Repeated Measures ANOVA: Understanding RM Designs in Psychology, Study Guides, Projects, Research of Design

Download Repeated Measures ANOVA: Understanding RM Designs in Psychology and more Study Guides, Projects, Research Design in PDF only on Docsity! 1 Repeated Measures ANOVA Cal State Northridge Ψ320 Andrew Ainsworth PhD 2 Major Topics What are repeated-measures? An example Assumptions Advantages and disadvantages Effect size Psy 320 - Cal State Northridge 3 Repeated Measures? Between-subjects designs – different subjects serve in different treatment levels – (what we already know) Repeated-measures (RM) designs – each subject receives all levels of at least one independent variable – (what we’re learning today) Psy 320 - Cal State Northridge 2 4 Repeated Measures All subjects get all treatments. All subjects receive all levels of the independent variable. Different n’s are unusual and cause problems (i.e. dropout or mortality). Treatments are usually carried out one after the other (in serial). Psy 320 - Cal State Northridge 5 Example: Counseling For PTSD Foa, et al. (1991) – Provided supportive counseling (and other therapies) to victims of rape – Do number of symptoms change with time? • There’s no control group for comparison • Not a test of effectiveness of supportive counseling Psy 320 - Cal State Northridge 6 Example: Counseling For PTSD 9 subjects measured before therapy, after therapy, and 3 months later We are ignoring Foa’s other treatment conditions. Psy 320 - Cal State Northridge 5 13 Deviation Sums of Squares ( ) 2 2 2 2 [__*(____ ____) ] [__*(____ ____) ] [__*(13.222 17.593) ] 562.074 BG j j GMSS n Y Y= − = = − + − + + − = ∑ Psy 320 - Cal State Northridge 14 Deviation Sums of Squares ( ) 2 2 2 2 2 2 2 2 2 [__*(____ ____) ] [__*(____ ____) ] [__*(____ ____) ] [__*(20.333 17.593) ] [__*(21.667 17.593) ] [__*(21.333 17.593) ] [__*(12.333 17.593) ] [__*(19.667 17.593) ] [__*(10.333 Subject i GMSS g Y Y= − = = − + − + + − + − + + − + − + + − + − + + ∑ 217.593) ] 397.852− = Psy 320 - Cal State Northridge 15 Deviation Sums of Squares ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 (___ ____) (___ ____) (___ ____) (26 23.889) (32 23.889) (27 23.889) (21 23.889) (25 23.889) (18 23.889) (15 15.667) (15 15.667) (17 15.667) ( Error i j i GM i j SS Y Y g Y Y Y Y  = − − − =   − = − + − + − + + − + − + − + + − + − + − + + − + − + − + + + ∑ ∑ ∑ L 2 2 2 8 13.222) (15 13.222) (3 13.222) 552.444 552.444 397.852 154.592 − + − + − = = = − = Psy 320 - Cal State Northridge 6 Computational Approach 16 Patient Pre Post Follow-Up Subject Sum 1 21 15 15 51 2 24 15 8 47 3 21 17 22 60 4 26 20 15 61 5 32 17 16 65 6 27 20 17 64 7 21 8 8 37 8 25 19 15 59 9 18 10 3 31 Sum 215 141 119 475 ΣY² 9471 Psy 320 - Cal State Northridge Computational Sums of Squares ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 j bg i Subject j i Error Total A T SS s as S T SS a as A S T SS Y s a as T SS Y as = − = − = − − + = − ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ 17 Computational SS Example 2 2 2 2 2 2 2 2 2 2 2 2 2 ___ ___ 119 ___ _____ _____ __ __(__) __ __ _______ 8356.481 562.075 ___ ___ ___ 61 65 64 37 59 31 8356.481 __ _____ 8356.481 _______ 8356.481 397.852 __ 9471 8918.556 8754.333 bg S Error SS SS SS + + = − = − = = − = + + + + + + + + = − = = − = − = = − − 8356.481 154.592 9471 8356.481 1114.519TSS + = = − = 18Psy 320 - Cal State Northridge 7 Degrees of Freedom 19 1 3 1 2 ( 1) 27 3 24 1 9 1 8 ( 1)*( 1) 8*2 16 1 27 1 26 bg ws s error total df g df g n N g df n df n g df N = − = − = = − = − = − = → = − = − = → = − − = = = − = − = F ro m B G A N O V A Psy 320 - Cal State Northridge 20 Summary Table Fcrit with 2 and 16 degrees of freedom is 3.63 we would reject h0 Source SS df MS F Time 562.074 2 281.037 29.087 WS (from BG design) 552.444 24 Subject 397.852 8 49.731 Error 154.593 16 9.662 Total 1114.519 26 Psy 320 - Cal State Northridge 21 Plot of the Data 0 5 10 15 20 25 30 PreTest PostTest FollowUp R e p o rt e d S y m p to m s Psy 320 - Cal State Northridge