Tables of the probability integral of the studentized range
成果类型：
Article
署名作者：
Pearson, ES; Hartley, HO
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2333622
发表日期：
1943
页码：
8999
关键词：
摘要：
Denote by x 1, . . . , xn a random sample of n observations arranged in ascending order of magnitude and drawn from a normal population with standard deviation o. The range, or spread, in the sample is Xn[long dash]X1 and may be expressed in units of the standard deviation by the ratio [image] Let a 2d independent sample X1 . . . , xv+1 be drawn from the same population. [image] Tables are given which enable one to obtain the probability integral of q and the lower and upper percentage points of the studentized range q. The probability integral v P n (Q) is expressed approx. by the quadratic equation [image] Table 1 contains values of P n (Q), an(Q) and bn (Q) for value of Q from 0.00-6.00 by intervals of 1/4 and for values of n from 3 to 20. Table 2 provides gauge values for the actual range when some information about s is known. Applications pertaining to accuracy of chemical analyses, quality control limits and manufactoring certain articles are given.