12_SPF_1

12_SPF_1 - Split Plot Factorial Design (SPF-pq) (Ch.12,...

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Split Plot Factorial Design (SPF- p q ) • 2 treatment factors (usually fixed effects) n blocks Æ The set up is similar to RBF- pq . • What are the differences between SPF- p . q and RBF- pq ? – One of the factors is a between-block effect (or between- subject effect, specifically for a repeated measure design). – The researcher is maily interested in • The main effect of within-blocks effect . • The interaction effects of the within-blocks effect and the between-blocks effects. (Ch.12, Kirk) (notation) p is the number of levels for the between-subject factor. q is the number of levels for the within-subject factor. (example - Kirk, p.516) • Dependent measure … vigilant performance • Factor A … the mode of signal presentation Æ a 1 = auditory signal, a 2 = visual signal ( j = 1, 2) • Factor B … four successive hours of monitoring periods Æ b 1 = 1st hour, b 2 = 2nd hour, b 3 = 3rd hour, b 4 = 4th hour. ( k = 1, 2, 3, 4) b 1 b 2 b 3 b 4m e a n s 1 3 4 7 7 5.25 s 2 6 5 8 8 6.75 s 3 3 4 7 9 5.75 s 4 3368 5 s 51 2 04 . 5 s 6 2 3 6 10 5.25 s 7 2459 5 s 82 3 61 15 . 5 a 1 a 2 b 1 b 2 b 3 b 4 mean a 1 3.75 4 7 8 5.69 a 21 . 7 53 5 . 05 . 0 6 mean 2.75 3.50 6.25 9.00 ( ABS summary Table) ( AB summary table) The entry is Y ijk The entry is jk Y
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Estimated Marginal Means of MEASURE_1 HOURS 4 3 2 1 Estimated Marginal Means 12 10 8 6 4 2 0 SIGNAL 1.00 2.00 Estimated Marginal Means of MEASURE_1 SIGNAL 2.00 1.00 12 10 8 6 4 2 0 HOURS 1 2 3 4 (model) () () () i j k j ij k j k k Y =µ+α +π +β + αβ + βπ Where µ … grand mean α j … effect the j th level of factor A π i ( j ) … effect of i th block within factor A (error term for A ) β k … effect of the k th level of factor B ( αβ ) jk AB interaction effect ( βπ ) ki ( j ) B x Block effect within factor A (error term for B and A x B )
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(Sum of squares and Degrees of freedom) (ANOVA table) SS df A = 3.125 p -1 ±= ±1 BL = 9.375 p ( n -1)±= ±6 B = 194.5 q ±3 AB = 19.375 ( p -1)( q -1) B x BL = 9.125 p ( n q -1)±=±18 Sourse SS df MS F p-value Between Blocks A 3.125 1 3.125 2 0.207 BL 9.375 6 1.562 Within Blocks B 194.5 3 64.833 127.88 p < .001 AB 19.375 3 6.458 12.74 p < .001 BxBL 9.125 18 0.507 (See Kirk, p.517 for E ( MS ) formulas) (SPSS Analysis) • Use the repeated measure procedure (GLM Æ
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12_SPF_1 - Split Plot Factorial Design (SPF-pq) (Ch.12,...

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