On the use and interpretation of certain test criteria for purposes of statistical inference Part I
成果类型：
Article
署名作者：
Neyman, J; Pearson, ES
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2331945
发表日期：
1928
页码：
175240
关键词：
摘要：
The problem: Given a sample 2 and a hypothesis A that it has been drawn at random from a population n[long dash]how shall the hypothesis be tested? The 1st attempt to solve this problem resulted in Bayes'' Theorem. However, the application of that theorem requires knowledge of the a priori probability law, which follows directly from the problem under consideration only in exceptional cases. All that can be done is to assume some definite form of the a priori law, for instance, that it is constant for all possible hypotheses. Such an assumption is arbitrary, and results based on it are of doubtful value. It is difficult to form a judgment on the hypothesis A with out considering alternative hypotheses concerning the sampled population; however small the probability of drawing the observed sample from the hypothetical population n may be, we are inclined to accept the hypothesis A if there is no alternative hypothetical population n, such that the probability of drawing 2 is larger. In testing hypotheses, 2 sorts of errors can be committed: (1) Sometimes we reject a true hypothesis, and (2) more often, probably, we accept a false one. It is not difficult to give rules for testing hypotheses which would reduce the probability of committing errors of the 1st kind to any given level as low as desired; but it is much more difficult to control errors of the 2nd kind. All we can do is avoid the acceptance of hypothesis A in cases when there are possible different populations II[image] such that the probability of drawing the observed sample is much greater than that corresponding to the population II, specified by the hypothesis. Starting from that principle, the authors re-discovered several methods of testing different kinds of hypothesis A and found some new methods, partly for problems which have been already considered, and partly for new ones. The theoretical considerations are followed by several examples of testing hypotheses and by diagrams and tables computed to facilitate the application of a new method.