F test

F test An F test is a type of statistical test that is used to determine if there are significant differences between the variances of two or more groups. It is named after the F-distribution, which is used to calculate the test statistic. The F test is commonly used in the context of analysis of variance (ANOVA), regression analysis, and hypothesis testing.

Overview

The F test compares the ratio of two variances to determine if they are significantly different from each other. The test statistic is calculated as:

F = \frac{S_1^2}{S_2^2}

where \( S_1^2 \) and \( S_2^2 \) are the sample variances of the two groups being compared. The resulting F value is then compared to a critical value from the F-distribution table, which depends on the degrees of freedom of the numerator and the denominator.

Applications

The F test is widely used in various statistical analyses, including:

• Analysis of variance (ANOVA): Used to compare the means of three or more groups.
• Regression analysis: Used to test the overall significance of a regression model.
• Hypothesis testing: Used to compare the variances of two populations.

Assumptions

The F test relies on several key assumptions:

• The samples are independent.
• The populations from which the samples are drawn are normally distributed.
• The variances of the populations are equal (homogeneity of variance).

Calculation

To perform an F test, follow these steps: 1. Calculate the sample variances (\( S_1^2 \) and \( S_2^2 \)). 2. Compute the F statistic using the formula \( F = \frac{S_1^2}{S_2^2} \). 3. Determine the degrees of freedom for the numerator (\( df_1 \)) and the denominator (\( df_2 \)). 4. Compare the calculated F value to the critical value from the F-distribution table.

Related Pages

• Analysis of variance
• Regression analysis
• Hypothesis testing
• F-distribution
• Statistical test
• Variance

See Also

• T-test
• Chi-squared test
• Z-test