论文标题
具有辅助信息的独立性和同质性卡方检验的力量的指数增加
Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information
论文作者
论文摘要
本文是关于两项非参数测试功率的指数增加的作品的扩展：$ z $ - 检验和卡方拟合测试。在拥有辅助信息的情况下，可以相对于样本的大小，著名的卡方检验的独立性和同质性测试的能力相对于指数级提高。通过使用辅助信息来提高这些统计检验的功能，可以减少接受替代假设下接受无原假设的可能性，或者减少达到预定义功率所需的样本大小。建议的方法是计算，并且提出了一些简单的统计应用程序来说明这些结果。这项工作的框架是非参数的，因此可以将其应用于使用统计信息的任何类型的数据和任何领域。
This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the $ Z $-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve exponentially relative to the size of the sample the power of the famous chi-square tests of independence and homogeneity. Improving the power of these statistical tests by using auxiliary information makes it possible either to reduce the probability of accepting the null hypothesis under the alternative hypothesis, or to reduce the size of the sample necessary to reach a predefined power. The suggested method is computational and some simple statistical applications are presented to illustrate these results. The framework of this work is non-parametric, so it can be applied to any kind of data and any area using statistics.
