topic Re: Negatively skewed data in Discussions

Negatively skewed data

StacyKJones — Sat, 13 Jul 2024 21:22:59 GMT

I am trying to run a multiple regression test in JMP, but my residual data did not meet the distribution assumption. Skewness was -1.21, and kurtosis was 4.52, so my data is negatively skewed. How do I proceed? (I'm somewhat of a newbie.) We haven't learned about transformations such as log or square root. I tried both of these by adding them separately as formulas for the residual data column, but all I got was unworkable dots in the column.

Re: Negatively skewed data

dlehman1 — Sun, 14 Jul 2024 13:01:14 GMT

I assume you did a multiple regression analysis (the word "test" here is a strange use of that term). If so, the first thing I would say is that your residuals do not look that worrisome. Multiple regression assumptions are very forgiving - they are rarely satisfied but it usually doesn't matter much. However, to the extent that your residuals are skewed, it is natural to try a log transformation. The easiest way to do that is when you put your Y variable in the box for the response variable, click on the drop down next to "Transform" in that window and ask for the log. Then use the same Model Effects that you were using.

My guess is that the log transform may not improve things much here since the residuals had a negative skew (I think they would be more appropriate for a positive skew). So, you could try some of the other transformations. However, as I said, I don't think your residuals look that much in need of modifying the model. I'd look at the other aspects of your model (are the coefficients for the effects significant and do they make sense? is the overall model fit good? what other data do you have that you did not use? what does the residual plot look like - is the scatter reasonably random?) before worrying too much about the distribution of the residuals.

Re: Negatively skewed data

txnelson — Sun, 14 Jul 2024 13:21:32 GMT

You might want to look into a Box-Cox transformation

Re: Negatively skewed data

shampton82 — Sun, 14 Jul 2024 20:08:29 GMT

Hey @StacyKJones, I second what @txnelson suggested with the Box Cox option being located here:

Not only will this find the best transformation, you can refit the model as a new analysis window so you can compare both models to see how the transformation improved it. Also, it keeps the units in the original units for profiler which is nice.

Steve

Re: Negatively skewed data

P_Bartell — Mon, 15 Jul 2024 11:10:43 GMT

The only other thing I'll add to both @dlehman1 and @txnelson 's responses (with which I concur) are, let's for the moment forget about statistics. And deal with practicality. If at the end of the day, if you can solve/resolve the practical problem with the model you ended up with...who cares about statistics? I came from industry as a practicing statistician...the teams I was on were paid to solve problems...not get perfect models that satisfied all 'assumptions' associated with various statistical methods.