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

  1. Provide sums of squares from your ANOVA table (between and within).
  2. Enter the associated degrees of freedom (groups − 1 and N − groups).
  3. Review mean squares, F-statistic, and the right-tailed p-value.
  4. 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.