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

Large coefficients of variation (>30%) are often associated with increased experimental variability. The objective of this study was to examine the re lationships between mean square errors, yield means, coefficients of variat ion (CV), and plot size using statistical information compiled from past wh eat field research projects. Three hundred and sixty two wheat field resear ch projects were selected from over 2,000 published wheat experiments that included soil fertility, weed, tillage, and variety evaluation. Little or n o 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 u nits 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 va riability of trials from similar experiments. Attempts to compare variation from similar experiments should be done using the MSE since unit differenc es would not be a problem. The CV should only be used when comparing variat ion from experiments using different metrics. Plot size in plant breeding v ariety trials (average of 3.59 m(2)) was much smaller than that in fertiliz er/weed/tillage trials (average of 37.2 m(2)). The smaller plot size employ ed in the variety trials reduced the variability encountered in the estimat ion of the mean and is consistent with the resolution where detectable diff erences in soil test parameters exist and that should be treated independen tly.