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║ ███ ▄ ███ ║  CHAPTER 3
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║ ▄▄▄▄▄▄▄▄▄ ║  MEASURES OF ASSOCIATION
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  A number of the commonly used measures of association and
correlation are available for use right on screen.  They provide
quick and easy solutions to the computation of various
correlations 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 raw scores and you will
quickly have the answers you need. 


                       PEARSON CORRELATION

  You may easily compute a Pearson correlation by entering the
continuous values of Y and X.  You may also elect to transform
either or both variables and the program will accept an unlimited
number of observations.  The following is an example of the
output that you will receive from this procedure.

           r = 0.89381
     F-ratio = 19.86209
     p(r=0) <= 0.00367
     95% Confidence interval
     0.66280 <= r <= 0.96946


                     RANK ORDER CORRELATION

  You may compute a Spearman Rho by entering the ranked values of
Y and X.  You may also elect to transform either or both
variables and the program will accept an unlimited number of
observations.  The following is an example of the output that you
will receive from this procedure.

           r = 0.90527
     F-ratio = 13.62244
     p(r=0) <= 0.01636
     95% Confidence interval
     0.35896 <= r <= 0.98957


                   POINT BISERIAL CORRELATION

  You may compute a point-biserial correlation by entering the
continuous values of Y and dichotomous values of X.  You may also
elect to transform either or both variables and the program will
accept an unlimited number of observations.  The following is an
example of the output that you will receive from this procedure.

           r = 0.93285
     F-ratio = 46.93595
     p(r=0) <= 0.00025
     95% Confidence interval
     0.83279 <= r <= 0.97389


                         PHI COEFFICIENT

  You may compute a Phi coefficient by entering the dichotomous
values of Y and X.  You may also elect to transform either or
both variables and the program will accept an unlimited number of
observations.  The following is an example of the output that you
will receive from this procedure.

           r = 0.43301
     F-ratio = 2.53846
     p(r=0) <= 0.06835
     95% Confidence interval
     0.11508 <= r <= 0.67048


                  ETA: FROM SUMMARY STATISTICS

  Although most of the procedures for computing simple measures
of association or correlation require the input of raw data, the
procedure for computing the Eta statistic is an exception.  In
this case you will need to enter your degrees of freedom for
hypothesis (dfh), the degrees of freedom for error (dfe), and the
F-ratio.  Eta and its squared value are then computed along with
a shrunken value and the confidence interval.  The following is
an example of the results you will obtain from this procedure.

       dfh = 3
       dfe = 189
         F = 4.67
     Eta   = 0.26270
     Eta^2 = 0.06901
      95% Confidence interval
     0.12540 <= Eta <= 0.39013
     Shrunken Eta   = 0.23288
     Shrunken Eta^2 = 0.05423
      95% Confidence interval
     0.09401 <= Eta <= 0.36287


                     TETRACHORIC CORRELATION

  The tetrachoric correlation is obtained by entering the cell
frequencies of a four-fold table and the following is a sample of
the output that you will receive from this procedure.

     Dep/Indep   FALSE      TRUE

        TRUE     29         11
        FALSE    9          32

    r(tet) = -0.71549
     95% Confidence interval
    -0.80824 <= r <= -0.58808


                    SEMI-PARTIAL CORRELATION

  Semi-partial correlations are obtained by entering the sample
size and the zero-order correlations among the variables Y, X1,
and X2.  The following is an example of the output that you will
obtain. 

     Enter the correlation between:
     Y  and X1, r(y,x1)   = .34
     Y  and X2, r(y,x2)   = .27
     X1 and X2, r(x1,x2)  = .17
     Enter sample size, N = 89
     Semi-partial  r = 0.29844
      95% Confidence interval
     0.09312 <= r <= 0.47942


                       PARTIAL CORRELATION

  Partial correlations are obtained by entering the sample size
and the zero-order correlations among the variables Y, X1, and
X2.  The following is an example of the output that you will
obtain. 

     Enter the correlation between:
     Y  and X1, r(y,x1)   = .21
     Y  and X2, r(y,x2)   = .37
     X1 and X2, r(x1,x2)  = .04
     Enter sample size, N = 137
     Partial r = 0.21028
      95% Confidence interval
      0.04303 <= r <= 0.36607


                     PART-WHOLE CORRELATION

  Part-whole correlations are handy for removing the item-self
correlations among items in psychometric investigations, among
other applications.  You will need to enter the correlation
between an item, i, and a total score, T.  You will then need to
enter the standard deviation for the item and the total score.
Finally, enter the sample size and you will obtain outputs like
the one shown below.

     Enter the item-total correlation
     r(i,T)         =  .37
     Std Dev Xi     =  0.89
     Std Dev T      =  28.5
     Sample size, N =  375
     Corrected r = 0.34258
     95% Confidence interval
     0.25024 <= r <= 0.42875


                         END OF CHAPTER
