/* 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; PROC FORMAT; VALUE GROUP 1 = 'Boys' 2 = 'Girls'; PROC MEANS; PROC SORT; BY GROUP; PROC MEANS; BY GROUP; FORMAT GROUP GROUP. ; /* 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; TITLE2 'Univariate Repeated Measures Analysis'; PROC GLM; CLASS GROUP TIME SUBJECT; MODEL DENTAL = GROUP SUBJECT(GROUP) TIME 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 ; CONTRAST 'GrpLinear' GROUP*TIME -3 -1 1 3 3 1 -1 -3 ; CONTRAST 'GrpQuad' GROUP*TIME 1 -1 -1 1 -1 1 1 -1 ; CONTRAST 'GrpCubic' GROUP*TIME -1 3 -3 1 1 -3 3 -1 ; RUN; /* set up the data for plotting the group means across time */ PROC SUMMARY NWAY DATA=PROYDATA; CLASS GROUP; VAR AGE8--AGE14; OUTPUT OUT=NEW MEAN=MDENT1-MDENT4; DATA PLOT; SET NEW; ARRAY MDENT(4) MDENT1-MDENT4; DO TIME = 1 TO 4; MDENTAL = MDENT(TIME); OUTPUT; END; DROP MDENT1-MDENT4; PROC PLOT; PLOT MDENTAL*TIME=GROUP; FORMAT GROUP GROUP.; RUN; Pothoff & Roy Data - Dental Measurements in Boys & Girls 1 16:06 Monday, January 11, 1999 Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------- GROUP 27 1.4074074 0.5007117 1.0000000 2.0000000 ID 27 7.4814815 4.3444958 1.0000000 16.0000000 AGE8 27 22.1851852 2.4343225 16.5000000 27.5000000 AGE10 27 23.1666667 2.1572775 19.0000000 28.0000000 AGE12 27 24.6481481 2.8175781 19.0000000 31.0000000 AGE14 27 26.0925926 2.7666873 19.5000000 31.5000000 -------------------------------------------------------------------- Pothoff & Roy Data - Dental Measurements in Boys & Girls 2 16:06 Monday, January 11, 1999 GROUP=Boys Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------- ID 16 8.5000000 4.7609523 1.0000000 16.0000000 AGE8 16 22.8750000 2.4528895 17.0000000 27.5000000 AGE10 16 23.8125000 2.1360009 20.5000000 28.0000000 AGE12 16 25.7187500 2.6518468 22.5000000 31.0000000 AGE14 16 27.4687500 2.0854156 25.0000000 31.5000000 -------------------------------------------------------------------- GROUP=Girls Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------- ID 11 6.0000000 3.3166248 1.0000000 11.0000000 AGE8 11 21.1818182 2.1245320 16.5000000 24.5000000 AGE10 11 22.2272727 1.9021519 19.0000000 25.0000000 AGE12 11 23.0909091 2.3645103 19.0000000 28.0000000 AGE14 11 24.0909091 2.4373980 19.5000000 28.0000000 -------------------------------------------------------------------- Pothoff & Roy Data - Dental Measurements in Boys & Girls 3 Univariate Repeated Measures Analysis 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 4 Univariate Repeated Measures Analysis 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 32 769.56428872 24.04888402 12.18 0.0001 Error 75 148.12784091 1.97503788 Corrected Total 107 917.69212963 R-Square C.V. Root MSE DENTAL Mean 0.838587 5.850026 1.4053604 24.023148 Source DF Type I SS Mean Square F Value Pr > F GROUP 1 140.46485690 140.46485690 71.12 0.0001 SUBJECT(GROUP) 25 377.91477273 15.11659091 7.65 0.0001 TIME 3 237.19212963 79.06404321 40.03 0.0001 GROUP*TIME 3 13.99252946 4.66417649 2.36 0.0781 Source DF Type III SS Mean Square F Value Pr > F GROUP 1 140.46485690 140.46485690 71.12 0.0001 SUBJECT(GROUP) 25 377.91477273 15.11659091 7.65 0.0001 TIME 3 209.43697391 69.81232464 35.35 0.0001 GROUP*TIME 3 13.99252946 4.66417649 2.36 0.0781 Contrast DF Contrast SS Mean Square F Value Pr > F Linear 1 208.26600379 208.26600379 105.45 0.0001 Quad 1 0.95880682 0.95880682 0.49 0.4881 Cubic 1 0.21216330 0.21216330 0.11 0.7440 GrpLinear 1 12.11415194 12.11415194 6.13 0.0155 GrpQuad 1 1.19954756 1.19954756 0.61 0.4382 GrpCubic 1 0.67882997 0.67882997 0.34 0.5595 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 Pothoff & Roy Data - Dental Measurements in Boys & Girls 5 Univariate Repeated Measures Analysis 16:06 Monday, January 11, 1999 Plot of MDENTAL*TIME. Symbol is value of GROUP. MDENTAL ‚ 28 ˆ ‚ ‚ ‚ ‚ B ‚ ‚ 27 ˆ ‚ ‚ ‚ ‚ ‚ ‚ 26 ˆ ‚ ‚ B ‚ ‚ ‚ ‚ 25 ˆ ‚ ‚ ‚ ‚ ‚ ‚ G 24 ˆ ‚ B ‚ ‚ ‚ ‚ ‚ G 23 ˆ ‚ B ‚ ‚ ‚ ‚ G ‚ 22 ˆ ‚ ‚ ‚ ‚ ‚ ‚ G 21 ˆ ‚ Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ 1 2 3 4 TIME