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║ ███ ▄ ███ ║  CHAPTER 6
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║ ▄▄▄▄▄▄▄▄▄ ║  NON-PARAMETRIC HYPOTHESIS TESTS
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  Several of the commonly used non-parametric hypothesis tests
are available for use right on screen.  They provide quick and
easy solutions to the computation of various non-parametric tests
that are often very difficult to perform by hand or by use of a
calculator.  The computations are rapid and very accurate.  All
you need to do is enter a few items of information and you will
quickly have the answers you need.  


               CHI-SQUARE MEASURES OF ASSOCIATION

  This procedure enables you to enter summary data for any
contingency table and it then provides you with several
frequently used measures of association that are based on the
Chi-square statistic.  The program requires the number of rows in
the table, the number of columns, the sample size and the value
of Chi-square.  The following are exaples of the output that is
obtained from the procedure.

     Number of rows    = 3
     Number of columns = 4
     Sample size       = 213
     Chi-square        = 4.89000
     df                = 6
     p                <= 0.55800
     Pearson's C       = 0.14981
     Cramer's V        = 0.10714
     Tschuprow's T     = 0.09681

     Number of rows    = 2
     Number of columns = 2
     Sample size       = 89
     Chi-square        = 4.78000
     df                = 1
     p                <= 0.02879
     Phi               = 0.23175
     Pearson's C       = 0.22577
     Cramer's V        = 0.23175
     Tschuprow's T     = 0.23175


                         2x2 CHI-SQUARE

  The 2x2 Chi-square procedure enables you to enter cell
frequencies for a four-fold table.  When you do that, it computes
the value of Chi-square and Phi and provides a confidence
interval for Phi.  The procedure also gives you the option of
using Yates correction.  The following are sample outputs from
the procedure in which the first uses the Yates correction.

             B1         B2
         _____________________
        |          |          |
     A1 |  38      |  11      |
        |          |          |
        |----------|----------|
        |          |          |
     A2 |  19      |  46      |
        |__________|__________|

      df    = 1
      Chi^2 = 24.19592
         p <= 0.00000

     With Yates Correction
         Phi   = 0.46070
         Phi^2 = 0.21224

      95% Confidence interval
     0.30068 <= Phi <= 0.59549

             B1         B2
         _____________________
        |          |          |
     A1 |  121     |  28      |
        |          |          |
        |----------|----------|
        |          |          |
     A2 |  32      |  156     |
        |__________|__________|

      df    = 1
      Chi^2 = 138.15160
         p <= 0.00000
         Phi   = 0.64027
         Phi^2 = 0.40995

      95% Confidence interval
     0.57260 <= Phi <= 0.69927


                         NxM CHI-SQUARE

  The NxM Chi-square procedure enables you to enter a contingency
table, cell by cell, right on screen.  The program will ask you
to indicate the number of rows and columns in your table and it
will then enable you to enter the cell frequencies for each row.
As soon as you have entered all the cell frequencies you will
obtain results such as those illustrated below.

     Number of rows    = 3
     Number of columns = 4
     Sample size       = 446
     Chi-square        = 40.48369
     df                = 6
     p                <= 0.00000
     Pearson's C       = 0.28847
     Cramer's V        = 0.21304
     Tschuprow's T     = 0.19250


                          KENDALL'S TAU

  As you well know, Kendall's Tau enables you to compute a
measure of association for ranked data.  When you choose this
option, the program will ask you to enter the rank values of X
and Y.  Please note, you MUST enter the values of X in their rank
order.  The program accomodates tied ranks on the values of Y and
the following is a sample of the results you will obtain.

       N = 4
     Tau = -0.1826     
       z = -0.3721     
      p <= 0.0000      


                       MANN-WHITNEY U-TEST

  When using the Mann-Whitney U-test, you may enter any number of
values for X and Y provided that N1+N2 <= 200.  If N1 or N2 is
less than 10, you will have to consult a table of U values to
determine the significance of your results as noted in the first
example.  The program orders the values of U and U' so that U is
always the smaller of the two.

     N1 = 11        N2 = 9
     R1 = 102       R2 = 108
     U  = 36        U' = 63
     Consult table of U values.

     N1 = 14        N2 = 14
     R1 = 147       R2 = 259
     U  = 42        U' = 154
     z  = 2.583     p <= 0.0049


                         END OF CHAPTER
