A Problem Related to Grubbs Technique: The Distribution of Method Variance Estimates for Known Product Variance

The distribution of estimates of measurement method variance made by subtracting a known product variance from the total variance in a finite number of observations can be shown to be the non-central chi-square. Probabilities of finding that estimate to be negative or zero have been calculated for various numbers of observations and ratios of product variance to method variance, as well as the probability of finding the estimate in a range of twice its expected standard deviation centered on its expected value. Results are compared with those to be expected from an ordinary regression analysis.