参考资料：

https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test

https://en.wikipedia.org/wiki/Mann–Whitney_U_test

https://explorable.com/mann-whitney-u-test

   在统计学中，当数据符合正态分布、方差齐性时，常用参数检验，如u检验、t检验等，但当数据不符合正态分布或方差不齐时，则需要利用非参数检验。此处介绍的Wilcoxon-signed-rank-test和Mann-Whitney-U-test均属于非参检验方法。

   其中，Wilcoxon-signed-rank-test主要用于成对样品。The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed.

   而Mann-Whitney-U-test用于两组样品。In statistics, the Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that two samples come from the same population against an alternative hypothesis, especially that a particular population tends to have larger values than the other. Unlike the t-test it does not require the assumption of normal distributions. It is nearly as efficient as the t-test on normal distributions.

   针对Wilcoxon-signed-rank-test的数据案例如下：

    针对Mann-Whitney-U-test的数据案例如下：

    这是两种方法所适用的数据类型。对于具体的计算过程中，目前在R、SAS、SPSS中均有成熟的计算代码，可直接使用。