Why is my data not normally distributed while I have an almost perfect QQ plot and histogram? I am doing a thesis and I am stuck with my statistics on time series data. And when I run a Shapiro test, or any test, it says:
Statistics=0.998, p=0.000
Sample does not look Gaussian (reject H0)

And that it is not normally distributed. But when I look to my QQ plot and histogram the data looks normally distributed. And even when it would not pass the test, it is strange that it results in p = 0.000.
I also have two other groups where the QQ plot and histogram looks way worse than this one, but the tests say those are normally distributed.
I am looking in my script, but I can’t find any mistakes so far. Is it likely that there is something wrong or is it very normal for this data to be nonparametric (even with this graphs)?
I am using Python btw, not R.
QQ plot:

Histogram:

PS. I also have a box plot:


Ben has already explained much.
If you only want some kind of classifier based on, say, variance, then you could use a common variance estimator and you don't need normality. Your distributions should have second moments, though.
You wrote that you did "many tests" - this is rather suspicious. Are you aware of the multiple hypothesis testing issues? Are you aware of the "formulating hypotheses on the data" issues? I got the impression, that you'd prefer estimators, not hypothesis testing. Your statistical work seems to have some basic flaws...
