SAS PROCs and Output for Fuel Economy Experiment


DATA MPG;
    INPUT VEHICLE $ MPG @@;
CARDS;
M 23.8  M 24.7  M 25.1  M 24.7  M 24.5  M 24.8  M 25.0  M 25.0
O 18.6  O 18.9  O 19.2  O 19.2  O 19.3  O 19.7  O 19.7  O 19.8
P 23.9  P 23.3  P 24.1  P 23.3  P 24.0  P 24.7  P 25.0  P 25.3
V 40.1  V 40.1  V 40.5  V 40.4  V 40.9  V 41.8  V 42.0  V 43.0
PROC ANOVA;
    CLASS VEHICLE;
    MODEL MPG = VEHICLE;
    MEANS VEHICLE;
    MEANS VEHICLE/LSD BON;
RUN;

The $ after VEHICLE in the INPUT statement indicates to SAS that the data for VEHICLE will be letters not numbers. PROC ANOVA performs an analysis of variance. The CLASS statement is used to identify the grouping (or classification) variable. The MODEL statement is of the form RESPONSE = PREDICTOR. The MEANS statement asks SAS to compute means and standard deviation for each level of VEHICLE. The /LSD BON, at the end of the MEANS statement performs multiple comparisons of means using Fisher's Least Significant Difference and the BONferroni method.
                       Analysis of Variance Procedure
                          Class Level Information

                         Class    Levels    Values
                         VEHICLE       4    M O P V

                  Number of observations in data set = 32

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

Model                    3     2166.46000     722.15333   1434.06     0.0001

Error                   28       14.10000       0.50357

Corrected Total         31     2180.56000

                  R-Square           C.V.      Root MSE             MPG Mean

                  0.993534       2.596991       0.70963              27.3250

Source                  DF       Anova SS   Mean Square   F Value     Pr > F

VEHICLE                  3     2166.46000     722.15333   1434.06     0.0001

          Level of          ----------------MPG---------------
          VEHICLE      N          Mean                 SD

          M            8      24.7000000            0.41403934
          O            8      19.3000000            0.42088342
          P            8      24.2000000            0.74258237
          V            8      41.1000000            1.05559733



                      T tests (LSD) for variable: MPG

        NOTE: This test controls the type I comparisonwise error rate not
              the experimentwise error rate.

                     Alpha= 0.05  df= 28  MSE= 0.503571
                         Critical Value of T= 2.05
                    Least Significant Difference= 0.7268

        Means with the same letter are not significantly different.

                T Grouping              Mean      N  VEHICLE

                         A           41.1000      8  V

                         B           24.7000      8  M
                         B
                         B           24.2000      8  P

                         C           19.3000      8  O


                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= 28  MSE= 0.503571
                         Critical Value of T= 2.84
                   Minimum Significant Difference= 1.0073

        Means with the same letter are not significantly different.

               Bon Grouping              Mean      N  VEHICLE

                          A           41.1000      8  V

                          B           24.7000      8  M
                          B
                          B           24.2000      8  P

                          C           19.3000      8  O