F ratio

Definition

The F-ratio is a statistic used to compare the variances between groups in ANOVA. 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 $F = \frac{MS_{between}}{MS_{within}}$, where $MS$ stands for Mean Square.
2. A larger F-ratio indicates greater variability between group means relative to within-group variability.
3. The F-distribution varies depending on degrees of freedom, both for numerator (between groups) and denominator (within groups).
4. In one-way ANOVA, a significant F-ratio suggests that at least one group mean is different from the others.
5. The critical value of F depends on the chosen level of significance (alpha), typically 0.05 or 0.01.

Review Questions

• What does a large F-ratio indicate in an ANOVA test?
• How do you calculate the F-ratio?
• What does it mean if your calculated F-ratio exceeds the critical value?

Related terms

ANOVA: Analysis of Variance, a statistical method used to test differences between two or more means by analyzing variance.

Degrees of Freedom: Values that specify which specific distribution to use when looking up critical values; they depend on sample size.

Mean Square: An average of squared deviations, calculated separately for between-group and within-group variations in ANOVA.