T-test for the comparison of standard deviations

The significance tests described so far are used for comparing means, and hence for detecting systematic errors. In many cases it is also important to compare the standard deviations, i.e. the random errors of two sets of data. As with tests on means, this comparison can take two forms. Either we may wish to test whether Method A is more precise than Method B (i.e. a one-sided test) or we may wish to test whether Methods A and B differ in their precision (i.e. a two-sided test). For example, if we wished to test whether a new analytical method is more precise than a standard method, we would use a onesided test if we wished to test whether two standard deviations differ significantly (e.g. before applying a t-test - see Section 3.3 above), a two-sided test is appropriate. 

The F-test considers the ratio of the two sample variances, i.e. the ratio of the squares of the standard deviations, s s.  

In order to test whether the difference between two sample variances is signifi- 

The numbers of degrees of freedom of the numerator and denominator are - 1 and 2 - 1 respectively. 

The test assumes that the populations from which the samples are taken are normal. 

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