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One possible reason for the continued neglect of statistical power analysis in research in the behavioral sciences is the inaccessibility of or difficulty with the standard material. A convenient, although not comprehensive, presentation of required sample sizes is provided here. Effect-size indexes and conventional values for these are given for operationally defined small, medium, and large effects. The sample sizes necessary for .80 power to detect effects at these levels are tabled for eight standard statistical tests: (a) the difference between independent means, (b) the significance of a product-moment correlation, (c) the difference between independent rs, (d) the sign test, (e) the difference between independent proportions, (f) chi-square tests for goodness of fit and contingency tables, (g) one-way analysis of variance, and (h) the significance of a multiple or multiple partial correlation.
Intelligence tests are widely assumed to measure maximal intellectual performance, and predictive associations between intelligence quotient (IQ) scores and later-life outcomes are typically interpreted as unbiased estimates of the effect of intellectual ability on academic, professional, and social life outcomes. The current investigation critically examines these assumptions and finds evidence against both. First, we examined whether motivation is less than maximal on intelligence tests administered in the context of low-stakes research situations. Specifically, we completed a meta-analysis of random-assignment experiments testing the effects of material incentives on intelligence-test performance on a collective 2,008 participants. Incentives increased IQ scores by an average of 0.64 SD, with larger effects for individuals with lower baseline IQ scores. Second, we tested whether individual differences in motivation during IQ testing can spuriously inflate the predictive validity of intelligence for life outcomes. Trained observers rated test motivation among 251 adolescent boys completing intelligence tests using a 15-min "thin-slice" video sample. IQ score predicted life outcomes, including academic performance in adolescence and criminal convictions, employment, and years of education in early adulthood. After adjusting for the influence of test motivation, however, the predictive validity of intelligence for life outcomes was significantly diminished, particularly for nonacademic outcomes. Collectively, our findings suggest that, under low-stakes research conditions, some individuals try harder than others, and, in this context, test motivation can act as a third-variable confound that inflates estimates of the predictive validity of intelligence for life outcomes.
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