Histogramm vs. Shapiro – Wilk Test for normality

[Christopher Helmreich]

Hello,

In my data I have variables that shwon in a histogramm look more or less like a normal distribution, which makes me happy. Unfortunately, the Shapiro – Wilk test for normality always says, that I must reject the hypothesis that the variables follow a normal distribution.

What could be a reason for this?

Thank you!

Christopher

[Nick Cox]

Many possibilities. One is that your "looks like" impression is wrong. Another is that Shapiro-Wilk is just telling you that you have a large enough sample to detect a small difference from normality, which may or may not be important.

Neither answers the real question, which is whether your distributions are sufficiently different from the normal to have an impact on what you intend to do with the data? Poor textbooks and courses often convey the impression that most statistical methods require normal marginal distributions, but really very little does.

[Jorrit Gosens]

One reason could be there's a bell curve shape but with either fat or slim tails. Not to worry too much, as Nick indicates.

[Marcos Almeida]

Another reason (just to underline an interesting aspect of the matter), is the bin size, that is, the way you split your data under intervals.

[Nick Cox]

The best single graphic for checking normality in my view is qnorm. See also qenv (SSC).

[Svend Juul]

Some people prefer to look at histograms (I do). Adding a normal curve and a kernel density curve helps a lot to see what is going on:

histogram varname , normal kdensity

[Maarten Buis]

If you want to compare a histogram with a nomal curve, then it is often easier to see patterns in a hanging rootogram rather than a histogram with a normal curve. A hanging rootogram is a histogram "hung" from the normal curve. This way the deviations are shown as deviations from the horizontal line y=0. Several examples can be seen here: http://maartenbuis.nl/software/hangroot.html

[Christopher Helmreich]

Many thanks!