回复 第3楼 的 zeamxie：
两组样品的 Wilcoxon test 就是 Mann-Whitney test。这种方法和t test有不同的假设。MW是非参数方法（non-parametric）而t test 是有参数的（parametric）。换句话说，有参数就是要求数据服从某种分布，无参数就指对数据的分布没有要求。在参数方法中，通过样品参数来估计对分布参数从而进行检验。对于t test而言，数据分布必须符合正态分布，而MW仅仅假设两个样本具有同样的分布（对于具体什么样的分布没有具体要求）。两者主要不同在于statistical power 和 robustness。在符合正太分布的时候，t test 的statistical power （在备择假设正确时拒绝零假设的概率，即 sensitivity）更高一些，但是如果数据不符合正态分布，MW更准确一些。
这里有个很好的解释
http://uk.answers.yahoo.com/question/index?qid=20100109093525AAEufIF
有可能打不开，我复制过来
Firstly, allow me to discuss the basic difference between assumptions made in the Mann-Whitney U test and the independent sample t-test.
Parametric implies that a distribution is assumed for the population.
Non-parametric implies that there is no assumption of a specific distribution for the population.
You use the independent sample t-test when you want to test the mean between two groups of data.
You use the Mann-Whitney U test when you want to test the median between two groups of data.
Two independent sample t-test holds the following assumptions:
1) The populations follow normal distributions
2) The two independent samples are equal in size
3) The variances for both populations are identical
(There are also t-test with unequal sizes and/or unequal variances, so assumptions to 2) and 3) can be voided.)
Mann-Whitney U test holds the following assumptions:
1) The populations do not follow any specific parametrized distributions
1) The populations of interest have the same shape
2) The populations are independent of each other
When the assumptions hold, the power of rejecting H₀ when it is false is higher for a parametric test than for a corresponding nonparametric test with equal sample sizes. To put it simply, parametric tests have more statistical power than non-parametric tests.
However, the nonparametric test results are more robust against violation of the assumptions.
Thus, if assumptions are violated for a test based on a parametric model, then the conclusions based upon the parametric test may be more misleading than conclusions based upon nonparametric test.
Also, Mann-Whitney U test is more appropriate when dealing with skewed data. This is because the parametric t-test are sensitive towards outliers or extreme values. When a data is skewed, then the position of the mean would be more towards the skewed part of the data. This condition is made more relaxed by the Mann-Whitney U test.
But even if the assumptions for the independent sample t-test are well met, the Mann-Whitney U test is hardly less powerful with large enough sample size. Hence, whenever the validity of the parametric assumptions are potentially doubtful, Mann-Whitney U test is used instead.
You said that you obtained the same result from both tests. What do you mean by same result? Is it that both tests produce the same hypotheses? i.e. for example, for independent sample t-test, mean is the same, and for Mann-Whitney U test, the median is the same? Or is it that the value of the mean equals the value of the median?
Now, if the former is true, then it could be due to both of the data have the same shape/distribution, even if it's skewed. Therefore, the positions of the mean for both data would be similar, and this also goes to the median. Hence the result. In this case, the Mann-Whitney U test would be more appropriate than the independent sample t-test due to the skewness of the data (not normal), where the mean gives misleading value while the median gives more accurate value of central tendency.
If the latter is true, then it is most likely that both data are bell-shaped. (i.e. the mean and the median lies in the centre of the bell-curve. Bell-curve implies normality and hence, assumptions for the independent sample t-test are justified. Now in this case, the independent sample t-test would be more appropriate than the Mann-Whitney U test.
Another case when Mann-Whitney U test could be more appropriate than the independent sample t-test is when you use ordinal scale for your data. For example, you used 'Low' to represent $10000 below, 'Medium' to represent $10000-$25000 and 'High' to represent $25000 above. Then you assign 'Low'=1, 'Medium'=2, 'High'=3 (Ranking).
So, depending on the situation, each test has its own pros and cons. In any case, whenever the assumptions for a parametric test are justified, there is no way that a non-parametric test will be more statistically powerful, and thus be more appropriate, than a parametric test.
