雙樣本位置問題的無母數方法

A Signed-Rank Test For The Two-Sample Location Problem

張佳琪(Chia-Chie Chang)

指導教授 ： 鄭秀麗

中原大學/理學院/應用數學研究所/碩士(2003年)

https://doi.org/10.6840/cycu200300383

摘要

本文是用來探討經由兩連續且變異相似之母體隨機抽取兩組獨立樣本來作檢定，用以比較兩母體中位數的關係。我們是由Mann-Whitney Wilcoxon test的方法而引發的想法，將兩樣本差的sign值，再乘上其加上絕對值後排序的序值，也就是考慮兩樣本差的權重以充分利用收集到的樣本所提供的訊息，並且比較由不同分配的母體抽出的樣本做出的統計量，經由蒙地卡羅研究(Monte Carlo Study)，做模擬比較。另外，也模擬在不同母體之下所提出的方法和其他方法在檢定力(power)上的表現亦有不同，提供使用者在無母數方法中的另一個選擇。

關鍵字

雙樣本 ； 無母數方法

並列摘要

This paper discusses a median test for two continuous populations with similar variance structure from which samples are independently drawn. Our ideas are based on the Mann-Whitney Wilcoxon test. We take the sign of the difference of two observations to multiply its ordered rank after applying the absolute value operation to the difference. Our method takes into account weighing the differences of these observations in order to make better use of the embedded information in the sample. We also perform several Monte Carlo experiments to simulate the resulting test statistics from simulated populations with different distributions. Furthermore, based on our simulation studies, we also discuss and compare the testing power of our median test with other related tests in the literature. Our test can serve as an alternative nonparametric analysis in the field of two-population median test problems.

並列關鍵字

location problem ； two sample

參考文獻

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