The following is from Dave Howell's book, "Statistical Methods for Psychology" (1997, 4th edition, pp. 522-523). --------- Start of excerpt -------- As you can tell from the formula for an adjusted R square and from the preceding formula for F, our estimate of the correlation depends on both the size of the sample (N) and the number of predictors (p). People often assume that if there is no relation between the criterion [i.e., dependent variable] and the predictors, R should come out near 0. In fact, the expected value of R for random data is p/(N-1). Thus, with 5 predictors and 50 cases, an R = .10 would be the expected value. A rule of thumb that has been kicking around for years is that we should have at least 10 observations for every predictor. Harris (1985) points out, however, that he knows of no empirical evidence supporting this rule. It certainly fails in the extreme, because no one would be satisfied with 10 observations and 1 predictor. Harris advocates an alternative rule dealing not with the ratio of p to N, but with their difference. His rule is that N should exceed p by at least 50. Others have suggested the slightly more liberal N = or > p + 40. Whereas these two rules relate directly to the reliability of a correlation coefficient, Cohen and Cohen (1975) approach the problem from the direction of statistical power. They show that in the one-predictor case, to have power = .80 for a population correlation of .30 would require N = 124. With 5 predictors, a population correlation of .30 would require 187 subjects for the same degree of power. As you can see, a reasonable amount of power requires fairly large samples. Perhaps Darlingon's (1990) rule of thumb is best--"more is better." --------- End of excerpt -------- References Cohen, J., & Cohen, P. (1975). Applied multiple regression/correlation analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum. Darlington, R.B. (1990). Regression and linear models. New York: McGraw-Hill. Harris, R.J. (1985). A primer of multivariate statistics (2nd Ed.). New York: Academic Press Howell, D.C. (1987). Statistics for psychology (4th Ed.). Belmont, CA: Duxbury. NOTE: The McMaster library has a copy of Harris (1985): Location: THODE LIBRARY Collection: THODE Bookstacks (1st floor) Call No.: QA 278 .H35 1985 ---------------------------------------------------------------- Bruce Weaver 24/Jun/2003