We consider the one-way random effects model with unequal sample sizes and heterogeneous variances. Using the method of generalized confidence intervals, we develop a new confidence interval procedure for the mean. Additionally, we investigate two alternative models based on different sets of assumptions regarding between group variability and derive generalized confidence interval procedures for the mean. These procedures are applicable to small samples. Statistical simulation is used to demonstrate that the coverage probabilities of these procedures are close enough to the nominal value so that they are useful in practice. Although the methods are quite general, the procedures are explained with the backdrop of interlaboratory studies.
Citation: Journal of the American Statistical Association
Pub Type: Journals
coverage probability, generalized pivotal quantity, heterogeneous error variances, ISO gum, one-way random effects model, type-B assumptions