Repeated Measures One-Way ANOVA Practice Problems SET 3 Another special education teacher argues autistic children exhibit substantial individual differences. She decides to use the same group of autistic children to evaluate verbal behavior across the four different types of rewards. She randomly picks six autistic children from another classroom and examines the ability of each reward to promote verbal behavior in each child. The number of verbal episodes for each reward across each child are below. Reward Reward Reward Reward Person Type 1 Type 2 Type 3 Type 4 Totals (P) 3 6 9 12 30 5 7 1o 13 35 6 9 15 15 45 2 7 12 18 39 1 11 11 15 38 2 6 1o 13 31 T=19; T=46; T=67; T=86; M=3.17; M=7.67; M=11.17; M=14.33; 55:18.83 55:19.33 55:22.83 55:23.33 N = 24 G = 218 ZXZ = 2478 H CH n \fStep 2: Locate the Critical Region for the F-ratio df between = k- 1 = df within = N- k = df subjects= n- 1 = Sum to df df error = (k-1) (n-1) =_ within df total = N- 1 = The F-ratio will have df = at p=.05. Critical F =Step 3a: Compute the Test Statistic It is best to compute all the Sum of Squares (between, subjects error, and total) and check that SSsubjects + SSerror = SSwithin and SSbetween + SSsubjects + SSerror = SSTotal SS Between =[ (T2) -G2/N = SS Within = [ SS = SS, + SS2+ SS3 = SS Subjects = [ (P2/k) -G2/N = SS Error = SSwithin - SSsubjects = SS Total =[X2 - (G2/N) = _ CHECK: DOES SSs + SSE = SSw and SSB + SSw = SST If yes, go to step 3b. If no, repeat step 3a.Step 3b: Compute the Test Statistic (continued) . MS between = SS between/ df between = . MS error = SS error/ df = error . F = MSbetween / MS errorFill in the source table below Repeated- Measures One-way ANOVA able below ures One-way ANOVA Sources of Sum of df Mean F Variation Square Square Between groups Within groups Subjects Error TotalStep 4 Make Decision and State Conclusion Critical F (Fcrit) = Obtained F (Fobt) = Which hypothesis is supported by the data?? Ho H What is the conclusion of the study? (State in words). a Step 5 Calculate Effect Size n2 (Eta squared) for Repeated-Measures One-way ANOVA . n2 = SSBetween / (SS Between + SS Error)= Interpreting n2 .01 -.09 = small effect 09 - .25 = medium effect > .25 = large effect . The effect size is: small medium large