Bounds for a nonparametric t table

Abstract

A simple inequality for bounding the tail probabilities of normalized sums of independent, symmetric random variables is used to produce bounds on the tail probabilities of the usual Student t statistic under the same hypothesis. The relative difference between the resulting t scores and the usual ones is shown to be asymptotically negligible as the sample size increases and the tail probability decreases to zero. As an example, a table of upper 0·025 cutoff bounds is given and compared to the usual bounds.