F Distribution Table
The F table provides critical values for the F-distribution, which is commonly used in analysis of variance (ANOVA), comparing variances, and testing the overall significance of regression models.
How to Use the F Table
- Select your desired significance level (α) from the dropdown menu
- Find your numerator degrees of freedom (df₁) in the leftmost column
- Locate your denominator degrees of freedom (df₂) in the top row
- The intersection gives you the critical F-value for your test
- Hover over any value to visualize the corresponding area in the F-distribution chart
Important Notes
- The table shows critical values for right-tailed tests (most common for F-tests)
- Numerator df₁ = number of groups - 1 (for one-way ANOVA)
- Denominator df₂ = total sample size - number of groups (for one-way ANOVA)
- The F-distribution is always positive and right-skewed
- As both df₁ and df₂ increase, the distribution becomes more symmetric
Common Applications
- Analysis of Variance (ANOVA) for comparing means of multiple groups
- Testing equality of variances between populations
- Assessing overall significance in multiple regression analysis
- Model comparison in statistical modeling
Reading F Critical Values
If your calculated F-statistic exceeds the critical value from the table:
- Reject the null hypothesis (H₀)
- Conclude there are significant differences between groups
- The probability of this occurring by chance is less than your chosen α level