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

0.000

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.