Analysis of Tire Experiment (Latin Square Design)

data tires;
     input truck day brand mpg @@;
cards;
1 1 2 6.63  1 1 1 6.26  1 3 4 7.31  1 4 3 6.57
2 1 4 7.06  2 2 2 6.59  2 3 3 6.64  2 4 1 6.71
3 1 1 6.31  3 2 3 6.73  3 3 2 7.00  3 4 4 7.38
4 1 3 6.55  4 2 4 7.13  4 3 1 6.54  4 4 2 7.11
proc anova;
     class truck day brand;
     model mpg = brand truck day;
     means brand/bon;
run;

                       Analysis of Variance Procedure
                          Class Level Information

                         Class    Levels    Values

                         TRUCK         4    1 2 3 4

                         DAY           4    1 2 3 4

                         BRAND         4    1 2 3 4

                  Number of observations in data set = 16

Dependent Variable: MPG
                                   Sum of          Mean
Source                  DF        Squares        Square   F Value     Pr > F

Model                    9     1.63770000    0.18196667     11.77     0.0036

Error                    6     0.09280000    0.01546667

Corrected Total         15     1.73050000

                  R-Square           C.V.      Root MSE             MPG Mean

                  0.946374       1.833617       0.12437              6.78250

Source                  DF       Anova SS   Mean Square   F Value     Pr > F

BRAND                    3     1.30705000    0.43568333     28.17     0.0006
TRUCK                    3     0.06765000    0.02255000      1.46     0.3170
DAY                      3     0.26300000    0.08766667      5.67     0.0348

                Bonferroni (Dunn) T tests for variable: MPG

        NOTE: This test controls the type I experimentwise error rate, but
              generally has a higher type II error rate than REGWQ.

                     Alpha= 0.05  df= 6  MSE= 0.015467
                         Critical Value of T= 3.86
                   Minimum Significant Difference= 0.3397

        Means with the same letter are not significantly different.

                Bon Grouping              Mean      N  BRAND

                           A           7.22000      4  4

                           B           6.83250      4  2
                           B
                   C       B           6.62250      4  3
                   C
                   C                   6.45500      4  1