# Visual inspection versus Shapiro-Wilk test for normality

I have a data set which gives a p value of $$9.661\times10^{-7}$$ under the Shapiro-Wilk test - in other words not very normal.

But the common advice is use visual inspection and the qq Plot for this data set is as below and it looks sufficiently normal - especially at the top end (which is what I am interested in).

My question is: how safe is it to look at this sort of visual display and say that, because the top end looks normal I am ok to base calculations about the behaviour of the right side of the distribution on that assumption?

• How many data do you have? (At least 260, I'm guessing.) What are these data? Why does there seem to be a floor? What is it that you really want such that you only care about the top end? Commented Jan 28, 2019 at 20:55
• The data is about times a benchmark takes to complete a task in a complex computing system. In this case I have 3085 observations but I am seeking a general answer if possible - I am interested in the top end because I want to apply statistical methods to estimate worst case execution times. Commented Jan 28, 2019 at 20:58
• @gung I would have guessed approximately $-1/2 / \Phi^{-1}(-3.6)\approx 3150$ observations because the most extreme "norm quantiles" are near $\pm 3.6.$
– whuber
Commented Jan 28, 2019 at 22:49
• Do not interpret p-value as effect size. "- in other words not very normal". With large samples you may have very low p-values with small effect sizes. Commented Jan 29, 2019 at 7:29