## Normal Probability Plots - Testing for Normality

Suppose we have n observations– which we assume are in ascending order - and we want to know whether they could have arisen from a normal distribution. We plot the data points against the corresponding standard normal quantilesgiven byforIf the data is from a normal population then the pointsshould lie approximately on a straight line. This is called anormal probability plot and is especially suited to small data sets.

Example:

We have some silver coins from ancient Byzantine. We want to test whether the % silver content follows a normal distribution.

 5.9 6.8 6.4 7 6.6 7.7 7.2 6.9 6.2

First arrange the data in order.

 5.9 6.2 6.4 6.6 6.8 6.9 7 7.2 7.7

Now find the quantiles:etc.

 1 2 3 4 5 6 7 8 9 5.9 6.2 6.4 6.6 6.8 6.9 7 7.2 7.7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -1.282 -0.842 -0.524 -0.253 0 0.253 0.524 0.842 1.282

Plot the points

The correlation coefficient () indicates a very good fit to a straight line, hence we may take the silver content as normally distributed.