Between-Subjects One-Way AN OVA Practice Problems SET 3 A special education teacher was interested in whether different rewards would promote verbal behavior in the autistic children in her class. She split the 24 children into four equal groups and provided a reward to each child after every verbal episode. The type of reward the child received depended on which group the child was in. The number of verbal episodes for each reward type are below. Reward Reward Reward Reward Type 1 Type 2 Type 3 Type 4 3 6 9 12 5 7 1o 13 5 9 15 15 2 7 12 18 1 11 11 15 2 5 1o 13 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 Step 1: State the Hypotheses and Select an Alpha Level H: U1 = U2 = U3 = U4 Hail, * U2 * U3 * U4 a=.05Step 2: Locate the Critical Region for the F-ratio df total = N-1= 24-1 = 23 df between = k - 1 = k-1 = 4-1 =3 df within = N - k = 24 - 4 = 20 The F-ratio will have df = 3_, _20_at p=.05. Critical F = 3.10Step 3a: Compute the Test Statistic It is best to compute all 3 Sum of Squares, (between, within, and total) and check that between and within add to the total SS Total =[X2 - (G2/N) = SS Within [ SS = SS, + SS2 + SS3 + SS4= SS Between =[ (T2) - G2/N = CHECK: DOES SSw + SSB = 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 within = SS within/ df within . F = MSb between / MS within =Fill in the source table below Between-Subjects One-way ANOVA Sources of Sum of df Mean F Variation Square Square Between groups Within groups Total