If the Normal Distribution Is So Normal, How Come My Data Never Are?

Andrew J. Vickers, PhD

Disclosures

May 08, 2007

In This Article

How Normal Is Normal?

One of the first data sets that I looked at when I was learning statistics had a number of missing observations. I was told that this was totally normal. I also noticed that the main endpoint followed the bell-shaped curve that is often described as a "normal distribution." This, I was told, was not normal at all; indeed, one of my lecturers became rather excited, commenting, "They say it never happens, but look, here is an example, which just goes to show that you can get a normal curve." I think what they were trying to tell me was that it wasn't normal to get normal data. Nonnormality seemed to be the norm, but I couldn't be sure.

The fact that I then decided to become a statistician no doubt raises some interesting characterological questions, but here I am, and here are some data that I have been reviewing. This graph shows the distribution of prostate-specific antigen levels in men undergoing surgery for prostate cancer.

Distribution of prostate-specific antigen levels in men undergoing surgery for prostate cancer.

And, just for the sake of it, here are data from a totally different area of medicine: These are baseline pain scores from a headache trial.

Baseline scores of patients in a headache trial.

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