Tables of Range and Studentized Range

TLDR

The paper presents tables of percentage points and moments for the range and studentized range of normal samples. The authors compute standardized range percentiles for probabilities from 0.0001 to 0.9999 across sample sizes 2 to 100, provide moments of the range to eight significant figures, and tabulate studentized range percentiles for probabilities 0.9 to 0.999 with degrees of freedom up to infinity. All tabulated values are accurate to within one unit in the last place.

Abstract

A description is given of the computation of tables of percentage points of the range, moments of the range, and percentage points of the studentized range for samples from a normal population. Percentage points of the (standardized) range $W = w/\sigma$ corresponding to cumulative probability $P = 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.025, 0.05, 0.1 (0.1) 0.9, 0.95, 0.975, 0.99, 0.995, 0.999, 0.9995$ and $0.9999$ are given to six decimal places for samples of size $n = 2 (1) 20 (2) 40 (10) 100$. Moments (mean, variance, skewness, and elongation) of the range $W$ are given to eight or more significant figures for samples of size $n = 2 (1) 100$. Percentage points of the studentized range $Q = w/s$ corresponding to cumulative probability $P = 0.9, 0.95, 0.975, 0.99, 0.995$, and $0.999$ are given to four significant figures or four decimal places, whichever is less accurate, for samples of size $n = 2 (1) 20 (2) 40 (10) 100$, with degrees of freedom $\nu = 1 (1) 20, 24, 30, 40, 60, 120$, and $\infty$ for the independent estimate $s^2$ of the population variance. All tabular values are accurate to within a unit in the last place.