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What consititutes a non-normal distribution of residuals?

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What consititutes a non-normal distribution of residuals?

I have used PROC MIXED to fit a repeated measures spatial model to some spectrogram data (i.e. time-frequency representations). The datasets are quite large, 10800 data points. Following the advice stom Steve Denham in an earlier post, I checked the distribution of residuals. Despite looking like a very nice gaussian distribution, the skew is -0.016 and kurtosis 1.347. The Kolmogorov-Smirnov D test = 0.0185 Pr > D <0.0100. So, strictly speaking this distribution departs significantly from normal. I assume that the reason for this has more to do with the (relatively) large sample, and that I probably should not worry. Nevertheless, being a worrier i would really appreciate some advice.

 

Many thanks in advance

 

Piers_C


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‎10-18-2016 05:02 AM
SAS Super FREQ
Posts: 3,475

Re: What consititutes a non-normal distribution of residuals?

As you say, the K-S test will reject for such as large sample. Clearly the residuals are symmetric, which is probably the most important feature. There is evidence of kurtosis, which could mean a heavier-tailed distribution of errors, but might also indicate slight heteroscedasity. 

 

Without seeing the data, this looks like a good fit. If these were my data, I would plot residuals versus explanatory variables. Do any of the patterns of residuals look "fan shaped"?

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‎10-18-2016 05:02 AM
SAS Super FREQ
Posts: 3,475

Re: What consititutes a non-normal distribution of residuals?

As you say, the K-S test will reject for such as large sample. Clearly the residuals are symmetric, which is probably the most important feature. There is evidence of kurtosis, which could mean a heavier-tailed distribution of errors, but might also indicate slight heteroscedasity. 

 

Without seeing the data, this looks like a good fit. If these were my data, I would plot residuals versus explanatory variables. Do any of the patterns of residuals look "fan shaped"?

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