**ERIC Number:**ED223657

**Record Type:**RIE

**Publication Date:**1982-Jun

**Pages:**16

**Abstractor:**N/A

**Reference Count:**0

**ISBN:**N/A

**ISSN:**N/A

The Correlation Coefficient as the Ratio of Two Means: An Interpretation Due to Galton and Brogden.

Price, James M.; Nicewander, W. Alan

A standard interpretation of the coefficient of correlation may be obtained from the ratio of two variances. If it is assumed that two variables, X and Y, are bivariate normal and scaled to have zero means and unit variances, it can be shown that the correlation between X and Y is the ratio of two conditional means. Galton's statistical studies of inheritance used the "ratio of means" expression for the correlation coefficient to illustrate the proportion of regression towards the mean for the progeny of parents in the extremes of a distribution for a selected trait. In the area of personnel selection, Brogden showed that the correlation coefficient may be interpreted as the ratio of the mean criterion score for persons selected on a test to the mean criterion score for "perfect" selection (i.e., selecting on the basis of criterion score). Monte Carlo studies indicate that the Galton-Brogden approach may be useful for dealing with extreme group studies. (Author/PN)

**Publication Type:**Speeches/Meeting Papers; Reports - Research

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers:**Brogden (H E); Data Interpretation; Galton (Sir Francis); Monte Carlo Studies; Pearson Product Moment Correlation

**Note:**Paper presented at the Annual Meeting of the Psychometric Society (Montreal, Canada, May 30-June 2, 1982).