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Weighted vs. Unweighted Mean Performance of Varieties across Environments

Limagrain Genetics, 737 Co. Rd. 1200 N. Champaign, IL 61821.

^* Corresponding author.

If within-environment error and variety x 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 (Y_A) and two types of weighted means (Y_R and Y_E) as estimators of varietal performance. Weights were inversely proportional to Shukla's residual variance estimates in Y_R and to withinenvironment error mean squares in Y_E. Fifty-threenvironments used in a corn (Zea mays L.) yield trial were repeatedly partitioned into model data and validation data. Compared with Y_R and Y_E, Y_A had slightly higher correlations with validation data means. Least significant differences of Y_A were 2 and 11% smaller than those of Y_R and Y_E, respectively. The failure of Y_R to be superior over Y_A 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 x environment interaction variances are heterogeneous.

Received for publication May 24, 1991.

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