Shapiro wilk effect size?


Well-Known Member

Like any other test, using only the Shapiro-Wilk p-value is sometimes useless., especially with a large sample size ...
I did some searches and didn't find any suggested way to calculate the SW effect size. (and interpretation)

Usually, the direction is to run the SW test (or other) and estimate the effect size by the QQ plot. (a subjective way ...)

Do you know any suggested way to calculate the effect size? (the effect size of the deviation from normality )

If not, I thought about something like running a linear regression over the QQ-plot data, and calculate the effect using the R squared

Effect = 1- R-Squared


PS I know some wise people think it is useless...
But I IMOHs effect size will add some contribution, at least some times


No cake for spunky
I suggest QQ plots.

There are frequent complaints about the validity of test of normality given any degree of power. The QQ plot is not that subjective, its usually obvious if the data is normal or not.

I don't think the effect size of the test you are interested is substantively important.


Well-Known Member
Hi Noetsi :)

I agree that the combination of SW and QQ plot is good, but the QQ plot is not subjective. (maybe it is not so critical to be ...)

I the R square of the QQ plot good as an effect size of the normality test?
or better: 1- R-Squared, as we want to see the non-normal effect?


No cake for spunky
I just look at the lines in QQ plots not the R squared. I did not realize that even mattered until now.

But this reminds me of a conversation on another board. I was asking about how to test non linearity. I liked Box Tidwel because it had a p value and thus was concrete to me. But many posters held out for analyzing the residuals which seemed too subjective to me. Now that you know something is non-linear or non-normal (as with a formal test) what do you really know was their point. You know better how non-normal something is with residuals.

There are some, many, who argue all real world data is non-normal unless you make it up. And the longer I do analysis the less important normality seems. It does not bias the results only the p values. If you have a few hundred cases your results probably asymptotically correct regardless if you sampled correctly (or have the whole population as I do).

Bias not normality is my concern.


Well-Known Member
I agree with you, it is also better to use a test for linearity, instead of just looking at a chart :)

Yes, in many cases the normality is not so important.