Journal ArticleDOI
Properties of some tests in sequential analysis
TLDR
It was desired to see what could be expected if an estimate of the variance replaced the variance in this test, and so obtain an indication of what might result for a test in which the variance was replaced by an estimate.Abstract:
known, has been given by Wald (1945) It was desired to see what could be expected if an estimate of the variance replaced the variance in this test The performance characteristics of Wald's test are expressed in terms of certain inequalities It was therefore decided first to examine these by means of a large-scale sampling experiment, and so obtain an indication of what might result for a test in which the variance was replaced by an estimate This experiment was designed under the guidance of Dr H 0 Hartley, and the results are discussed in ? 3 The three points investigated are: (i) the accuracy of the first and second types of error, (ii) the distribution of the number of samples necessary to reach a decision and (iii) the effects of truncation The results obtained are described below and are consistent with Wald's theory Wald (1945) and Barnard (1946, 1950) give sequential tests for discriminating between means when o is unknown Armitage (1947) compares the first and second of these tests, giving the results of their application to sixty samples In a later paper it is hoped to give the results of further sampling experiments on all these tests, together with the results for a new test which is discussed in ? 4 The three tests referred to above for the case where o- is unknown are none of them altogether satisfactory, since they are unsymmetrical in Ito and atl Also they differentiate between means of #o and It1 = dto + &r, where o is unknownread more
Citations
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Journal ArticleDOI
Shewhart x-charts with estimated process variance
TL;DR: In this article, the authors investigated the effect of using small sample sizes in estimating O2is to increase the average run length of the Shewhart X-chart and showed that the chart signals with probability one but the ARL may not be finite if the size of the 2 sample used to estimate O2 is sufficiently small.
Journal ArticleDOI
Sequential Analysis: A Survey
TL;DR: Attention will be concentrated on those techniques in which the sequential element is well in evidence; in particular, on techniques embodying a "stopping rule", so that they include directions on when to cease the investigation.
Journal ArticleDOI
A family of closed sequential procedures
TL;DR: In this article, the authors describe a family of closed sequential plans for normal variates, which retain the same outer boundaries as the Sobel-Wald and the restricted plans.
Journal ArticleDOI
A History of Distribution Sampling Prior to the Era of the Computer and its Relevance to Simulation
TL;DR: The first part of this paper contains an historical survey of distribution sampling as used by statisticians, originally prepared in 1953 and reproduced here in slightly revised form to bring this history to the attention of present day simulators.
References
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Book ChapterDOI
Sequential Tests of Statistical Hypotheses
TL;DR: A sequential test of a statistical hypothesis is defined as any statistical test procedure which gives a specific rule, at any stage of the experiment (at the n-th trial for each integral value of n), for making one of the following three decisions: (1) to accept the hypothesis being tested (null hypothesis), (2) to reject the null hypothesis, (3) to continue the experiment by making an additional observation.
Journal ArticleDOI
Tracts for Computers
TL;DR: An erratum slip is printed and can be obtained by purchasers of the above series by sending a stamped and addressed envelope to Mr. C. F. Clay, Cambridge University Press, Fetter Lane, E.G.C.