F-statistic Calculator
Enter between-group and within-group sums of squares with their degrees of freedom to evaluate the F-statistic.
Mean square between (MSB): 8.1667
Mean square within (MSW): 1.6722
F-statistic: 4.8837
Right-tailed p-value: 0.005974
How to Use This Calculator
- Provide sums of squares from your ANOVA table (between and within).
- Enter the associated degrees of freedom (groups − 1 and N − groups).
- Review mean squares, F-statistic, and the right-tailed p-value.
- Compare the p-value with your significance level to decide whether to reject the null hypothesis of equal means.
Formula
MSB = SSbetween / dfbetween
MSW = SSwithin / dfwithin
F = MSB / MSW
p-value = P(Fdf₁,df₂ ≥ observed F)
Full Description
The F-statistic compares between-group variance to within-group variance. Large values suggest group means differ more than expected under the null hypothesis. This calculator derives the F-statistic from ANOVA components and uses the F distribution to compute p-values.
Frequently Asked Questions
Can SS or df be zero?
No. Zero values invalidate the F-statistic. Ensure each group has at least two observations overall.
Is the p-value one-tailed or two-tailed?
ANOVA uses a right-tailed test because the F distribution is non-negative and asymmetric.
Can I obtain critical values?
Use the reported df with a critical value calculator or F tables to find threshold values for chosen α.
Does this support repeated-measures designs?
No. Provide sums of squares and df from the appropriate ANOVA table for your design before using this tool.