I have some data I'm trying to analyze in SAS Studio (university edition). I am using the Distribution Analysis feature to try to test some data for normality.

It gives me the following histogram:

enter image description here

Skewness is approximately 2.934 and Kurtosis is approximately 9.013. I would have assumed based on that (and the fact that the shape of the histogram looks so different than the normal curve) that this is not normally distributed. However, my goodness-of-fit tests are:

enter image description here

The Kolmogorov-Smirnov D Statistic is 0.2820865, PR > d < 0.010.

The Cramer-von Mises W-Sq statistic is 2.5706303 with Pr > W-Sq <0.005.

The Anderson-Darling A-Sq statistic is 13.2288360 with Pr > A-Sq <0.005.

Unless I'm misreading that horribly, isn't that implying that this is, in fact, normal?

Can someone point out what I'm missing?


1 Answer 1


You have mixed up the null and alternative hypotheses.

The null hypotheses are that the data are normally distributed. You get three small p-values that would lead most people to reject the null hypotheses I’m favor of the alternative hypotheses of non-normal distributions.

This is completely consistent with your visual examination and inspection of the skewness and kurtosis values.

  • $\begingroup$ As a tangent, it is poor practice to run a KS test for a parametric distribution by estimating the parameter(s) from the data. That may or may not be what SAS is doing, testing a null of $H_0: X\sim N(\bar{x}, s^2)$. $\endgroup$
    – Dave
    Commented Jun 18, 2021 at 3:04

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