F-test, F-Distribution

The F-test

The F-test is designed to test the hypothesis that the variances calculated from two samples are estimates of the same population variance. It is valid when the samples are independent and the populations from which they are drawn are Normal.

The F-test for comparing two variances Example see: (referenced from http://www.gnome.org/projects/gnumeric/doc/ftest-two-sample-for-variances-tool.shtml)

Figure 6-31 Some Example Data

Example 6-7 Using the F-Test Tool

Figure 6-31 shows some example data and Figure 6-32 the corresponding output.

Figure 6-32 F-Test Tool Output

Thus, we accept the hypothesis.

F-Distribution:

The F distribution,also known as Snedecor's F distribution or the Fisher-Snedecor distribution, is related to the chi-square distribution. If X and Y and independent chi-square random variables with df m and n, then the ramdom variable is said to have the F distribution with m and n df, as below:

A random variate of the F-distribution arises as the ratio of two chi-squared variates:

where

• U₁ and U₂ have chi-square distributions with d₁ and d₂ degrees of freedom respectively, and


• U₁ and U₂ are independent (see Cochran's theorem for an application).

Fisher-Snedecor

Probability density function