Error of Measurement and the Power of a Statistical Test

Formulae are developed from the assumptions of classical test theory to demonstrate the effect of error of measurement on the power of the F test for a fixed‐effects one‐way analysis of variance model. A simple model specifying the fixed and variable costs of testing is adopted and equations are derived that indicate the sample size that maximizes the non‐centrality parameter subject to the cost constraints. Given the sample size, the corresponding test length is then implied by the cost model. A computer program used for the estimation of power for permissible allocations of resources is described.