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Repeated Measures ANOVA. Between Subjects Variance Is Partitioned From the Error Variance Conceptual Approach Using The Source Table. Total Variability. Effect Variability (MS Between). Error Variability (MS Within). The Source Table. Keeps track of all data in complex ANOVA designs
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Repeated Measures ANOVA • Between Subjects Variance Is Partitioned From the Error Variance • Conceptual Approach • Using The Source Table Anthony Greene
Total Variability Effect Variability(MS Between) ErrorVariability(MS Within) The Source Table • Keeps track of all data in complex ANOVA designs • Source of SS, df, and Variance (MS) • Partitioning the SS, df and MS • All variability is attributable toeffect differences or error (all unexplained differences) Anthony Greene
Source Table for 1-Way ANOVA Anthony Greene
Source Table for 1-Way ANOVA Effect Variability Error Variability
Repeated Measures ANOVA Treatment 1 Treatment 2 Treatment 3 Measurement 1 Measurement 2 Measurement 3 M1 M3 M2 Anthony Greene
Repeated Measures ANOVA • Recall the differences between a t-test a tD-test: • The same group is used in the experimental and control group via the before-after design • Thereby individual differences are removed from the error term • Identical concepts to repeated measures ANOVA • Individual Variation is computed and subtracted from the error term Anthony Greene
Total Variability { Stage 1 Effect Variability(MS Between) MS Within { Individual Variability ErrorVariability Stage 2 Partitioning Variability For Repeated Measures ANOVA Anthony Greene
Total Variability { Stage 1 Effect Variability(MS Between) MS Within Numerator of F-ratio { Individual Variability ErrorVariability Stage 2 Denominator of F-ratio Partitioning Variability For Repeated Measures ANOVA
Source Table For Repeated Measures ANOVA Tests of Within-Subjects Effects Source SS df MS F p FACTOR1 30.0 3 10.0 6.3 .005 Error 23.5 15 1.5 Subj. 72.5 5 Within 96.0 20 Total 126.0 23 Source SS df MS F p FACTOR1 30.0 3 10.0 2.1 n.s. Error 23.5 15 Subj. 72.5 5 Within 96.0 20 4.8 Total 126.0 23 Anthony Greene
Source Table For Repeated Measures ANOVA Tests of Within-Subjects Effects Source SS df MS F Sig. FACTOR1 30.0 3 10.0 6.3 .005 Error 23.5 15 1.5 Subj. 72.5 5 Within 96.0 20 Total 126.0 23 Anthony Greene
Source Table For Repeated Measures ANOVA Tests of Within-Subjects Effects Source SS df MS F Sig. FACTOR1 30.0 3 10.0 6.3 .005 Error 23.5 15 1.5 Subj. 72.5 5 Within 96.0 20 Total 126.0 23 Anthony Greene
Source Table For Repeated Measures ANOVA Tests of Within-Subjects Effects Source SS df MS F Sig. FACTOR1 30.0 3 10.0 6.3 .005 Error 23.5 15 1.5 Subj. 72.5 5 Within 96.0 20 Total 126.0 23 Anthony Greene
Source Table For Repeated Measures ANOVA Tests of Within-Subjects Effects Source SS df MS F Sig. FACTOR1 30.0 3 10.0 6.3 .005 Error 23.5 15 1.5 Subj 72.5 5 Within 96.0 20 Total 126.0 23 Tests of Within-Subjects Contrasts Source SS df MS F Sig. Linear 4.8 1 4.8 1.5 .263 Quadratic 24.0 1 24.0 18.4 .008 Cubic 1.2 1 1.2 3.1 .136 Anthony Greene
Total Variability { Stage 1 Effect Variability(MS Between) MS Within { Individual Variability ErrorVariability Stage 2 • New computation: • Compute SS for P and deg freedom • Subtract those from SS w/in and d.f. w/in • This leaves SS error and d.f. error Anthony Greene
Tests of Within-Subjects Effects Source SS df MS F Sig. FACTOR1 30.0 3 Error Subj. STAGE 1 Within 96.0 20 Total 126.0 23 Source SS df MS F Sig. FACTOR1 30.0 3 Error Subj. 72.5 5 STAGE 2 Within 96.0 20 Total 126.0 23 Source SS df MS F Sig. FACTOR1 30.0 3 10.0 6.3 .005 Error 23.5 15 1.5 Subj. 72.5 5 Within 96.0 20 Total 126.0 23 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 11.67 Within 12 Subject 3 3 Residual Total 15 51 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 3 11.67 Within 12 Subject 3 3 Residual Total 15 51 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 3 35 11.67 Within 12 Subject 3 3 Residual Total 15 51 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 3 35 11.67 Within 12 16 Subject 3 3 Residual Total 15 51 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 3 35 11.67 Within 12 16 Subject 3 3 Residual 9 Total 15 51 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 3 35 11.67 Within 12 16 Subject 3 3 Residual 9 13 Total 15 51 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 3 35 11.67 Within 12 16 Subject 3 3 Residual 9 13 1.44 Total 15 51 Anthony Greene
Repeated Measures ANOVA Source d.f. SS MS F Between 3 35 11.67 9.0 Within 12 16 Subject 3 3 Residual 9 13 1.44 Total 15 51 Anthony Greene
Repeated-Measures ANOVA An experimenter wishes to examine whether a certain therapy for Attention Deficit Disorder is effective. Four ADD children, 12 years old, are selected. The dependent measure is a standard test of attention wherein the child hears a narrative and is then asked questions about its content Anthony Greene
Repeated-Measures ANOVA Compute the treatment totals, T, and the grand total, G Anthony Greene
Repeated-Measures ANOVA Count n for each treatment, the total N, and k Anthony Greene
Repeated-Measures ANOVA Compute the treatment means Anthony Greene
Repeated-Measures ANOVA (5-3)2=4 (2-3)2=1 (4-3)2=1 (1-3)2=4 sum Compute the treatment SSs Anthony Greene
Repeated-Measures ANOVA Compute all X2s and sum them Anthony Greene
Repeated-Measures ANOVA Add in Person totals column Anthony Greene
Repeated-Measures ANOVA Compute SSTotal SSTotal= X2 – G2/N SSTotal=62 Anthony Greene
Repeated-Measures ANOVA Compute SSbetween SSbetween= T2/n – G2/N SSbetween=8 Anthony Greene
Repeated-Measures ANOVA Compute SSWithin SSWithin= SSi SSWithin = 54 Anthony Greene
Repeated-Measures ANOVA Compute SSBtw sub SSBtw Sub= P2/k – G2/N SSBtw Sub=22.66 SSerror = SSwithin-SSbtw sub = 54-22.66 = 31.34 Anthony Greene
Repeated-Measures ANOVA Determine d.f.s d.f. Within=N-k d.f. Between=k-1 d.f. Total=N-1 d.f. error = (N-k) – (n-1) Anthony Greene
Repeated-Measures ANOVA Ready to move it to a source table Anthony Greene
Repeated Measures ANOVA Source SS d.f. MS F Between 8 2 4 0.766 Within 54 9 Subject 22.66 3 Error 31.34 6 5.22 Total 62 11 Compare to critical value of F(2,6) = 5.14 Fail to reject (no significant difference) Anthony Greene