方差分析F统计量计算器 — 公式

One-Way ANOVA F-Test

ANOVA tests whether the means of two or more groups are significantly different by comparing between-group variance to within-group variance.

Formula

F = MSB / MSW

where MSB = SSB/(k-1) is the mean square between groups and MSW = SSW/(N-k) is the mean square within groups. A large F indicates that group means differ more than expected by random chance.

计算示例

MSB = 120, MSW = 30, k = 4 groups, N = 40 total observations.

  1. F = 120 / 30 = 4.000
  2. df1 = 4 - 1 = 3, df2 = 40 - 4 = 36
  3. Critical F(3,36) at alpha=0.05 ≈ 2.87
  4. F = 4.0 > 2.87, so groups differ significantly