CHAPTER  8

                 NON-PARAMETRIC HYPOTHESIS TESTS



  A  wide  variety 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. 

  None  of  the  non-parametric  hypothesis  tests  will send the 
results to your printer.  However, all of your results are  saved
for you as you work along.  Then, when you exit the SPPC you will
be  given  the  option of reviewing your work on screen, printing
it, or storing it in a disk file of your choice.


               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