Generalized SAMPLE SIZE Determination Formulas for Investigating Contextual Effects by a Three-Level Random Intercept Model

Satoshi Usami ()
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Satoshi Usami: University of Tsukuba

Psychometrika, 2017, vol. 82, issue 1, No 7, 133-157

Abstract: Abstract Behavioral and psychological researchers have shown strong interests in investigating contextual effects (i.e., the influences of combinations of individual- and group-level predictors on individual-level outcomes). The present research provides generalized formulas for determining the sample size needed in investigating contextual effects according to the desired level of statistical power as well as width of confidence interval. These formulas are derived within a three-level random intercept model that includes one predictor/contextual variable at each level to simultaneously cover various kinds of contextual effects that researchers can show interest. The relative influences of indices included in the formulas on the standard errors of contextual effects estimates are investigated with the aim of further simplifying sample size determination procedures. In addition, simulation studies are performed to investigate finite sample behavior of calculated statistical power, showing that estimated sample sizes based on derived formulas can be both positively and negatively biased due to complex effects of unreliability of contextual variables, multicollinearity, and violation of assumption regarding the known variances. Thus, it is advisable to compare estimated sample sizes under various specifications of indices and to evaluate its potential bias, as illustrated in the example.

Keywords: sample size determination; multilevel model; statistical power; confidence interval; contextual effects (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11336-016-9532-y

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