Determining the power of a 1-sided z-test given only the power of the corresponding 2-sided test.

Abstract

Estimating statistical power is essential for designing behavioral medicine studies efficiently and conserving finite resources. Sometimes behavioral medicine researchers are interested in calculating power for 1-sided z-tests of individual parameters (e.g., slopes) in complex models such as multilevel structural equation models or multilevel mixture regression models. For such models, calculating power for 1-sided z-tests is cumbersome because: (a) online z-test power calculator tools are inapplicable, (b) commonly-used power analysis software provides power only for 2-sided z-tests and does not allow changing alpha, and (c) published power tables typically provide power results only for 2-sided z-tests. Hence, here we introduce straightforward and resource-efficient conversion formulas to estimate the power of 1-sided z-tests of individual parameters in any model by using direct power conversions from the corresponding 2-sided tests. We then implement these conversion formulas in accessible R and Excel software. This brief report thus provides behavioral medicine researchers with a convenient and practical solution for power calculation that minimizes the time, financial, and computational resources typically needed for power estimation.