*F* – Test

The *F*-test is used to test for differences among sample variance. Like the
Student's *t*, one calculates an *F* and compares this to a table value.

The formula for *F* is simply

The variance are arranged so that *F*>1. That is; *s*_{1}^{2}>*s*_{2}^{2}.

We use the *F*-test as the Student's *t* test, only we are testing for
significant differences in the variances.

1) Invoke the null hypothesis that states that the two variances we are comparing are
from the same population. (*i.e*., they are not statistically different)

2) Calculate the *F* value (the ratio of the two variances)

3) Look up the table value of *F* for the degrees of freedom used to calculate
both variances and for a given confidence level.

4) If the calculated *F* is greater than the table value, then the null hypothesis
is not correct. Else, the two could have come from the same population of measurements.

This page was created by Professor Stephen Bialkowski, Utah State University.

*Tuesday, August 03, 2004*