## Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 31, Number 4 (1960), 1122-1147.

### Tables of Range and Studentized Range

#### 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.

#### Article information

**Source**

Ann. Math. Statist., Volume 31, Number 4 (1960), 1122-1147.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177705684

**Digital Object Identifier**

doi:10.1214/aoms/1177705684

**Mathematical Reviews number (MathSciNet)**

MR123384

**Zentralblatt MATH identifier**

0106.13602

**JSTOR**

links.jstor.org

#### Citation

Harter, H. Leon. Tables of Range and Studentized Range. Ann. Math. Statist. 31 (1960), no. 4, 1122--1147. doi:10.1214/aoms/1177705684. https://projecteuclid.org/euclid.aoms/1177705684