Applications of the k 4 Statistic to Genetic Variance Component Analyses

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Abstract
The k4 statistic, or fourth sample cumulant, is used to derive unbiased estimates of the variance of estimated genetic variance components. The model assumes a hierarchal classification with equal number of F3 plants within each randomly selected F3 family. No assumption other than independence is made concerning the distribution functions so the mean squares of the hierarchal analysis of variance are correlated. Lower bound estimates of the number of genes controlling a quantitative character are also derived from fourth degree statistics under the additional assumption of no epistasis. The lower bound property is based upon the fact that the absolute value of a sample correlation coefficient is bounded above by 1.