Power and measures of effect size in analysis of variance with fixed versus random nested factors.
Ignoring a nested factor can influence the validity of statistical decisions about treatment effectiveness. Previous discussions have centered on consequences of ignoring nested factors versus treating them as random factors on Type I errors and measures of effect size (B. E. Wampold & R. C. Serlin). The authors (a) discuss circumstances under which the treatment of nested provider effects as fixed as opposed to random is appropriate; (b) present 2 formulas for the correct estimation of effect sizes when nested factors are fixed; (c) present the results of Monte Carlo simulations of the consequences of treating providers as fixed versus random on effect size estimates, Type I error rates, and power; and (d) discuss implications of mistaken considerations of provider effects for the study of differential treatment effects in psychotherapy research.
Siemer
Matthias
M
Department of Psychology, Ernst Moritz Arndt University, Greifswald, Germany. masiemer@uni-greifswald.de
Joormann
Jutta
J
D000704:Analysis of Variance; D015982:Bias; D006801:Humans; D009010:Monte Carlo Method; D017063:Outcome Assessment, Health Care / Q000706:statistics & numerical data; D011594:Psychometrics / Q000706:statistics & numerical data*; D011613:Psychotherapy / Q000706:statistics & numerical data*; D016032:Randomized Controlled Trials as Topic / Q000523:psychology*