Statistical Power Analysis and Reliability of Measurement

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Abstract
Reliability of measurement as a determinant of the power of significance tests is investigated using concepts from statistical power analysis and from test and measurement theory. Results of specific power calculations based on measures of effect size together with particular reliability coefficients are presented in the form of tables. The importance of assumptions about true variance, error variance, and observed variance in determining the relation between reliability and power is emphasized, and a formula relating power and test length, analogous to the Spearman-Brown formula in test theory, is derived.