F Statistics, NDF=8, DDF=4 for Squared Distance to Known                      

                                                                                                      

                           From                                                                      

                           Known              E             L             M                          

                                                                                                      

                           E                  0       1.27019       2.01770                          

                           L            1.27019             0       2.40692                          

                           M            2.01770       2.40692             0                          

                                                                                                     

                                                                                                      

                       Prob > Mahalanobis Distance for Squared Distance to Known                     

                                                                                                      

                           From                                                                      

                           Known              E             L             M                          

                                                                                                      

                           E             1.0000        0.4354        0.2598                          

                           L             0.4354        1.0000        0.2066                          

                           M             0.2598        0.2066        1.0000                          

                                                                                                     

                        Pairwise Generalized Squared Distances Between Groups                        

                                                                                                     

                                   2         _   _       -1  _   _                                   

                                  D (i|j) = (X - X )' COV   (X - X )                                 

                                              i   j           i   j                                  

                                                                                                      

                                                                                                     

                                Generalized Squared Distance to Known                                

                                                                                                     

                           From                                                                      

                           Known              E             L             M                          

                                                                                                     

                           E                  0      11.17767      19.97527                          

                           L           11.17767             0      23.82850                          

                           M           19.97527      23.82850             0                           

                                            The SAS System          13:03 Friday, December 1, 2006 252

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                     

                                     Univariate Test Statistics                                       

                                                                                                     

                               F Statistics,    Num DF=2,   Den DF=11                                

                                                                                                      

                    Total       Pooled      Between                                                  

                 Standard     Standard     Standard                 R-Square                          

    Variable    Deviation    Deviation    Deviation    R-Square    / (1-RSq)    F Value    Pr > F    

                                                                                                     

    FreqA         20.8159      22.3489       3.8554      0.0246       0.0253       0.14    0.8718    

    FreqB         38.1841      31.4104      29.4623      0.4274       0.7465       4.11    0.0466    

    FreqC         70.1399      61.5959      48.7929      0.3474       0.5324       2.93    0.0956    

    ClustA         1.1563       1.0630       0.7284      0.2849       0.3984       2.19    0.1582    

    ClustB         0.8812       0.9027       0.3482      0.1121       0.1262       0.69    0.5201    

    ClustC         2.3859       2.3631       1.1606      0.1699       0.2047       1.13    0.3591    

    dbhA           2.6707       2.6065       1.3883      0.1940       0.2407       1.32    0.3053    

    dbhC           0.5790       0.5435       0.3447      0.2544       0.3412       1.88    0.1990    

                                                                                                     

                                                                                                     

                                          Average R-Square                                           

                                                                                                     

                                  Unweighted              0.2268454                                   

                                  Weighted by Variance    0.3436799                                  

                                                                                                     

                                                                                                      

                            Multivariate Statistics and F Approximations                             

                                                                                                      

                                         S=2    M=2.5    N=1                                         

                                                                                                     

           Statistic                        Value    F Value    Num DF    Den DF    Pr > F           

                                                                                                     

           Wilks' Lambda               0.04786501       1.79        16         8    0.2051           

           Pillai's Trace              1.54512169       2.12        16        10    0.1147           

           Hotelling-Lawley Trace      7.50335734       1.88        16         4    0.2866           

           Roy's Greatest Root         5.05027910       3.16         8         5    0.1105           

                                                                                                     

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

                            NOTE: F Statistic for Wilks' Lambda is exact.