非参数检验能不能分析正态分布数据呢？

统计问题（22）：非参数检验知多少（多选）

Question

Which if any of the following statements are false?

a) Non-parametric statistics may be used for normally distributed data

b)Correlation coefficients are inappropriate for non-normally distributed data

c)Medians are always a more valid way than means are to compare non-normally distributed data

d) The significance level of a test should be increased when multiple tests are made in a study

Answer

Parametricstatistics (like t tests)work well for data from a normally distributed population but non-parametricstatistics may also be used. Non-parametric statistics do not requireassumptions about the distribution of the data, but they will be a little lesssensitive at picking up real differences if used when a parametric test wasappropriate. Also, 95% confidence intervals are harder to compute and will be widerwhen based on non-parametric statistics.

Pearson’s rank correlation coefficient makes no assumption about the distribution of thevariables, only that there is an order to the values.

A dichotomous variable has only two values. An example of a dichotomous variable is a person’s vital status—either dead or alive. This variable is certainly not normally distributed, but comparing two treatments on the basis of the median value would be unhelpful. On the other hand if the variable were coded as 0 for dead and 1 for alive, then the mean value would be the proportion surviving ineach group. So the mean would be more informative than the median.

Multiple testing increases the chance of a false positive finding so, if anything, the significance level should be reduced to guard against this.

中文解释：

参数检验（如t检验）对于来自正态分布总体的数据非常有效，但也可以使用非参数检验。非参数检验不需要关于数据分布的假设，但是如果在合适的参数检验中使用的话，它们在获取实际差异方面将不那么敏感。而且，基于非参数检验时，95％的置信区间很难计算，并且会更宽。

皮尔逊（Pearson）的等级相关系数不对变量的分布做任何假设，而是对数值进行排序(翻译如此，一般我们教学称之为Spearman相关分析)。

二分类变量只有两个值。一个二分类变量的例子是一个人的生命状态-死亡或活着。该变量当然不是正态分布的，但是基于中位数比较两种治疗将无济于事。另一方面，如果将变量编码为0（表示死亡）和1（表示存活），则平均数将是每个组中幸存的比例。因此，平均数将比中位数更有意义。

多重比较会增加出现假阳性结果的机会，因此，如果有的话，应降低显著性水平以防止这种情况。

所以答案是选择 BCD

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