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I'm a beginner at stats and I'm trying to understand p-values for paired t-test and Shapiro-Wilks using the JASP Moon and Aggression data set (hope the screenshot resolution is ok - click on the image to zoom in):

My understanding is that the null hypothesis for Shapiro-Wilks is that the data is normal. My Shapiro-Wilks p-value is >0.05 so I thought I should not reject the null hypothesis. The data is normal.

However, the plot of the data indicates that the data is not normal?

enter image description here

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  • $\begingroup$ These data look consistent with a Normal distribution to me. With such a small dataset it's easy to confuse random variability with real differences. That's why you apply a formal test in the first place: to make sure you are not fooling yourself. $\endgroup$
    – whuber
    Dec 28 '20 at 13:53
  • $\begingroup$ Thanks @whuber. I've learnt something new! If you would like to post this as an answer, I would be happy to accept it. $\endgroup$
    – Chris Snow
    Dec 28 '20 at 14:01

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