/* Analysis of Pothoff & Roy Data This study was conducted in 16 boys and 11 girls, who at ages 8, 10, 12, and 14 had their distance (mm) from the center of the pituitary gland to the pteryomaxillary fissure measured. Changes in pituitary-pteryomaxillary distances during growth is important in orthodontal therapy. The goals of the study were to describe the distance in boys & girls as simple functions of age, and then to compare the functions for boys & girls. */ OPTIONS NOCENTER; TITLE1 'Pothoff & Roy Data - Dental Measurements in Boys & Girls'; DATA PROYDATA; INPUT GROUP ID AGE8 AGE10 AGE12 AGE14 @@; CARDS; 1 1 26.0 25.0 29.0 31.0 1 2 21.5 22.5 23.0 26.5 1 3 23.0 22.5 24.0 27.5 1 4 25.5 27.5 26.5 27.0 1 5 20.0 23.5 22.5 26.0 1 6 24.5 25.5 27.0 28.5 1 7 22.0 22.0 24.5 26.5 1 8 24.0 21.5 24.5 25.5 1 9 23.0 20.5 31.0 26.0 1 10 27.5 28.0 31.0 31.5 1 11 23.0 23.0 23.5 25.0 1 12 21.5 23.5 24.0 28.0 1 13 17.0 24.5 26.0 29.5 1 14 22.5 25.5 25.5 26.0 1 15 23.0 24.5 26.0 30.0 1 16 22.0 21.5 23.5 25.0 2 1 21.0 20.0 21.5 23.0 2 2 21.0 21.5 24.0 25.5 2 3 20.5 24.0 24.5 26.0 2 4 23.5 24.5 25.0 26.5 2 5 21.5 23.0 22.5 23.5 2 6 20.0 21.0 21.0 22.5 2 7 21.5 22.5 23.0 25.0 2 8 23.0 23.0 23.5 24.0 2 9 20.0 21.0 22.0 21.5 2 10 16.5 19.0 19.0 19.5 2 11 24.5 25.0 28.0 28.0 RUN; /* perform Multivariate Repeated Measures Analysis to test for sphericity */ TITLE2 'Multivariate & Univariate Repeated Measures Analysis'; PROC GLM; CLASS GROUP; MODEL AGE8--AGE14 = GROUP / NOUNI ; REPEATED TIME POLYNOMIAL / SUMMARY PRINTM PRINTE; RUN; Pothoff & Roy Data - Dental Measurements in Boys & Girls Multivariate & Univariate Repeated Measures Analysis The GLM Procedure Class Level Information Class Levels Values GROUP 2 1 2 Number of observations 27 Repeated Measures Level Information Dependent Variable AGE8 AGE10 AGE12 AGE14 Level of TIME 1 2 3 4 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 25 AGE8 AGE10 AGE12 AGE14 AGE8 1.000000 0.570699 0.661320 0.521583 0.0023 0.0002 0.0063 AGE10 0.570699 1.000000 0.563167 0.726216 0.0023 0.0027 <.0001 AGE12 0.661320 0.563167 1.000000 0.728098 0.0002 0.0027 <.0001 AGE14 0.521583 0.726216 0.728098 1.000000 0.0063 <.0001 <.0001 TIME_N represents the nth degree polynomial contrast for TIME M Matrix Describing Transformed Variables AGE8 AGE10 AGE12 AGE14 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 59.1673 -11.2242 4.5278 TIME_2 -11.2242 26.0412 -1.2819 TIME_3 4.5278 -1.2819 62.9193 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 25 TIME_1 TIME_2 TIME_3 TIME_1 1.000000 -0.285945 0.074209 0.1567 0.7186 TIME_2 -0.285945 1.000000 -0.031669 0.1567 0.8779 TIME_3 0.074209 -0.031669 1.000000 0.7186 0.8779 Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 5 0.7353334 7.2929515 0.1997 Orthogonal Components 5 0.7353334 7.2929515 0.1997 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=10.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.19479424 31.69 3 23 <.0001 Pillai's Trace 0.80520576 31.69 3 23 <.0001 Hotelling-Lawley Trace 4.13362211 31.69 3 23 <.0001 Roy's Greatest Root 4.13362211 31.69 3 23 <.0001 Manova Test Criteria and Exact F Statistics for the Hypothesis of no TIME*GROUP Effect H = Type III SSCP Matrix for TIME*GROUP E = Error SSCP Matrix S=1 M=0.5 N=10.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.73988739 2.70 3 23 0.0696 Pillai's Trace 0.26011261 2.70 3 23 0.0696 Hotelling-Lawley Trace 0.35155702 2.70 3 23 0.0696 Roy's Greatest Root 0.35155702 2.70 3 23 0.0696 Tests of Hypotheses for Between Subjects Effects Source DF Type III SS Mean Square F Value Pr > F GROUP 1 140.4648569 140.4648569 9.29 0.0054 Error 25 377.9147727 15.1165909 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 3 209.4369739 69.8123246 35.35 <.0001 <.0001 <.0001 TIME*GROUP 3 13.9925295 4.6641765 2.36 0.0781 0.0878 0.0781 Error(TIME) 75 148.1278409 1.9750379 Greenhouse-Geisser Epsilon 0.8672 Huynh-Feldt Epsilon 1.0156 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 1 208.2660038 208.2660038 88.00 <.0001 GROUP 1 12.1141519 12.1141519 5.12 0.0326 Error 25 59.1673295 2.3666932 Contrast Variable: TIME_2 Source DF Type III SS Mean Square F Value Pr > F Mean 1 0.95880682 0.95880682 0.92 0.3465 GROUP 1 1.19954756 1.19954756 1.15 0.2935 Error 25 26.04119318 1.04164773 Contrast Variable: TIME_3 Source DF Type III SS Mean Square F Value Pr > F Mean 1 0.21216330 0.21216330 0.08 0.7739 GROUP 1 0.67882997 0.67882997 0.27 0.6081 Error 25 62.91931818 2.51677273