When we introduced the Pearson correlation coefficient, r, in the beginning of this chapter, we pointed out that we were doing this in order to show its relations to some of the elements of the regression model. In the course of the presentation, we discussed r in connection with standardized and unstandardized regression coefficients. Also, we showed that r square is the proportion of variance attributed to the independent variable.

Although we will not go into the details, we cannot leave the topic of regression analysis without alerting you to the very important point that it is distinct from the correlation model. In thebivariate correlation model, both variables are random and assumed to follow a bivariate normal distribution. Further, in contrast to the regression, no distinction is made between an independent and a dependent variable. Instead, the interest is in the relation between the two variable.

In addition to other serious difficulties concerning the interpretation of r, one of its most serious shortcomings is that it is population specific. The magnitude of the correlation coefficient is affected by the variability of the population from which the sample was drawn. It wil be recalled that, other things equal, the more homogeneous the population, the lower the correlation coefficient. Tukey(1954), who confessed to being a member of the "informal society for the suppression of the correlation coefficient--whose guiding principleis that most con, correlation coefficient should never be calculated. branded r as t"he enemy of generalization, a focuser on the 'here and now' to the exclusion of the 'there and then'."

The deficiencies of r aside and regardless of whether or not one agrees with authors who counsel avoiding its use, it is of utmost importance to recognize that, unless it is used for descriptive purpose in the group being stdied, r must be calculated on the basis of data obtained from a probability sample. It seems superfluous to state that, when calculated on the basis of some haphazard group of people or what has been euphemistically termed "convenience sampling", r has little meaning. Yet, it is necessary to state the obvious because most correlation studies (including factor analysis of correlation matrices) reported in the literature are not based on probability samples.

One final word of caution. Computer programs for regression analysis routinely report correlation results as well. It is very important that you learn what is and what is not relevant output for the specific study under consideration. For example, when, as in the illustration we have given, the independent variable is fised, it makes no sense whatsoever interpret the correlation between it and the dependent variable. In fact, through the selection of values for the independent variable, the magnitude of r may be determined at will. do not be misled by the fact that r square is still interpretable under such circumstances. As was shown, r square indicates the proportion of  variance, or sum of squares, attributed to the independent variable. In contrast, r is ment to indicate the linear relation between two random variables.

Fisher's (1958) succinct statement aptly summarzes the issues reviewed briefly in this section:" the regression coefficients are of interest and scientific importance in many classes of data where the correlation coefficient, if used at all, is an artificial concept of no real utility".

                ----------------From Measurement, design, and analysis: an integrated approach. (Elazar J. Pedhazur, Liora Pedhazur Schmelkin,1991, Lawrence Erlbaum Associates, Publishers

Certainly, some views have changed for these years. Correlation analysis has been adopted in many papers. Sometimes it is used as a pilot study of regression analysis.-----by Fang Wang.

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