5:2 LAB RESULTS - FOLLOW-UP ANALYSES FOR FACTORIAL
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1 5:2 LAB RESULTS - FOLLOW-UP ANALYSES FOR FACTORIAL T1. n F and n C for main effects = = 6 (i.e., 2 observations in each of 3 cells for other factor) Den t = SQRT[3.333x(1/6+1/6)] = Den q = SQRT[3.333x(1/6)] =.7453 t 12 = ( )/1.054 =.949 DNR H0 q 12 = ( )/.7453 = 1.34 =.949xSQRT(2) Stretch for Critical Value of q: LSD (2), TUKEY (3), SNK (2 for 12 & 23, 3 for 13) C1 - not justified ps >.05 for main effects; no difference close to significant. /POST = font(lsd SNK TUKEY BONF). Source Type III Sum of df Mean Square F Sig. Squares Corrected Model (a) Intercept color font color * font Total Corrected Total a R Squared =.706 (Adjusted R Squared =.444) Post Hoc Tests font (I) (J) Mean Difference Std. Sig. 95% Confidence Interval font font (I-J) Error Lower Bound Upper Bound LSD Tukey HSD Bonferroni Homogeneous Subsets font N Subset 1 Student-Newman Keuls(a,b,c) Sig..195 Tukey HSD(a,b,c) Sig..195 c Alpha =.050.
2 *C1 alternative (not done in class) - EMMEANS for LSD (default) or BONF. /EMMEANS = TABLE(font) COMPARE ADJ(LSD). Estimated Marginal Means (I) (J) Mean Difference Std. Sig.(a) 95% Confidence Interval for font font (I-J) Error Difference(a) Lower Bound Upper Bound T2 - planned contrasts for font. Font M f L SS (6x3 2 )/6 = (6x1 2 )/2 = 3.0 Sum = 12.0 = SS Font Normalized coefficients: divided by SQRT(6) x = 9.0 Helmert contrasts: c j = 2; L = difference between means = (6+7)/ (6x1.5 2 )/1.5 = 9.0 Calculating SS for main effects contrast using Cell Means Color Font M ab L SS Contrast = (2x9 2 )/18 OR Font Color M ab L SS Contrast = (2x9 2 )/18 *C2 - planned contrasts for font using GLM; various versions. /CONTRAST (font) = SPECIAL( ). L1 Contrast Estimate = L for above L2 Contrast Estimate Std. Error Sig..368 Contrast
3 *C2 - separate /CONTRAST options to obtain separate summary tables. /CONTRAST (font) = SPECIAL(-2 1 1) /CONTRAST (font) = SPECIAL( 0-1 1). #1 L1 Contrast Estimate #2 L1 Contrast Estimate Std. Error Sig..368 Contrast *C2 - Note Helmert NOT normalized coefficients; c j = 2; p values same. /CONTRAST (font) = HELMERT. Level 1 vs. Contrast Estimate Later Std. Error.913 Level 2 vs. Contrast Estimate Level 3 Std. Error Sig..368 Contrast
4 *C3. MANOVA errors BY color(1 3) font(1 3) /PRINT = SIGN(SINGLEDF) /CONTRAST(font) = SPECIAL( ). WITHIN CELLS color ST Parameter ND Parameter font ST Parameter ND Parameter color BY font ST Parameter ND Parameter RD Parameter TH Parameter R-Squared =.706 Adjusted R-Squared =.444 Estimates for errors --- Individual univariate.9500 confidence intervals color font color BY font MANOVA errors BY color(1 3) font(1 3) /CONTRAST(font) = HELMERT. font MANOVA errors BY color(1 3) font(1 3) /CONTRAST(font) = HELMERT /DESIGN color font(1) font(2) color BY font. FONT(1) FONT(2) COLOR BY FONT /LMATRIX = font color BY font -2/3 1/3 1/3-2/3 1/3 1/3-2/3 1/3 1/3. L1 Contrast Estimate 3.000
5 *T3 - simple effects of font. M fc Font M c M fc -M c SS FwC1 = 52.0 = 2( ) df = 3-1 = 2 Color M fc -M c SS FwC2 = 4.0 = 2( ) df = 3-1 = M fc -M c SS FwC3 = 4.0 = 2( ) df = 3-1 = 2 SS FwC = 60.0 = SS Font + SS FxC *C4 - simple effects of font: MANOVA. MANOVA errors BY color(1 3) font(1 3) /DESIGN color font W color(1) font W color(2) font W color(3). FONT W COLOR(1) FONT W COLOR(2) FONT W COLOR(3) *C5 - simple effects of font: GLM and EMMEANS. /EMMEANS = TABLE(color BY font) COMPARE(font). Estimated Marginal Means Pairwise Comparisons color (I) (J) Mean Difference Std. Sig.(a) 95% Confidence Interval for font font (I-J) Error Difference(a) Lower Bound Upper Bound (*) (*) color Sum of Squares df Mean Square F Sig Contrast Contrast Contrast
6 T4 - partition simple effects of font. C1 C2 C3 F1 F2 F3 F1 F2 F3 F1 F2 F3 M fc L SS f1wc = (2x12 2 )/6 f2wc = (2x-2 2 )/2 f1wc f2wc =52.0=SS FwC1 f1wc f2wc T4 - Helmert Coefficients. f1wc = (2x6 2 )/1.5 *C6 - partition simple effects: MANOVA SINGLEDF. MANOVA errors BY color(1 3) font(1 3) /PRINT = SIGN(SINGLEDF) /CONTR(font) = SPEC( ) /DESIGN color font W color(1) font W color(2) font W color(3). 1ST Parameter ND Parameter FONT W COLOR(1) ST Parameter ND Parameter FONT W COLOR(2) ST Parameter ND Parameter FONT W COLOR(3) ST Parameter ND Parameter COLOR FONT W COLOR(1) FONT W COLOR(2) FONT W COLOR(3) MANOVA errors BY color(1 3) font(1 3) /PRINT = SIGN(SINGLE) /CONTRAST(font) = HELMERT /DESIGN color font W color(1) font W color(2) font W color(3). FONT W COLOR(1)
7 *C7 - partition without SINGLEDF. MANOVA errors BY color(1 3) font(1 3) /CONTR(font) = SPEC( ) /DESIGN color font(1) W color(1) font(2) W color(1) font(1) W color(2) font(2) W color(2) font(1) W color(3) font(2) W color(3). FONT(1) W COLOR(1) FONT(2) W COLOR(1) FONT(1) W COLOR(2) FONT(2) W COLOR(2) FONT(1) W COLOR(3) FONT(2) W COLOR(3) COLOR FONT(1) W COLOR(1) FONT(2) W COLOR(1) FONT(1) W COLOR(2) FONT(2) W COLOR(2) FONT(1) W COLOR(3) FONT(2) W COLOR(3) *C8 - LMATRIX commands: 1 st is simple effect and 2 nd 3 rd main effect (compare to C2). /LMATRIX font color BY font L1 Contrast Estimate Std. Error Sig..004 Contrast /LMATRIX font color BY font -2/3 1/3 1/3-2/3 1/3 1/3-2/3 1/3 1/3. L1 Contrast Estimate /LMATRIX font color BY font L1 Contrast Estimate Std. Error 5.477
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