Output from manova3.sas	Source 0 Graphs

                      Two Way Manova Example (Morrison)                      1

        Plot of Y2*Y1=DRUG.                       Plot of Y2*Y1=SEX.

  15 +                     C               15 +                     M
     |                                        |
     |                                        |
     |                                        |
  14 +                                     14 +
     |                                        |
     |                                        |
     |                                        |
  13 +          B                          13 +          F
     |                                        |
     |                                        |
     |                                        |
  12 +         B      CC                   12 +         M      FM
     |                                        |
     |                                        |
     |                                        |
  11 +              C                      11 +              M
     |                                        |
     |                                        |
     |                                        |
W 10 +       AA   C                      W 10 +       FF   M
e    |                                   e    |
e    |                                   e    |
k    |                                   k    |
2  9 +      B  A    C                    2  9 +      F  M    F
     |                                        |
     |                                        |
     |                                        |
   8 +      B       C                       8 +      M       F
     |                                        |
     |                                        |
     |                                        |
   7 +       BBA                            7 +       MFF
     |                                        |
     |                                        |
     |                                        |
   6 +     AAA                              6 +     MFM
     |                                        |
     |                                        |
     |                                        |
   5 +          C                           5 +          F
     |                                        |
     |                                        |
     |                                        |
   4 +     A                                4 +     M
     -+---------+---------+---------+         -+---------+---------+---------+
      0        10        20        30          0        10        20        30

                   Week1                                    Week1

NOTE: 2 obs hidden.                      NOTE: 2 obs hidden.

                      Two Way Manova Example (Morrison)                      2

                       General Linear Models Procedure
                           Class Level Information

                          Class    Levels    Values

                          SEX           2    F M

                          DRUG          3    A B C


                   Number of observations in data set = 24

                            E = Error SS&CP Matrix

                                      Y1                Y2

                    Y1              94.5              76.5
                    Y2              76.5               114

                      Two Way Manova Example (Morrison)                      3

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

  Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|

                        DF = 18           Y1        Y2

                        Y1          1.000000  0.737043

                                      0.0001    0.0003

                        Y2          0.737043  1.000000

                                      0.0003    0.0001

                      Two Way Manova Example (Morrison)                      4

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

                      H = Type III SS&CP Matrix for SEX

                                      Y1                Y2

                    Y1      0.6666666667      0.6666666667
                    Y2      0.6666666667      0.6666666667

          Characteristic Roots and Vectors of: E Inverse * H, where
          H = Type III SS&CP Matrix for SEX   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Y1             Y2

            0.00751918    100.00            0.07175780     0.03444374
            0.00000000      0.00           -0.13423121     0.13423121

               Manova Test Criteria and Exact F Statistics for
                   the Hypothesis of no Overall SEX Effect
          H = Type III SS&CP Matrix for SEX   E = Error SS&CP Matrix

                             S=1    M=0    N=7.5

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.99253694     0.0639         2        17  0.9383
 Pillai's Trace             0.00746306     0.0639         2        17  0.9383
 Hotelling-Lawley Trace     0.00751918     0.0639         2        17  0.9383
 Roy's Greatest Root        0.00751918     0.0639         2        17  0.9383

                      H = Type III SS&CP Matrix for DRUG

                                      Y1                Y2

                    Y1               301              97.5
                    Y2              97.5      36.333333333

          Characteristic Roots and Vectors of: E Inverse * H, where
         H = Type III SS&CP Matrix for DRUG   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Y1             Y2

            4.57602675     98.63            0.14784109    -0.07693601

                      Two Way Manova Example (Morrison)                      5

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

          Characteristic Roots and Vectors of: E Inverse * H, where
         H = Type III SS&CP Matrix for DRUG   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Y1             Y2

            0.06350991      1.37           -0.03619684     0.11526161

                Manova Test Criteria and F Approximations for
                   the Hypothesis of no Overall DRUG Effect
         H = Type III SS&CP Matrix for DRUG   E = Error SS&CP Matrix

                            S=2    M=-0.5    N=7.5

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.16862952    12.1991         4        34  0.0001
 Pillai's Trace             0.88037810     7.0769         4        36  0.0003
 Hotelling-Lawley Trace     4.63953666    18.5581         4        32  0.0001
 Roy's Greatest Root        4.57602675    41.1842         2        18  0.0001

         NOTE: F Statistic for Roy's Greatest Root is an upper bound.
                NOTE: F Statistic for Wilks' Lambda is exact.

