ISO 5479:1997

This International Standard gives guidance on methods and tests for use in deciding whether or not the hypothesis of a normal distribution should be rejected, assuming that the observations are independent.

Whenever there are doubts as to whether the observations are normally distributed, the use of a test for departure from the normal distribution may be useful or even necessary. In the case of robust methods, however (i.e. where the results are only altered very slightly when the real probability distribution of the observations is not a normal distribution), a test for departure from the normal distribution is not very helpful. This is the case, for example, when the mean of a single random sample of observations is to be checked against a given theoretical value using a t-test.

It is not strictly necessary to use such a test whenever one refers to statistical methods based on the hypothesis of normality. It is possible that there is no doubt at all as to the normal distribution of the observations, whether theoretical (e.g. physical) reasons are present which confirm the hypothesis or because this hypothesis is deemed to be acceptable according to prior information.

The tests for departure from the normal distribution selected in this International Standard are primarily intended for complete data, not grouped data. They are unsuitable for censored data.

The tests for departure from the normal distribution selected in this International Standard may be applied either to observed values or to functions of them, such as the logarithm or the square root.

Tests for departure from the normal distribution are very ineffective for samples of size less than eight. Accordingly, this International Standard is restricted to samples of eight or more.