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Multivariate Behavioral Research 6 3), 499-510Copyright 991 Lawrenc e Erlbaum Associates, Inc.

How Many SubjectsDoes It TakeTo Do A Regression Analysis?

SamuelB. GreenUniversity of Kansas

Numerous rules-of-thumb have been suggested for determining the minimum number ofsubjects required to con duct multiple regression analyses. These rules-of-thumb are evaluatedby com paring their results against those based on power analyses for tests of hyp otheses ofmultiple and partial correlations. The results did not support the use of rules-of-thumb thatsimply specify some constant e.g., 100 subjects) as the minimum number of subjects or aminimum ratio of number of subjects N) to number of predictors m). Some support wasobtained for a rule-of-thumb that N 50 8 for the m ultiple correlation andN 104 forthe partial correlation. How ever, the rule-of-thumb for the multiple correlation yields Values toolarge for N when 7 and both rules-of-thumb assume all studies have a medium-sizerelationship between criterion and predictors. Accordingly, a slightly more com plex rule-of-thumb is introduced hat estimates minimum samp le size as function of effect size asw ell as thenumber of predictors. It is argued that researchers should use methods o determine sample sizethat incorp orate effect size.How many subjects does it take to do a regression analysis? Itsounds likea line delivered by a comedian at a nightclub for applied statisticians. In fact, theline would probably bring jeers from such n audience n that applied statisticiansroutinely are asked some variant of this question by researchers and are forced torespond with questions of their own, some of which have no good answers. Inparticular, because many researchers want a sample size that ensures a reasonablechance of rejecting null hypotheses involving regression parameters, appliedstatisticians arelikely o present their responseswithinapower analytic ramework.From this perspective, sample size can be determined if thtee values are specified:alpha, the probability of cammittinga Type I error (i.e., incorrectly rejecting thenull hypothesis); power, one minus the probability ofm king Type I1 error (i.e.,not rejecting a false null hypothesis); and effect size, the degree to which thecriterion variable is related to the predictor variables n the population. Althoughalpha by tradition is set at .05 the choiceof values for power and effect size is lessclear and, in some cases, seems rather arbitrary.As an alternative to determining sample size based on power analytictechniques, some individuals have chosen to offer rules-of-thumb for regressionanalyses. These rules-of-thumb come in various forms. One form indicates thatthe number of subjects,N should always be equal to or greater than some constant,

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S GreenHarris, R. J In press). MIDS Minimally Important Difference Significant) criterion for samplesize. Journal of Educational Statistic s,Marks, M. R. 196 6, Septemb er). Two kinds ofregre ssion weights that are better than betas incrossedsamples.Paper presentedat he meeting of the American PsychologicalAssociation.Nunnally, J 1978).Psychometric theory 2nd ed.). New York: McGraw-Hill.Pedhakur, E. J 1982). Multiple regression in behavioral research 2nd ed.). New York: HoltRinehart Winston,SAS Institute Inc. 1985). SAS user s guide: Statistics Version 5) . Cary, NC: SAS InstituteInc.Schmidt, F. L. 1971). The relative efficiency of regression in simp le unit predictor weights in

applied d ifferential psychology. Educationalm P~chologicalMeasurement, 31 699-714.Tabachnick, B G. Fidell,L. S 1989). Using multivariate statistics (2nd. ed.). Cambridge,MA: Harper Row.

51 MULTIVARIATE BEHAVIORAL RESEARCH

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MULTIVARIATE BEHAVIORALRESEARCHVOLUME6 NUM ER

C O N T E N T S

The Structure and Intensity of Emotional Experiences: Method andContext Convergence HAIM MA N0 89Some M athematical Relationships Between Three-Mode ComponentAnalysis and Stationary Componen t Analysis ROGER EMILLSAP and WILLIAM MEREDITH 413Approximating Confidence Intervals for Factor Loadings ZARRELV. LAMBERT A LBERT R. WILDT and RICHARD M.DURAND 421Classifying Variables o n the si is of Disaggregate CorrelationsKARL SCHWEIZER 435Empirical Comparison Between Factor Analysisand Multidimensional

Item Response Models DIRK L. KNOL and MARTIJN P.FBERGER 457Confirmatory Measurement M odel Comparisons Using Latent Means

ROGER E MILLSAP and HOWARD EVERSON 479How Many Subjects Does It Take ToDo a Regression Analysis?SAMUEL B GREEN 499Latent Structure of Self-Monitoring RICK H . HOYL andRICHARD D. LENNOX 511

First Annual Saul B Sells Memorial LectureTowers of Babe1 PAUL HORST 54