The distribution of range in samples from a normal population, expressed in terms of an independent estimate of standard deviation
成果类型：
Article
署名作者：
Newman, D
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/31.1-2.20
发表日期：
1939
页码：
2030
关键词：
摘要：
The object of the paper is to consider the ratio q[long dash]w/s, where w is the range of a sample of n individuals from a normal population, and s is an independent estimate of the population standard deviation with f/ degrees of freedom. The expectation of q is first considered and a short table given, by use of which, in conjunction with existing tables, this expectation can be calculated. The methods of calculating the upper 5% and 1% levels of the distribution of q (exact for n=2, 3, approximate larger n) are given. Framework tables, correct to two decimal places, together with fuller tables, correct to one decimal place, are given. The paper concludes with 3 examples of the use of these tables in problems of analysis of variance.