On the use and interpretation of certain test criteria for purposes of statistical inference Part I
On the use and interpretation of certain test criteria for purposes of statistical inference Part I
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DOI：
10.1093/biomet/20a.1-2.175
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发表时间：
1928-07-01
期刊：
影响因子：
2.7
通讯作者：
Pearson, ES
中科院分区：
文献类型：
--
作者：
Neyman, J;Pearson, ES
问题是：给定一个样本2和一个假设A，它是从一个总体n中随机抽取的，如何检验这个假设？解决这个问题的第一次尝试导致了贝叶斯定理。然而，应用这一定理需要先验概率定律的知识，而先验概率定律仅在例外情况下才能从所考虑的问题中直接得出。我们所能做的只是假定先验定律的某种确定形式，例如，它对所有可能的假设都是不变的。这样的假设是武断的，基于此的结果是值得怀疑的。如果不考虑与抽样总体有关的备择假设，就很难对假设A作出判断;无论从假设总体n中抽取观察样本的概率有多小，如果没有备择假设总体n，那么抽取2的概率就更大，我们倾向于接受假设A。在检验假设时，可能犯两种错误：（1）有时我们拒绝一个真实的假设，（2）更多的时候，我们可能接受一个错误的假设。给出检验假设的规则并不困难，这些规则可以将犯第一类错误的概率降低到任何给定的水平，但要控制第二类错误就困难得多了。我们所能做的就是避免接受假设A，因为可能存在不同的群体II[image]，这样观察到的样本的概率远大于假设指定的群体II的概率。从这一原则出发，作者重新发现了检验不同类型假设A的几种方法，并发现了一些新的方法，部分用于已经考虑过的问题，部分用于新的问题。理论上的考虑，其次是几个例子的测试假设和图表计算，以方便应用一种新的方法。
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.