Testing for homogeneity: I. The binomial and multinomial distributions
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同质性检验：第一部分，二项与多项分布
- 研究问题
- 对于样本量不同的多组二项或多项样本，如何检验其分布参数是否相同，并针对指定的合理备择获得较高检验功效？
- 方法与思路
- 作者从特定备择下的最大功效目标出发构造同质性检验，讨论传统卡方检验，并将二项情形的新检验推广至多项情形。
- 材料陈述的贡献
- 摘要称，该思路产生若干新检验并给出数值说明；二项问题中所讨论的检验也适用于部分组样本量仅为二或三的情形。
- 阅读关注点
- 应核对所针对备择的定义、最大功效主张的范围、小组样本下的显著性水平控制，以及多项推广与传统卡方检验的比较。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；具体检验形式、功效结果和技术条件未提供，本篇内容不能外推到另篇讨论的泊松情形。
原文摘要
If we have k binomial samples of different sizes, we may sometimes be interested in the question of homogeneity, i.e. we may want to know whether the k samples all came from binomial distributions with the same parameter p. A similar question of homogeneity may arise if we have k samples from multinomial or Poisson distributions. This paper, which is the first of a series of two, treats the binomial and multinomial situations; the second paper will treat the Poisson case. Homogeneity tests already exist for the problems just mentioned, but these existing tests apparently were not constructed with any optimal power properties explicitly in mind. These papers approach the problems of homogeneity testing by attempting to construct tests having maximal power against certain reasonable alternative hypotheses. Some new tests result from this approach; these tests will be described and numerical illustrations will be presented. The traditional tests(i.e. the usual X2 tests) will also be discussed. For the binomial problem, all tests which are considered are applicable to the situation(frequently arising in genetics) in which some or all of the k sample sizes are small numbers(even as small as 2 or 3). Section 1 of this paper is concerned with testing for homogeneity for the binomial case; a number of biological applications are presented. In §3, we show briefly how the new test which is introduced in §1 may be generalized to the multinomial case. All of the more technical details have been relegated to the Mathematical Appendices, which form the last part of the paper.