One-Way ANOVA Calculator
Test whether the means of three or more independent groups differ, then find which pairs differ with Tukey’s HSD.
Updated · By Bibin XavierData 90 × 12
| IDtext · 90 levels | Grouptext · 3 levels | Gendertext · 2 levels | Agenumeric | Hours_Studynumeric | Anxietynumeric | Motivationnumeric | Pre_Scorenumeric | Post_Scorenumeric | Exam_Scorenumeric | Passednumeric · coded | Satisfactionnumeric · coded |
|---|---|---|---|---|---|---|---|---|---|---|---|
| S001 | Control | Male | 23 | 11.2 | 29 | 4.6 | 60 | 62 | 67 | 1 | 2 |
| S002 | Workshop | Female | 23 | 3.9 | 28 | 3.5 | 54 | 70 | 54 | 0 | 2 |
| S003 | Online | Female | 18 | 10.1 | 32 | 4 | 55 | 57 | 66 | 0 | 3 |
| S004 | Control | Male | 26 | 13.6 | 41 | 3.5 | 52 | 55 | 59 | 0 | 3 |
| S005 | Workshop | Female | 22 | 9.7 | 27 | 3.6 | 56 | 63 | 65 | 0 | 4 |
| S006 | Online | Female | 20 | 7.9 | 32 | 3.8 | 65 | 82 | 65 | 0 | 2 |
| S007 | Control | Female | 20 | 6.3 | 28 | 3 | 72 | 83 | 61 | 0 | 3 |
| S008 | Workshop | Male | 22 | 8 | 29 | 3.1 | 64 | 72 | 62 | 1 | 3 |
Variables and options
Results
90 rows · example dataDescriptive statistics
| Group | n | M | SD | SE | 95% CI |
|---|---|---|---|---|---|
| Control | 30 | 61.03 | 10.34 | 1.89 | [57.17, 64.89] |
| Online | 30 | 65.53 | 9.75 | 1.78 | [61.89, 69.17] |
| Workshop | 30 | 68.70 | 11.93 | 2.18 | [64.25, 73.15] |
ANOVA
| Source | SS | df | MS | F | p | η² | ω² |
|---|---|---|---|---|---|---|---|
| Between groups | 890.56 | 2 | 445.28 | 3.88 | .024 | .082 | .060 |
| Within groups | 9978.73 | 87 | 114.70 | ||||
| Total | 10869.29 | 89 |
Note. Levene’s test: F(2, 87) = 0.93, p = .399. Welch’s F(2, 57.62) = 3.64, p = .033.
Tukey HSD post-hoc comparisons
| Comparison | Mean difference | SE | q | padj | 95% CI |
|---|---|---|---|---|---|
| Control − Online | -4.50 | 2.77 | 2.30 | .240 | [-11.09, 2.09] |
| Control − Workshop | -7.67 | 2.77 | 3.92 | .018 | [-14.26, -1.07] |
| Online − Workshop | -3.17 | 2.77 | 1.62 | .489 | [-9.76, 3.43] |
Note. Tukey-Kramer adjustment, valid for unequal group sizes.
Group means with 95% CI
Interpretation
Mean Post_Score differed significantly across the 3 groups, with a medium effect (η² = .082). Tukey tests showed significant differences between Control and Workshop.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). One-Way ANOVA Calculator [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/one-way-anova-calculator/
BibTeX
@software{xavier_onewayanova_2026,
author = {Xavier, Bibin},
title = {One-Way ANOVA Calculator},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/one-way-anova-calculator/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free One-Way ANOVA Calculator tool on FreeStatisticalTools.com (Xavier, 2026).”
What is a one-way ANOVA?
One-way analysis of variance (ANOVA) tests whether three or more independent group means differ. When the overall F test is significant, Tukey’s HSD shows which pairs of groups differ, while keeping the family-wise error rate at 5%.
When to use a one-way ANOVA
Use it to compare one continuous outcome across three or more independent groups.
Assumptions
- Independent observations.
- Approximately normal residuals in each group.
- Equal variances. If Levene’s test is significant, report Welch’s F and consider Games-Howell comparisons.
How to set up your data
Long format: one outcome column and one group column.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the dependent variable and factor (groups).
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report a one-way ANOVA in APA style
“Group had a significant effect on post-test scores, F(2, 87) = 6.12, p = .003, η² = .12. Tukey tests showed the Workshop group outscored Control (p = .002).”
Frequently asked questions
What does the F statistic in ANOVA mean?
F is the ratio of variance between group means to variance within groups. A large F with a small p-value means the group means differ more than chance would explain.
Which post-hoc test should I use?
Tukey’s HSD is the standard choice when variances are equal; this calculator uses the Tukey-Kramer version, which handles unequal group sizes. If Levene’s test is significant, report Welch’s F.
What is a good eta squared?
η² of .01 is small, .06 medium and .14 large (Cohen, 1988). Omega squared is a less biased estimate of the population effect.
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