Open Access
December, 1960 Tables of Range and Studentized Range
H. Leon Harter
Ann. Math. Statist. 31(4): 1122-1147 (December, 1960). DOI: 10.1214/aoms/1177705684

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.

Citation

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H. Leon Harter. "Tables of Range and Studentized Range." Ann. Math. Statist. 31 (4) 1122 - 1147, December, 1960. https://doi.org/10.1214/aoms/1177705684

Information

Published: December, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0106.13602
MathSciNet: MR123384
Digital Object Identifier: 10.1214/aoms/1177705684

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 4 • December, 1960
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