                    H = Type III SS&CP Matrix for SEX*DRUG

                                      Y1                Y2

                    Y1      14.333333333      21.333333333
                    Y2      21.333333333      32.333333333

          Characteristic Roots and Vectors of: E Inverse * H, where
       H = Type III SS&CP Matrix for SEX*DRUG   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Y1             Y2

            0.28372273     97.94           -0.00284433     0.09555092
            0.00596889      2.06           -0.15218117     0.10037136

                      Two Way Manova Example (Morrison)                      6

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

                Manova Test Criteria and F Approximations for
                 the Hypothesis of no Overall SEX*DRUG Effect
       H = Type III SS&CP Matrix for SEX*DRUG   E = Error SS&CP Matrix

                            S=2    M=-0.5    N=7.5

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.77436234     1.1593         4        34  0.3459
 Pillai's Trace             0.22694905     1.1520         4        36  0.3481
 Hotelling-Lawley Trace     0.28969161     1.1588         4        32  0.3473
 Roy's Greatest Root        0.28372273     2.5535         2        18  0.1056

         NOTE: F Statistic for Roy's Greatest Root is an upper bound.
                NOTE: F Statistic for Wilks' Lambda is exact.

                   H = Contrast SS&CP Matrix for drug C:A,B

                                      Y1                Y2

                    Y1               300                95
                    Y2                95      30.083333333

          Characteristic Roots and Vectors of: E Inverse * H, where
      H = Contrast SS&CP Matrix for drug C:A,B   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Y1             Y2

            4.57407407    100.00            0.14775192    -0.07665325
            0.00000000      0.00           -0.03655912     0.11544985

               Manova Test Criteria and Exact F Statistics for
                the Hypothesis of no Overall drug C:A,B Effect
      H = Contrast SS&CP Matrix for drug C:A,B   E = Error SS&CP Matrix

                             S=1    M=0    N=7.5

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.17940199    38.8796         2        17  0.0001
 Pillai's Trace             0.82059801    38.8796         2        17  0.0001
 Hotelling-Lawley Trace     4.57407407    38.8796         2        17  0.0001
 Roy's Greatest Root        4.57407407    38.8796         2        17  0.0001

                      Two Way Manova Example (Morrison)                      7

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

                    H = Contrast SS&CP Matrix for drug A:B

                                      Y1                Y2

                    Y1                 1               2.5
                    Y2               2.5              6.25

          Characteristic Roots and Vectors of: E Inverse * H, where
       H = Contrast SS&CP Matrix for drug A:B   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Y1             Y2

            0.06546258    100.00           -0.06135792     0.12688579
            0.00000000      0.00            0.13929252    -0.05571701

               Manova Test Criteria and Exact F Statistics for
                 the Hypothesis of no Overall drug A:B Effect
       H = Contrast SS&CP Matrix for drug A:B   E = Error SS&CP Matrix

                             S=1    M=0    N=7.5

 Statistic                     Value          F      Num DF    Den DF  Pr > F

 Wilks' Lambda              0.93855947     0.5564         2        17  0.5833
 Pillai's Trace             0.06144053     0.5564         2        17  0.5833
 Hotelling-Lawley Trace     0.06546258     0.5564         2        17  0.5833
 Roy's Greatest Root        0.06546258     0.5564         2        17  0.5833

                      Two Way Manova Example (Morrison)                      8

                       General Linear Models Procedure

            Tukey's Studentized Range (HSD) Test for variable: Y1

         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= 18  MSE= 5.25
                  Critical Value of Studentized Range= 3.609
                    Minimum Significant Difference= 2.9239

         Means with the same letter are not significantly different.

                Tukey Grouping              Mean      N  DRUG

                             A            14.750      8  C

                             B             7.500      8  B
                             B
                             B             7.000      8  A

                      Two Way Manova Example (Morrison)                      9

                       General Linear Models Procedure

            Tukey's Studentized Range (HSD) Test for variable: Y2

         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= 18  MSE= 6.333333
                  Critical Value of Studentized Range= 3.609
                    Minimum Significant Difference= 3.2114

         Means with the same letter are not significantly different.

                Tukey Grouping              Mean      N  DRUG

                             A            10.250      8  C
                             A
                             A             8.500      8  B
                             A
                             A             7.250      8  A