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1991-04-11
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╔═══════════╗
║ ███ ▄ ███ ║ CHAPTER 3
║ ▀▀▀▀▀▀▀▀▀ ║
║ ▄▄▄▄▄▄▄▄▄ ║ MEASURES OF ASSOCIATION
║ ███ ▀ ███ ║
╚═══════════╝
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