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
- 区组实验存在组内相关或异方差时，如何比较处理效应，并在传统 t 统计量可能不适用时构造有效的非参数检验？
- 方法与思路
- 作者针对一种特定实验设计提出非参数检验，讨论区组独立且区组数至少为四时的有效性，并与标准正态同方差情形比较。
- 材料陈述的贡献
- 摘要称，方法在所述设计下通常有效，在独立正态同方差情形具有合理相对效率；较强组内正相关有时可提高精度。
- 阅读关注点
- 应核对实验设计和处理随机分配方式、Student 假设的具体含义，以及区组独立、区组数量和精度提升的条件。
- 阅读边界
- 来源为版本未注明的 OpenAlex 摘要；具体设计和有效性条件未展开，不能认为任意相关或异方差区组实验均适用。
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.