Design and Analysis, Fourth Edition, by Keppel and Wickens Chapter 5: Analysis of Trend | SAS Textbook Examples

Data from Chapter 5 from Table 5.1, page 90

data table5_1;
input time score;
datalines;
0 4
0 6
0 10
0 9
0 11
20 18
20 13
20 15
20 11
20 13
40 24
40 19
40 21
40 16
40 15
60 16
60 17
60 13 
60 23
60 21
;
run;

Table 5.1 page 90. One-way analysis of variance

proc glm data = table5_1;
class time;
model score = time/ ss3;
run; quit;

The GLM Procedure

      Class Level Information
Class         Levels    Values
time               4    0 20 40 60

Number of observations    20

Dependent Variable: score
                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        3     373.7500000     124.5833333      11.07    0.0004
Error                       16     180.0000000      11.2500000
Corrected Total             19     553.7500000

R-Square     Coeff Var      Root MSE    score Mean
0.674944      22.73967      3.354102      14.75000

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
time                         3     373.7500000     124.5833333      11.07    0.0004

Evaluating Linear, Quadratic and Cubic trend in a one-way design, page 92-100

proc glm data = table5_1;
class time;
model score = time/ ss3;
contrast 'linear'    time -3 -1  1 3;
contrast 'quadratic' time  1 -1 -1 1;
contrast 'cubic'     time -1  3 -3 1;
run; quit;

The GLM Procedure

      Class Level Information
Class         Levels    Values
time               4    0 20 40 60

Number of observations    20

Dependent Variable: score
                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        3     373.7500000     124.5833333      11.07    0.0004
Error                       16     180.0000000      11.2500000
Corrected Total             19     553.7500000

R-Square     Coeff Var      Root MSE    score Mean
0.674944      22.73967      3.354102      14.75000

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
time                         3     373.7500000     124.5833333      11.07    0.0004

Contrast                    DF     Contrast SS     Mean Square    F Value    Pr > F
linear                       1     306.2500000     306.2500000      27.22    <.0001
quadratic                    1      61.2500000      61.2500000       5.44    0.0330
cubic                        1       6.2500000       6.2500000       0.56    0.4669