Numerical tabulations for a statistic similar to student’s t

Abstract

Let X(1)≤X(2)≤...≤X(2m+1) be an ordered sample of a random variable X, which has a median μ and a continuous probability distribution function. We consider the statistic Sm,r=(X(m+1)−μ)/(X(m+1+r)−X(m+1−r)), for some integer r, 1≤r≤m. This statistic is independent of the scale parameter and has other properties similar to Student’s t, and can be computed when the values of X(m+1), X(m+1+r), X(m+1−r) are known while some or all other sample values are not available (e.g. are censored out). This paper presents tables of exact critical values of Sm,r for small sample sizes, under the assumption that X has a normal probability distribution. Furthermore, a table is also given of asymptotic critical values for Sm,r, which can be used for large sample sizes even when X is not normally distributed. These tables may make possible the practical use of Sm,r in some situations in which Student’s t cannot be used.