/* 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; /* set up the data for the univariate repeated measures ANOVA */ DATA UNIDATA; SET PROYDATA; ARRAY A(4) AGE8--AGE14; SUBJECT + 1; DO TIME = 1 TO 4; DENTAL = A(TIME); OUTPUT; END; DROP AGE8--AGE14; RUN; /* NOTE THAT THE MODEL WITHOUT THE GROUP BY TIME INTERACTION IS NOT */ /* POSSIBLE IN THE MULTIVARIATE APPROACH */ TITLE2 'Univariate Repeated Measures Analysis - MODEL WITHOUT GRP*TIME'; PROC GLM; CLASS GROUP TIME SUBJECT; MODEL DENTAL = GROUP SUBJECT(GROUP) TIME; TEST H=GROUP E=SUBJECT(GROUP); CONTRAST 'Linear' TIME -3 -1 1 3 ; CONTRAST 'Quad' TIME 1 -1 -1 1 ; CONTRAST 'Cubic' TIME -1 3 -3 1 ; RUN; Pothoff & Roy Data - Dental Measurements in Boys & Girls 1 Univariate Repeated Measures Analysis - MODEL WITHOUT GRP*TIME 16:06 Monday, January 11, 1999 General Linear Models Procedure Class Level Information Class Levels Values GROUP 2 1 2 TIME 4 1 2 3 4 SUBJECT 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Number of observations in data set = 108 Pothoff & Roy Data - Dental Measurements in Boys & Girls 2 Univariate Repeated Measures Analysis - MODEL WITHOUT GRP*TIME 16:06 Monday, January 11, 1999 General Linear Models Procedure Dependent Variable: DENTAL Sum of Mean Source DF Squares Square F Value Pr > F Model 29 755.57175926 26.05419860 12.54 0.0001 Error 78 162.12037037 2.07846629 Corrected Total 107 917.69212963 R-Square C.V. Root MSE DENTAL Mean 0.823339 6.001248 1.4416887 24.023148 Source DF Type I SS Mean Square F Value Pr > F GROUP 1 140.46485690 140.46485690 67.58 0.0001 SUBJECT(GROUP) 25 377.91477273 15.11659091 7.27 0.0001 TIME 3 237.19212963 79.06404321 38.04 0.0001 Source DF Type III SS Mean Square F Value Pr > F GROUP 1 140.46485690 140.46485690 67.58 0.0001 SUBJECT(GROUP) 25 377.91477273 15.11659091 7.27 0.0001 TIME 3 237.19212963 79.06404321 38.04 0.0001 Contrast DF Contrast SS Mean Square F Value Pr > F Linear 1 235.35601852 235.35601852 113.24 0.0001 Quad 1 1.44675926 1.44675926 0.70 0.4067 Cubic 1 0.38935185 0.38935185 0.19 0.6663 Tests of Hypotheses using the Type III MS for SUBJECT(GROUP) as an error term Source DF Type III SS Mean Square F Value Pr > F GROUP 1 140.46485690 140.46485690 9.29 0.0054