ERIC Number: ED336394
Record Type: RIE
Publication Date: 1991-Jan
Reference Count: N/A
Phi, Rho, P.M., Biserial and Point-Biserial "r": A Review of Linkages.
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)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Biserial Correlation; Heterogeneity of Variance; Linkage Analysis; Pearson Product Moment Correlation; Phi Coefficient; Point Biserial Correlation; Range Restriction; Rho Coefficient
Note: Paper presented at the Annual Meeting of the Southwest Educational Research Association (San Antonio, TX, January 24-26, 1991).