F distribution

Definition

The F distribution is a continuous probability distribution that arises frequently as the null distribution of a test statistic, especially in ANOVA. It is defined by two parameters: the degrees of freedom for the numerator and the denominator.

5 Must Know Facts For Your Next Test

1. The F distribution is used to compare variances between groups.
2. It is asymmetric and skewed to the right, becoming more symmetric as sample sizes increase.
3. Degrees of freedom for the numerator come from the number of groups minus one, while degrees of freedom for the denominator come from total observations minus number of groups.
4. The critical values for an F-test are found using F-tables or statistical software.
5. In ANOVA, a high F-ratio suggests that at least one group mean is different from others.

Review Questions

• What are the degrees of freedom in an F distribution?
• How does the shape of the F distribution change with increasing sample size?
• What does a high F-ratio indicate in an ANOVA test?

Related terms

ANOVA: Analysis of Variance (ANOVA) is a statistical method used to compare means across multiple groups to determine if at least one group mean differs significantly.

F-Ratio: The F-Ratio is a test statistic calculated as the ratio of variance between group means to variance within groups.

Degrees of Freedom: Degrees of Freedom refer to the number of independent values or quantities that can vary in an analysis without breaking any constraints.