CHAPTER 10 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. None of these correlation procedures 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. 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 recveive 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 recveive 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 recveive 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 recveive 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