Some Nonparametric Tests for Student's Hypothesis in Experimental Designs
实验设计中检验 Student 假设的若干非参数方法AI 解读 ↓
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实验设计中检验 Student 假设的若干非参数方法
- 研究问题
- 区组内相关和处理间、区组间异方差可能使 t 统计量不适用时，如何比较随机分配处理的实验效应？
- 方法与思路
- 作者针对一种实验设计提出非参数检验，摘要指出通常有效需区组相互独立且至少四个，并讨论效率与区组内相关。
- 材料陈述的贡献
- 摘要称在独立、正态、同方差基准下方法具有合理效率，某些情况下可结合较大的区组内正相关提高实验精度。
- 阅读关注点
- 应核对 Student 假设、适用设计和随机化方式，明确区组独立及至少四个区组的作用，并查看效率与精度比较。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；具体设计和检验规则未给出，不能推广到任意相关实验。
原文摘要
In experimental designs the quantities investigated are often grouped into blocks as a method of obtaining a higher precision for the experiment. This grouping may result in high correlation among observations within the same block. If the positions of the treatments within a block are assigned at random, the amount of correlation is difficult to determine and may vary greatly between treatments and from block to block. Also for many experiments the variances of the observations may differ substantially between treatments and from block to block. When one or both of these complications arise, the t-statistic is not necessarily applicable for comparing the effects of the treatments under investigation. This paper presents some nonparametric tests of Student's hypothesis which are usually valid for a well-known type of experimental design if there is statistical independence among blocks (number of blocks ≧4). These nonparametric results are reasonably efficient (compared to those based on the t-statistic) for the case where the totality of observations are independent, normally distributed, and have the same variance. High precision can sometimes be obtained by designing the experiment to yield large positive correlation within blocks and then using the non-parametric results.