Significance Test for Grubbs's Estimators

Comparison of the reproducibility of two instruments or two techniques involves statistical methods which are now available in textbooks whenever the variability of specimens employed in successive measurements can be effectively eliminated. However, conditions where variations of material under test between successive measures are unavoidable appear to be particularly common in biological work. A technique for separating these two sources of error (techniques and material being measured) was obtained by Grubbs [1948], but has previously lacked an adequate test by which the relative precision of the techniques compared can be evaluated. It is here shown that the Pitman-Morgan test for comparing marginal variances in a bivariate distribution can be applied directly. The power function of the test and graphs to estimate the sample size for specified power may be based on David's tables.