One-Way ANOVA Calculator with Tukey HSD

One-way ANOVA tests whether the means of three or more independent groups differ, for example exam scores under three teaching methods. This calculator gives you the descriptives, the full ANOVA table (sums of squares, df, mean squares, F, p), eta squared and omega squared, and Tukey HSD post hoc comparisons (Tukey-Kramer when group sizes differ), with an APA 7 paragraph that names the groups that differ.

How to use this calculator

  1. Put each group in its own column (groups can have different sizes).
  2. Copy the columns, ideally with group names in the first row, and paste them.
  3. Click Calculate.
  4. If the ANOVA is significant (p < .05), read the Tukey HSD table to see which pairs of groups differ.
  5. Copy the APA paragraph, which includes the post hoc results.

Formula

SS_between = Σ nⱼ (Mⱼ − M)²       df_between = k − 1
SS_within  = Σ Σ (x − Mⱼ)²        df_within  = N − k
F = MS_between / MS_within        η² = SS_between / SS_total

Tukey HSD: q = |Mᵢ − Mⱼ| / √[(MS_within / 2)(1/nᵢ + 1/nⱼ)]

Step-by-step example

  1. Three teaching methods: A (n = 6, M = 78.50), B (n = 7, M = 87.29), C (n = 7, M = 71.00).
  2. SS between = 930.02, SS within = 96.93.
  3. F(2, 17) = (930.02/2) / (96.93/17) = 81.56, p < .001, η² = .91.
  4. Tukey HSD: all three pairs differ significantly (p < .001).

How to interpret the results

A significant F (p < .05) tells you that at least two group means differ, but not which ones. The Tukey HSD table answers that: pairs marked Significant = Yes differ after controlling the family-wise error rate at .05. Eta squared shows the proportion of variance explained by group membership: about .01 is small, .06 medium and .14 large (Cohen, 1988). Omega squared is a less biased version, useful for small samples.

How to report it in APA 7 style

A one-way between-groups ANOVA showed a statistically significant difference in exam scores between the three teaching methods, F(2, 17) = 81.56, p < .001, η² = .91. Tukey HSD post hoc comparisons indicated that all three methods differed significantly from each other (all ps < .001).

Statistical symbols (t, F, p, r, M, SD, N, d) should be italicised in your thesis.

Assumptions

  • The dependent variable is continuous.
  • Groups are independent (different participants in each group).
  • The dependent variable is approximately normal in each group.
  • Homogeneity of variances across groups (if violated, consider Welch’s ANOVA with Games-Howell post hoc tests).
  • No extreme outliers.

How to do it in SPSS, R or Excel

SPSS: Analyze → Compare Means → One-Way ANOVA → Post Hoc → Tukey. R: TukeyHSD(aov(y ~ group)). Python: statsmodels.stats.multicomp.pairwise_tukeyhsd, which ScholarCalc’s Tukey results were validated against.

Roman Urdu mein khulasa

One-way ANOVA teen ya zyada groups ke averages aik saath compare karta hai, jaise teen teaching methods. Har group ko Excel ke alag column mein rakh kar paste karein. Agar p 0.05 se kam ho to kam az kam do groups mein farq hai. Kaun se groups mukhtalif hain, ye Tukey HSD table batata hai: jahan Significant = Yes likha ho. η² batata hai ke farq kitna bara hai.

Frequently asked questions

What is the difference between ANOVA and a t test?

A t test compares two means. ANOVA compares three or more means in a single test, which avoids the inflated error rate of running many t tests.

Why do I need a post hoc test?

A significant ANOVA only says that the group means are not all equal. A post hoc test such as Tukey HSD tells you which specific pairs of groups differ while controlling the overall Type I error rate.

Does Tukey HSD work with unequal group sizes?

Yes. With unequal sizes the calculator uses the Tukey-Kramer adjustment, which is the same method SPSS and statsmodels use.

Should I run Tukey if the ANOVA is not significant?

Generally no. If the overall F test is not significant you normally report that and stop. The calculator still shows the Tukey table for completeness.

What effect size should I report for ANOVA?

Eta squared (η²) is the most commonly reported effect size for one-way ANOVA. Omega squared (ω²) is less biased and is preferred by some journals, especially for small samples.

How do I report a one-way ANOVA in APA?

Report F(df_between, df_within) = value, p = value, η² = value, followed by the post hoc results, e.g. F(2, 17) = 81.56, p < .001, η² = .91.

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Cite this calculator

If ScholarCalc helped your analysis, you can cite it in APA 7 format:

ScholarCalc. (2026). One-Way ANOVA Calculator with Tukey HSD [Web application]. https://scholarcalc.com/one-way-anova-calculator/

Written and maintained by the ScholarCalc team. Last reviewed: November 2026.

Accuracy: results are computed in your browser and were validated against Python scipy, statsmodels and pingouin on test datasets. See Methodology and accuracy.