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I have a problem comparing results from shapiro test and qqplot. Shapiro tells me my data doesn't have normal distribution characteristics (pvalue = 1.94...e-08 <= 0.05) however when I look on QQ plot the points are pretty close to the reference line.

enter image description here

How should I interpret that?

I'm using shapiro function from: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html

Alienown
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    Why do you want to test normality? See this page for an introduction to extensive discussion about why strict testing for normality as with the Shapiro test seldom adds much. In practice, with enough data points real-world data will often deviate "significantly" from normal based on such tests, but not to an extent that substantially affects inference. – EdM Oct 18 '20 at 15:43

2 Answers2

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You seem to have quite a large sample size which is probably why the Shapiro-Wilk test returns a small p-value. In general statistical tests for normality are not a great idea in large part for this very reason.

There is some evidence, from the QQ plot, of slightly heavy tails. However, this is a fairly mild departure and in my opinion you are justified in considering these data to be approximately normally distributed.

I do wonder, however, why you are concerned about whether these data follow a normal distribution.

Robert Long
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You should not worry too much about the return of the Shapiro-Wilk test, especially with higher sample sizes this can happen as already mentioned, the Q-Q plot looks fine.

Another option I would like to add is to simply visually inspect the data with a histogram, this can help some times more than a plain number given out by a normality Test.

You could use the histogram function from package numpy: https://numpy.org/doc/stable/reference/generated/numpy.histogram.html#numpy.histogram

and get a result like this:

enter image description here

Ale
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SeppSeppenbauer
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