F ratio

Definition

The F-ratio is a statistical measure used to compare variances between groups in an ANOVA test. It is the ratio of the variance between group means to the variance within the groups.

5 Must Know Facts For Your Next Test

1. The F-ratio is calculated as $\frac{MS_b}{MS_w}$, where $MS_b$ is the mean square between groups and $MS_w$ is the mean square within groups.
2. A high F-ratio indicates that the group means are significantly different from each other.
3. The F-ratio follows an F-distribution under the null hypothesis.
4. Degrees of freedom for the numerator (between groups) and denominator (within groups) are required to determine the critical value from F-distribution tables.
5. The F-ratio is used in One-Way ANOVA to test if there are any significant differences among group means.

Review Questions

• How do you calculate the F-ratio?
• What does a high F-ratio indicate about group means?
• What distribution does the F-ratio follow under the null hypothesis?

Related terms

ANOVA:

Analysis of Variance, a statistical method used to compare means across multiple groups.

$MS_b$: $Mean\ Square\ Between$, which measures variation due to interaction between different sample means.

$MS_w$: $Mean\ Square\ Within$, which measures variation within individual samples.