Weighted vs. Unweighted Mean Performance of Varieties across Environments

Abstract

If within‐environment error and variety × environment interaction variances are heterogeneous across environments, weighted means may provide more precise estimates of varietal mean performance than the arithmetic (unweighted) mean. The objective of this study was to compare the arithmetic mean (YA) and two types of weighted means (YR and YE) as estimators of varietal performance. Weights were inversely proportional to Shukla's residual variance estimates in YR and to withinenvironment error mean squares in YE. Fifty‐threenvironments used in a corn (Zea mays L.) yield trial were repeatedly partitioned into model data and validation data. Compared with YR and YE, YA had slightly higher correlations with validation data means. Least significant differences of YA were 2 and 11% smaller than those of YR and YE, respectively. The failure of YR to be superior over YA was attributed to sampling error in the estimates of residual variances. The continued use of the arithmetic mean in estimating average varietal performance is suggested, even if error and variety × environment interaction variances are heterogeneous.