Problem in page 443 Freund 8th edition                    1
                                                  15:46 Friday, December 5, 2003

                             OBS    METHOD      X

                               1      l1      0.37
                               2      l1      0.70
                               3      l1      0.75
                               4      l1      0.30
                               5      l1      0.45
                               6      l1      0.16
                               7      l1      0.62
                               8      l1      0.73
                               9      l1      0.33
                              10      l2      0.86
                              11      l2      0.55
                              12      l2      0.80
                              13      l2      0.42
                              14      l2      0.97
                              15      l2      0.84
                              16      l2      0.24
                              17      l2      0.51
                              18      l2      0.92
                              19      l2      0.69
                     Problem in page 443 Freund 8th edition                    2
                                                  15:46 Friday, December 5, 2003

                       N P A R 1 W A Y  P R O C E D U R E

                   Wilcoxon Scores (Rank Sums) for Variable X
                         Classified by Variable METHOD


                           Sum of      Expected       Std Dev          Mean
    METHOD        N        Scores      Under H0      Under H0         Score

    l1            9          69.0          90.0    12.2474487     7.6666667
    l2           10         121.0         100.0    12.2474487    12.1000000


             Wilcoxon 2-Sample Test (Normal Approximation)
             (with Continuity Correction of .5)

             S =  69.0000     Z = -1.67382     Prob > |Z| = 0.0942

             T-Test Approx. Significance = 0.1115

             Kruskal-Wallis Test (Chi-Square Approximation)
             CHISQ =  2.9400     DF =  1     Prob > CHISQ = 0.0864

                  Example 13.5 from page 446 Freund 8th edition                3
                                                  15:46 Friday, December 5, 2003

                              OBS    DIET      X

                                1     d1     16.3
                                2     d1     10.1
                                3     d1     10.7
                                4     d1     13.5
                                5     d1     14.9
                                6     d1     11.8
                                7     d1     14.3
                                8     d1     10.2
                                9     d1     12.0
                               10     d1     14.7
                               11     d1     26.3
                               12     d1     15.1
                               13     d1     14.5
                               14     d1     18.4
                               15     d1     13.2
                               16     d1     14.0
                               17     d2     21.3
                               18     d2     23.8
                               19     d2     15.4
                               20     d2     19.6
                               21     d2     12.0
                               22     d2     13.9
                               23     d2     18.8
                               24     d2     19.2
                               25     d2     15.3
                               26     d2     20.1
                               27     d2     14.8
                               28     d2     18.9
                               29     d2     20.7
                               30     d2     21.1
                               31     d2     15.8
                               32     d2     16.2
                  Example 13.5 from page 446 Freund 8th edition                4
                                                  15:46 Friday, December 5, 2003

                       N P A R 1 W A Y  P R O C E D U R E

                   Wilcoxon Scores (Rank Sums) for Variable X
                          Classified by Variable DIET


                           Sum of      Expected       Std Dev          Mean
    DIET          N        Scores      Under H0      Under H0         Score

    d1           16    182.500000         264.0    26.5305667    11.4062500
    d2           16    345.500000         264.0    26.5305667    21.5937500
                       Average Scores Were Used for Ties


             Wilcoxon 2-Sample Test (Normal Approximation)
             (with Continuity Correction of .5)

             S =  182.500     Z = -3.05308     Prob > |Z| = 0.0023

             T-Test Approx. Significance = 0.0046

             Kruskal-Wallis Test (Chi-Square Approximation)
             CHISQ =  9.4367     DF =  1     Prob > CHISQ = 0.0021

                        Example 13.6 Freund 8th edition                        5
                                                  15:46 Friday, December 5, 2003

                              OBS    METHOD     X

                                1      1       94
                                2      1       87
                                3      1       91
                                4      1       74
                                5      1       87
                                6      1       97
                                7      2       85
                                8      2       82
                                9      2       79
                               10      2       84
                               11      2       61
                               12      2       72
                               13      2       80
                               14      3       89
                               15      3       67
                               16      3       72
                               17      3       76
                               18      3       69
                        Example 13.6 Freund 8th edition                        6
                                                  15:46 Friday, December 5, 2003

                       N P A R 1 W A Y  P R O C E D U R E

                   Wilcoxon Scores (Rank Sums) for Variable X
                         Classified by Variable METHOD


                           Sum of      Expected       Std Dev          Mean
    METHOD        N        Scores      Under H0      Under H0         Score

    1             6    84.0000000    57.0000000    10.6660539    14.0000000
    2             7    55.5000000    66.5000000    11.0301873     7.9285714
    3             5    31.5000000    47.5000000    10.1343105     6.3000000
                       Average Scores Were Used for Ties


             Kruskal-Wallis Test (Chi-Square Approximation)
             CHISQ =  6.6800     DF =  2     Prob > CHISQ = 0.0354