r - Normality test in R gives strange result?

Question

Possible Duplicate:
Seeing if data is normally distributed in R

I have 6 sets of residuals (fit - model) that I am testing for normality (I am trying to demonstrate that the deviation from the model is within instrumental noise).

The kernel density plots of all of them look approximately Gaussian, and the qqnorm plots look good. I have run all of them through two normality tests: shapiro.test {base} and ad.test {nortest}. These tests show that all the data sets are normal (p>>0.05, accept the null hypothesis of normality) except one. Usually I would not question these results, but the test that is coming back as 'not normal' (p<0.05, reject the null hypothesis of normality) is from the data set that looks MOST gaussian... I am confused, and would appreciate any help!

Here is the matrix of my residual kernel density plots, with the p-values from Anderson-Darling normality tests (ad.test) noted. All graphs are on the same scale (x & y). The non-normal peculiarity is the CvsD graph marked in red.

Here is a link to the data for the CvsD comparison.

Why aren't these residuals normal!?

Answer 1

事实上，这对我来说看起来不是很高斯；更像是具有大 n 的 t 分布——它比正态曲线更“尖锐”。ad.test和shapiro测试都返回 p < 0.05（shapiro.test根据您的数据返回 p = 0.002655）。

但是，请注意，正态性检验的有用性是有争议的；例如看这个问题。基本上，对于大样本量，即使是与正态分布的小偏差也会受到惩罚，并且 H0 会被拒绝。

也就是说，我仍然相信 - 鉴于您只有 328 个样本量 - 在您的情况下，分布并不真正正常。