Statistical Methods

Unit 8 - F-Distribution

8.1.Introduction
In the t-tests on paired and unpaired samples we had to assume that the two samples came from the same Normal Distribution. We were testing that the means were the same but still had to assume that standard deviation were the same. We can test whether this assumption is correct by using F- test is due to Snedecor.

If the standard deviations are the same then we would expect sample standard deviations to be similar i.e. s₁=s₂ or more precisely,
This can be written as σ₁²/ σ₂² =1
That is we can test for the closeness of this ratio to 1
The Variance ratio or F-Test formalises these ideas:
The ratio of variances (s₁²/ s₂²) of independent samples taken from a normal population follows a distribution called F-distribution with two degrees of freedom one for numerator and the other for denominator.