F test

An F test is used to examine and compare the different variances between different sets, or groups, of measurements or observations.  The F ratio that is generated by an ANOVA Table (calculated F) is compared to the F distribution value from the table (critical F) in the textbook determined by the degrees of freedom of the numerator (BG)and the denominator (WG) and the desired level of significance (α).  If the F ratio (from the ANOVA) is larger than the F distribution value given from the table, then you have proved that there is a significant difference (p < α) between the measurements of the groups.

*Note: "An F test tells us how sure we are that the groups are different." - Statmaster C

**Note: Remember to check these three things from an ANOVA:  significance (F test), effect size (eta squared or omega squared) and power (φ).

***Note: If homogeneity of variance is not proved, then the F test is invalid.

F test example problem

Perform an F test on the following observations to determine if there is a significant difference between the groups.