Power of Weighted and Ordinary Least Squares with Estimated Unequal Variances in Experimental Design

摘要

Response variances are estimated using replications for each experimental condition. The resulting estimated variances can be used to derive the correct variances of the Ordinary Least Squares (OLS) estimators. The estimates can also be used to compute the Estimated Least Squares (EWLS) estimators. The asymptotic covariance formula for EWLS might be used to test the EWLS estimators. The type 1 and 7 errors of this test procedure are compared with those for the OLS estimations. If the variances are constant, EWLS should not be used, but with strong heterogeneity EWLS is more efficient if the variance can be estimated from more than two observations.