ANOVA F-value

Analysis of Variance compares group means by partitioning variability into between-group and within-group components. The test statistic is F = MSB ÷ MSW with degrees of freedom (k−1, N−k).

Key Inputs

• SSB: between-group sum of squares
• SSW: within-group sum of squares
• dfb = k − 1 where k is number of groups
• dfw = N − k where N is total observations

Computation

• MSB = SSB ÷ dfb
• MSW = SSW ÷ dfw
• F = MSB ÷ MSW with df = (dfb, dfw)

Interpretation

Larger F indicates group means differ beyond random variability. Compare F to the F distribution with (dfb, dfw) or compute a p-value. If p ≤ α, reject equal-means hypothesis.

• Assumptions: independent observations, normality within groups, equal variances
• Post-hoc tests identify which groups differ when the overall test is significant

Example

Suppose SSB = 24.5, SSW = 120.3, dfb = 3, dfw = 48. Then MSB = 8.1667, MSW = 2.5063, F ≈ 3.259. Evaluate against F(3,48) to obtain the p-value.

Related tools: F-distribution mean, p-value, ANOVA power.