RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Computing F-ratio

The F-ratio is used to determine whether the variances in two independent samples are equal. If the F-ratio is not statistically significant, you may assume there is homogeneity of variance and employ the standard t-test for the difference of means. If the F-ratio is statistically significant, use an alternative t-test computation such as the Cochran and Cox method.

Set the Rejection Criteria

Determine the "degrees of freedom" for each sample

df = n1 - 1 (numerator = n for sample with larger variance)

df = n2 - 1 (denominator = n for sample with smaller variance)

Determine the level of confidence -- alpha

Compute the test statistic

where

= largest variance

= smallest variance

Compare the test statistic with the f critical value (Fcv) listed in the F distribution. If the f-ratio equals or exceeds the critical value, the null hypothesis (Ho)

(there is no difference between the sample variances) is rejected. If there is a difference in the sample variances, the comparison of two independent means should involve the use of the Cochran and Cox method.

Example