Nonparametric estimation of normal ranges given one-way ANOVA random effects assumptions

In this note, we compare three strategies that are commonly used in practice for estimating quantiles and quantile functions when data are assumed generated from a standard balanced one-way ANOVA random effects model, e.g. data from repeated assays, where the goal is to nonparametrically estimate/define a normal range. Strategy 1 consists of averaging the within subject values and then estimating quantiles based upon the averaged values in a standard fashion. Strategy 2 consists of estimating quantiles within each replication and then averaging the marginal quantiles over the replications. Strategy 3 consists of estimating quantiles and ignoring the repeated measures mechanism all together. We show that Strategy 1 is generally a poor choice when the goal is to refine the quantile estimation from a single replication through the application of repeated repetitions of an experiment. Strategy 2 and 3 are shown to be asymptotically equivalent.