The Pearson product moment (P.M.) correlation ("r") and four of its most widely used variations--the phi, the rho, the biserial, and the point-biserial coefficients--are reviewed. Using small data sets between one and nine, the conditions under which the various forms are restricted in power and robustness are explored. Seven sample data sets were constructed to illustrate the effects of the following conditions: (1) perfect correlation; (2) restriction of range; (3) measurement error (one variable); (4) measurement error (two variables); (5) extreme scores (one outlier); (6) extreme scores (two outliers); and (7) heterogeneity of sample distribution (one variable). Conceptual and algebraic linkages among the coefficients, and teaching practices that will facilitate the assimilation of these concepts and that will allow a student to predict the practical effects of the conditions are discussed. Two data tables are included. Appendix A contains definitions, formulas, and examples of the coefficients, which are presented as reproductions of a Macintosh computer hypercard stack designed for instructional purposes. Appendix B contains sample spreadsheet calculations for the seven conditions studied. (SLD)
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education