Relationship between mean yield, coefficient of variation, mean square error, and plot size in wheat field experiments

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Abstract
Large coefficients of variation (>30%) are often associated with increased experimental variability. The objective of this study was to examine the relationships between mean square errors, yield means, coefficients of variation (CV), and plot size using statistical information compiled from past wheat field research projects. Three hundred and sixty two wheat field research projects were selected from over 2,000 published wheat experiments that included soil fertility, weed, tillage, and variety evaluation. Little or no relationship between mean square error (MSE) and mean yield or plot size was found. However, mean yields and CVs demonstrated a significant negative correlation. This work proposes decreased variability among experimental units as defined by the CV can be accomplished simply by increasing the mean yield, suggesting that the use of the CV may be improper when comparing variability of trials from similar experiments. Attempts to compare variation from similar experiments should be done using the MSE since unit differences would not be a problem. The CV should only be used when comparing variation from experiments using different metrics. Plot size in plant breeding variety trials (average of 3.59 m2) was much smaller than that in fertilizer/weed/tillage trials (average of 37.2 m2). The smaller plot size employed in the variety trials reduced the variability encountered in the estimation of the mean and is consistent with the resolution where detectable differences in soil test parameters exist and that should be treated independently.

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