Repeated Measures ANOVA

Repeated Measures ANOVA ______________________________________ 1) Distinguish between repeated measures and between subjects ANOVA. 2) Discuss the factors that contribute to variance in a RM ANOVA design. • Treatment • Chance • Subject effects 3) Describe the process for calculating a RM ANOVA. • MStotal, MSb • MSw = MSbs + MSe Repeated Measures ANOVA __________________________________________ A repeated measures design is one in which the same subjects participate in more than one condition (treatment). That is, we measure the same subjects repeatedly. Sometimes called Within Subjects design • contrasted with Between Subjects Design Similar to Paired vs. Independent t-tests. • Key Issue: Independence of our samples RM ANOVA: Dwarf Example __________________________________________ Dwarf Industries is worried that it will fail to meet Wall Street expectations for the 3rd quarter this year. Below are the sales (in 1000s) of its best five sales people. Do these data suggest that their productivity has changed over the past three quarters? Subject Bashful Sneezy Grumpy Dopey Sleepy 1st Qrt 6 5 6 5 3 2nd Qrt 5 5 4 4 2 3rd Qrt 5 2 4 3 1 Comparing RM-ANOVA with BS-ANOVA: Sources of variance ______________________________________________ Dwarf Industries is worried that it will not meet Wall Street expectations for the 3rd quarter this year. Below are the sales (in 1000s) of its five best sales people. Do these data suggest that productivity has changed over the past three quarters? Subject Bashful Sneezy Grumpy Dopey Sleepy 1st Qrt 6 5 6 5 3 5.00 2nd Qrt 5 5 4 4 2 4.00 3rd Qrt 5 2 4 3 1 3.00 Avg. 5.33 4.00 4.67 4.00 2.00 4.00 What are the sources of variance in BS-ANOVA? • Treatment • Error What are the sources of variance in RM-ANOVA? • Treatment • Subject differences • Chance variation Comparing RM-ANOVA with BS-ANOVA: Calculations ________________________________________ All s equal SAME Alternative Hypothesis At least 2 differ SAME SSTOTAL (x2) – (G)2/N SAME [(T2/n)] - (G2/N) SAME [(x2) - (T2/n)] SAME [(P2/p)] - G2/N NEW SSWI - SSBS NEW Null Hypothesis SSBETWEEN TREATMENTS SSWITHIN SSBETWEEN SS SSERROR Where: 1. P = sum of each observation across conditions for a given subject 2. p = # of conditions in the experiment Calculating SSTOTAL and SSBT ______________________________________________ 1st Q x x2 6 36 5 25 6 36 5 25 3 9 2nd Q x x2 5 25 5 25 4 16 4 16 2 4 3rd Q x x2 5 25 2 4 4 16 3 9 1 1 P 16 12 14 12 6 25 20 15 60 Bashful Sneezy Grumpy Dopey Sleepy 131 86 SSTOTAL = = = = = (x2) - G2/N (131+86+55) - (602/15) 272 - (3600/15) 272 - 240 32 SSBT = = = = = = [(T2/n)] - G2/N (252/5 + 202/5 + 152/5) - 240 (625/5 + 400/5 + 225/5) - 240 (125 + 80 + 45) - 240 250 - 240 10 55 Calculating SSWI, SSBS, & SSE ______________________________________________ SSWI = = = = [(x2) - T2/n] (131-125) + (86-80) + (55-45) 6 + 6 + 10 22 SSBS = = [(P2/p)] - G2/N (162/3) + (122/3) + (142/3) + (122/3) + (62/3) - 240 (256/3) + (144/3) + (196/3) + (144/3) + (36/3) - 240 (85.33 + 48 + 65.33 + 48 + 12) - 240 258.67 - 240 18.67 = = = = SSE = SSWI = 22 = 3.33 SSBS - 18.67 Degrees of Freedom ______________________________________________ dfTOTAL N-1 SAME dfBT p-1 SAME dfWI N-p SAME n-1 (N-p)-(n-1) NEW NEW dfBS dfE Putting it all together: RM ANOVA table ______________________________________________ Source Between Within Subject Error Total SS 10.00 22.00 18.67 3.33 32.00 df MS 2 12 5.00 4 8 14 0.42 F 12.00 RM ANOVA: Gone Fishin’ example ________________________________________ Doc, Happy and Snow White don’t work because the other boys are such good providers. They decide to go fishing and rather than just relax and enjoy the day, they decide to test a new fly that Doc bought – the Ronco Riggler – against two standard types of bait: worms, and artificial lures. The table below contains the number of fish caught on three recent fishing excursions in which the three anglers rotated bait types. Do these data suggest any differences in the effectiveness of the different lures? Doc Happy SnowWhite Worms A. Lure Riggler 4 5 3 2 3 1 6 4 5 Calculating SSTOTAL and SSBT ______________________________________________ Worms x x2 4 5 3 Doc Happy SnowWhite A. Lure x x2 2 3 1 SSTOTAL = (x2) - G2/N SSBT = [(T2/n)] - G2/N Riggler x x2 6 4 5 P Calculating SSWI, SSBS, & SSE ______________________________________________ SSWI = [(x2) - T2/n] SSBS = [(P2/p)] - G2/N SSE = SSWI - SSBS Gone Fishin’: RM ANOVA table ______________________________________________ Source Between Within Subject Error Total df SS MS F ______________________________________________ Introduction: How does trauma affect memory? • Flashbulb memories • PTSD • Repression Compare memories of different types • Tromp, et al. (1995): between subjects design • Byrne, et al. (2001): within subjects design…why? Method: • TSS events vs. very negative vs. positive • MCQ, PTSD, BDI ______________________________________________ Take-home message: • Less sensory detail for traumatic events: • But no difference in emotional detail • Inconsistent with flashbulb memory hypothesis