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杨大发 · 2021年05月05日

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  1. CFA I
  2. Quantitative

NO.PZ2017092702000147

问题如下：

An analyst is examining the monthly returns for two funds over one year. Both funds’ returns are non-normally distributed. To test whether the mean return of one fund is greater than the mean return of the other fund, the analyst can use:

选项：

A.

a parametric test only.

B.

a nonparametric test only.

C.

both parametric and nonparametric tests.

解释：

B is correct.

There are only 12 (monthly) observations over the one year of the sample and thus the samples are small. Additionally, the funds’ returns are non-normally distributed. Therefore, the samples do not meet the distributional assumptions for a parametric test. The Mann–Whitney U test (a nonparametric test) could be used to test the differences between population means

我记得视频中讲test参数的都可以用参数检验，如果是test排序、符号等问题的才需要非参数检验。这道题是不是虽然提到了mean，但是本质是要看mean的大小（也就是类似排序或者符号）所以要用非参数检验？
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1 个答案

星星_品职助教 · 2021年05月06日

同学你好，

这道题检验的是两个均值之间的关系。如果对应的两个总体都是正态分布的话，那么我们需要使用t检验，也就是参数检验（对于t检验而言，参数就是自由度df）。

但这道题为非正态总体“Both funds’ returns are non-normally distributed”，所以t检验就不能用了。这个时候只能使用非参数检验。

-------------------

这道题目更多的是考察对于两个均值之间关系这种特殊的检验的理解。如果仅是考察参数/非参数检验之间的区别，则判断准则为你说的“test参数的都可以用参数检验，如果是test排序、符号等问题的才需要非参数检验”。

但无论是以上哪个考点，都不算是重点。


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