Inconsistency of the coefficient of variation for expressing the variabilityof an experiment in a model of analysis of variance

Abstract

From a variable distributed normally with meanzero and variance one, arose a succession of p treatments withconstant variance equal to one and whose mean increased kunits, valid to form two separate experiments; one with the tfirst treatments of the succession and the other with theremaining p; It was found that despite the fact that bothexperiments maintained equals its estimate of experimental errorvariance, its variation coefficients are different. As a practicalillustration were analyzed three experiments through an analysisof variance, which had the same variance and different structureof half of its four treatments. The three experiments presenteddifferent coefficients of variation in spite that their estimatesof variance of the experimental error were the same, whichshows that this statistician does not accurately reflect thevariability existing in an experiment when it is parsed throughan analysis of variance. Also the coefficient of variation wasassociated with the level of significance or capability of the Ftest to detect significant differences between treatments, orthe range between the values of the averages of treatments.