – 4 = 2812. dfindv diffs= n – 1 = 8 – 1 = 713. dferror= (N – k) – (n – 1) = N – k – n + 1 = 32 – 4 – 8 + 1 = 2114. MSbtwn= SSbtwn/dfbtwn = 335.59/3 = 111.8615. MSerror= SSerror/dferror = 194.66/2116. Fobs= MSbtwn/MSerror = 111.86/9.27ii. Lay Out Results of Step 3 (Fobs) in an ANOVA Source TableSource SS df MS FobsBetween 333.5 3 111.86 12.07Within 439.88 28 Indv. Diffs 245.22 7 Error 194.66 21 9.27Total 775.47 31d. Return to Hypothesis Testing Stepsi. Hypotheses1. H0: μ1 = μ2 = μ3 = μ4 2. H1: Not H0ii. Fcrit (dfbtwn, dferror) = (3, 21) = 3.071. Note: Go to next-lower option on table even if it is not as close as the higher option (like t, not z)iii. Fobs = 12.07iv. Reject H0; 12.07 > 3.071. We only know there are differences between means somewhere, but the pattern could be completely opposite of our hypothesis2. Sample Hypothesis: Baseline>Day 7>Day 14>Day
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