Softonic

ANOVA Calculator

Step 1 / 4 F-statistic
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Paste two or more groups of numbers and the calculator runs a one-way ANOVA to test whether the group means differ significantly. It returns the F-statistic, degrees of freedom, mean squares and sums of squares, the standard values any ANOVA table would report. Compare your F against the critical values table on this page to judge significance at your chosen alpha.

How to run a one-way ANOVA

  1. 1

    Enter group data

    Paste each group as a comma- or newline-separated list. Minimum two groups; at least 3-5 observations per group is recommended.

  2. 2

    Check assumptions

    One-way ANOVA assumes normally-distributed residuals and roughly equal variance across groups. Flag if your groups have wildly different spreads.

  3. 3

    Read the F-statistic

    F is the ratio of between-group variance to within-group variance. Larger F means stronger evidence of group differences.

  4. 4

    Compare with the critical F

    Look up the critical F for your degrees of freedom at your chosen alpha (usually 0.05). If your computed F is larger, reject the null hypothesis that all group means are equal. ANOVA does not tell you which groups differ: use a post-hoc test for that.

The ANOVA table

Source SS (sum of squares) df MS (mean square) F
Between groups SSB k - 1 MSB = SSB/(k-1) MSB/MSW
Within groups SSW N - k MSW = SSW/(N-k)
Total SST = SSB + SSW N - 1

Where k = number of groups, N = total observations.

F-distribution critical values (alpha = 0.05)

df1 \ df2 10 20 30 60 120
2 4.10 3.49 3.32 3.15 3.07
3 3.71 3.10 2.92 2.76 2.68
4 3.48 2.87 2.69 2.53 2.45
5 3.33 2.71 2.53 2.37 2.29

If your computed F exceeds the table value for your df1 (= k-1) and df2 (= N-k), reject the null at p < 0.05.

Assumptions to verify before citing ANOVA

  1. Independence of observations within and between groups.
  2. Normality of residuals (Shapiro-Wilk test, or visual: Q-Q plot).
  3. Homogeneity of variance (Levene’s test, or rule of thumb: largest SD is less than 2× smallest SD).

If normality fails: Kruskal-Wallis test is the non-parametric alternative. If homoscedasticity fails: Welch’s ANOVA handles unequal variances.

After a significant ANOVA: post-hoc tests

One-way ANOVA tells you some groups differ but not which. Follow up with:

  • Tukey HSD, conservative, controls family-wise error rate.
  • Bonferroni, simple adjustment: α / number of comparisons.
  • Scheffé, flexible but low power; good for exploratory analysis.
  • Dunnett, only compares each treatment to a control group.

Effect size

A significant p-value says “there is a difference.” Effect size says “how big.” Report eta-squared (η²) = SSB / SST. Rough guide: 0.01 small, 0.06 medium, 0.14 large.

Frequently Asked Questions

If you have three or more groups. Running multiple t-tests inflates the family-wise Type I error rate (α of 0.05 across three pairwise tests becomes roughly 0.14). ANOVA keeps the overall alpha at 0.05.

One-way has a single grouping factor (e.g. treatment type). Two-way has two factors (e.g. treatment × sex) and can test main effects plus interaction. This calculator handles the one-way case.

Statistically, no, they are almost identical. The 0.05 threshold is a convention, not a physical constant. Report the exact p-value and effect size so readers can judge, rather than treating 0.05 as a sharp cut-off.

Small samples produce unstable F values. A huge F on n=3 per group is suggestive but should be replicated. Report confidence intervals around group means alongside the F.

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