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Weighted vs. Unweighted Mean Performance of Varieties across Environments
Author(s) -
Bernardo Rex
Publication year - 1992
Publication title -
crop science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.76
H-Index - 147
eISSN - 1435-0653
pISSN - 0011-183X
DOI - 10.2135/cropsci1992.0011183x003200020041x
Subject(s) - statistics , estimator , residual , mathematics , variance (accounting) , mean squared error , weighted arithmetic mean , biology , algorithm , accounting , business
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 ( 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 × environment interaction variances are heterogeneous.