1. Review Memory scores for subjects given three different study sequences: Find the sum of squares between groups, SS treatment A.24 B.25 C.42 D.84 ABC 17128 14109 12114 13 M = 14M = 11M = 7

2. Review Memory scores for subjects given three different study sequences: Find the sum of squares within groups, SS residual A.14 B.30 C.104 D.114 ABC 17128 14109 12114 13 M = 14M = 11M = 7

3. Review Memory scores for subjects given three different study sequences: SS treatment = 84 SS residual = 30 df treatment = 2 df residual = 7 Calculate F, for testing whether the group means are reliably different A.0.8 B.1.25 C.9.8 D.180 ABC 17128 14109 12114 13 M = 14M = 11M = 7

4. Repeated-Measures ANOVA 11/11

5. Repeated-Measures Design Multiple measurements for each subject – Different stimulus types, conditions, times, etc. – All measurements are of the same variable, but in different situations – Generalizes paired-samples design Is there an effect of the treatment? – Variation due to condition, time, stimulus, etc. – Do the means of the measurements vary? Same null hypothesis as simple ANOVA –  1 =  2 = … =  k

6. Repeated-Measures Data Individual differences – Variation from one subject to another – Affects all the scores of any given subject Measurement Subject1234 178738275 2108105113106 384798980 494889892 5121115123117

7. Accounting for Individual Differences Individual differences complicate hypothesis testing – Inflate variability of scores – Don’t affect random variability of treatment means Contribute to all measurements equally Basic idea – Subtract subject mean for each score – Do simple ANOVA on these differences (df residual changes) MeasurementDifference Score Subject1234MsMs 1234 178738275771-45-2 21081051131061080-35-2 384798980831-46-3 494889892931-55 51211151231171192-44-2

8. Partitioning Variability Break total variability into treatment, subjects, and residual error Total variability – Same as before: Variability due to treatment – Same as before: Variability due to individual differences – Same idea as SS treatment – Variability of subject means: Residual variability – Remaining variability – Can calculate directly, but not intuitive

9. Partitioning Variability Measurement Subject1234MsMs 17873827577 2108105113106108 38479898083 49488989293 5121115123117119 MiMi 97921019496

10. Repeated-Measures ANOVA Does treatment explain significant portion of variability? – Don't want to penalize for variability due to individual differences – Removing SS subject reduces SS residual and makes it a fair comparison Hypothesis test for repeated-measures ANOVA: – Same as regular ANOVA, except we first remove SS subject – (SS subject not meaningful with simple ANOVA because each subject is only in one group) SS total

11. Degrees of Freedom df total  nk – 1 df treatment  k – 1 df residual  nk – 1 – (k–1) – (n–1)  nk – n – k + 1. SS total df subject  n – 1

12. Review Coffee drinkers are given arithmetic tests on 3 different days: one after drinking coffee, one after decaf, and one with nothing. Find the sum of squares for individual differences, SS subject A.152 B.558 C.1674 D.2232 Condition SubjectCDNMsMs 179738278 264575960 383758581 494879893 MiMi 80738178

13. Review Coffee drinkers are given arithmetic tests on 3 different days: one after drinking coffee, one after decaf, and one with nothing. SS total = 1860 SS treatment = 152 SS subject = 1674 SS residual = 34 What would SS residual be if these were 12 unrelated subjects? A.34 B.186 C.1708 D.1826 Condition SubjectCDNMsMs 179738278 264575960 383758581 494879893 MiMi 80738178

14. Review Coffee drinkers are given arithmetic tests on 3 different days: one after drinking coffee, one after decaf, and one with nothing. SS total = 1860 SS treatment = 152df treatment = 2 SS subject = 1674df subject = 3 SS residual = 34df residual = 6 Find the F statistic for testing differences across conditions A.0.14 B.13.41 C.98.47 D.111.88 Condition SubjectCDNMsMs 179738278 264575960 383758581 494879893 MiMi 80738178