/* Analysis of Vocabulary Data - Bock p. 454 "Data are drawn from test results on file in the Records Office of the Laboratory School of the University of Chicago. They consist of scores, obtained from a cohort of pupils at the eigth through eleventh gade level on alternative forms of the vocabulary section of the Cooperative Reading Tests." There are 64 students in all, 36 male, 28 female (ordered). */ OPTIONS NOCENTER FORMCHAR = "|----|+|---+="; TITLE1 'Trend in Vocabulary across Grades'; DATA VOCABDAT; infile 'c:\data\bio513\bockvoc.sas' firstobs=17 obs=80; INPUT SUBJECT VOCAB1 VOCAB2 VOCAB3 VOCAB4 ; TITLE2 'Multivariate Repeated Measures Analysis'; PROC GLM; MODEL VOCAB1--VOCAB4= / NOUNI SOLUTION; REPEATED TIME POLYNOMIAL / SUMMARY PRINTM PRINTE; RUN; Trend in Vocabulary across Grades Multivariate Repeated Measures Analysis The GLM Procedure Number of observations 64 Repeated Measures Level Information Dependent Variable VOCAB1 VOCAB2 VOCAB3 VOCAB4 Level of TIME 1 2 3 4 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 63 VOCAB1 VOCAB2 VOCAB3 VOCAB4 VOCAB1 1.000000 0.810077 0.866728 0.784510 <.0001 <.0001 <.0001 VOCAB2 0.810077 1.000000 0.784636 0.757102 <.0001 <.0001 <.0001 VOCAB3 0.866728 0.784636 1.000000 0.811462 <.0001 <.0001 <.0001 VOCAB4 0.784510 0.757102 0.811462 1.000000 <.0001 <.0001 <.0001 TIME_N represents the nth degree polynomial contrast for TIME M Matrix Describing Transformed Variables VOCAB1 VOCAB2 VOCAB3 VOCAB4 TIME_1 -.6708203932 -.2236067977 0.2236067977 0.6708203932 TIME_2 0.5000000000 -.5000000000 -.5000000000 0.5000000000 TIME_3 -.2236067977 0.6708203932 -.6708203932 0.2236067977 E = Error SSCP Matrix TIME_N represents the nth degree polynomial contrast for TIME TIME_1 TIME_2 TIME_3 TIME_1 50.4246 12.0463 -3.3640 TIME_2 12.0463 43.9505 -4.2717 TIME_3 -3.3640 -4.2717 60.5666 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 63 TIME_1 TIME_2 TIME_3 TIME_1 1.000000 0.255888 -0.060873 0.0413 0.6328 TIME_2 0.255888 1.000000 -0.082794 0.0413 0.5154 TIME_3 -0.060873 -0.082794 1.000000 0.6328 0.5154 Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 5 0.90274 6.3154607 0.2767 Orthogonal Components 5 0.90274 6.3154607 0.2767 Manova Test Criteria and Exact F Statistics for the Hypothesis of no TIME Effect H = Type III SSCP Matrix for TIME E = Error SSCP Matrix S=1 M=0.5 N=29.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.17411785 96.45 3 61 <.0001 Pillai's Trace 0.82588215 96.45 3 61 <.0001 Hotelling-Lawley Trace 4.74323660 96.45 3 61 <.0001 Roy's Greatest Root 4.74323660 96.45 3 61 <.0001 Univariate Tests of Hypotheses for Within Subject Effects Adj Pr > F Source DF Type III SS Mean Square F Value Pr > F G - G H - F TIME 3 194.3384156 64.7794719 79.02 <.0001 <.0001 <.0001 Error(TIME) 189 154.9417344 0.8197975 Greenhouse-Geisser Epsilon 0.9423 Huynh-Feldt Epsilon 0.9912 Analysis of Variance of Contrast Variables TIME_N represents the nth degree polynomial contrast for TIME Contrast Variable: TIME_1 Source DF Type III SS Mean Square F Value Pr > F Mean 1 177.5931003 177.5931003 221.88 <.0001 Error 63 50.4246097 0.8003906 Contrast Variable: TIME_2 Source DF Type III SS Mean Square F Value Pr > F Mean 1 13.57922500 13.57922500 19.46 <.0001 Error 63 43.95052500 0.69762738 Contrast Variable: TIME_3 Source DF Type III SS Mean Square F Value Pr > F Mean 1 3.16609031 3.16609031 3.29 0.0743 Error 63 60.56659969 0.96137460