The Probability of the Occurrence of Negative Estimates in the Variance Components Estimation by Nested Precision Experiments

Summary

Nested experiments are commonly used to estimate variance components especially for the precision experiments. The ANOVA (analysis of variance) estimators are expressed as linear combinations of the mean squares from the ANOVA. Negative estimates can occur, as the linear combinations are usually including negative coefficients. The probability of the occurrence of negative estimates depends on the degrees of freedom of the mean squares and the true values of the variance components themselves. Based on the probability, some practical recommendations concerning the number of laboratories can be derived for the precision experiments.