One-way ANOVA example: plant dry weight
Compare a control and two treatments.
ANOVA Calculator
FigranPaste your groups to get the ANOVA table, post hoc tests and a graph with brackets or letters.
- One-way, Welch or Kruskal–Wallis
- Tukey, Dunnett, Games–Howell, Dunn
- Graph with brackets or letters
Data
Test
Options
p = 0.016
One-way ANOVA F(2, 27) = 4.85 · η² = 0.26 · 1 of 3 pairs differ (Tukey)
ANOVA table
| Source | SS | df | MS | F | p |
|---|---|---|---|---|---|
| Between groups | 3.77 | 2 | 1.88 | 4.85 | 0.016 |
| Within groups | 10.49 | 27 | 0.39 | — | — |
| Total | 14.26 | 29 | — | — | — |
Post hoc comparisons
| Comparison | Difference | Lower | Upper | p | p < α |
|---|---|---|---|---|---|
| trt1 – ctrl | −0.37 | −1.06 | 0.32 | 0.39 | No |
| trt2 – ctrl | 0.49 | −0.20 | 1.19 | 0.20 | No |
| trt2 – trt1 | 0.87 | 0.17 | 1.56 | 0.012 | Yes |
Descriptive statistics
| Group | n | Mean | SD | SEM | 95% CI | Median | Q1 | Q3 | Min | Max |
|---|---|---|---|---|---|---|---|---|---|---|
| ctrl | 10 | 5.03 | 0.58 | 0.18 | [4.61, 5.45] | 5.15 | 4.55 | 5.29 | 4.17 | 6.11 |
| trt1 | 10 | 4.66 | 0.79 | 0.25 | [4.09, 5.23] | 4.55 | 4.21 | 4.87 | 3.59 | 6.03 |
| trt2 | 10 | 5.53 | 0.44 | 0.14 | [5.21, 5.84] | 5.44 | 5.27 | 5.73 | 4.92 | 6.31 |
Effect sizes
| η² | 0.26 (95% CI [0.0099, 0.46]) |
|---|---|
| ω² | 0.20 |
Assumption checks
| Test | Statistic | p |
|---|---|---|
| Levene (median) | F = 1.12 | 0.34 |
| Residual Shapiro–Wilk | W = 0.97 | 0.44 |
| Maximum/minimum SD | 1.79 | — |
Use these as a description, not as a gate for choosing the test.
Report
Results
One-way ANOVA: F(2, 27) = 4.85, p = .016, η² = .26. trt2 versus trt1: difference 0.87, 95% CI [0.17, 1.56], p = .012. Remaining pairs had p = .20 or larger.
Methods
Groups were compared using one-way ANOVA followed by Tukey’s HSD (α = 0.05).
ANOVA calculator examples
Explore common designs and load an example into the calculator.
Compact letters: chick weight by feed
Compare six feeds with compact letters.
Welch’s ANOVA and Games–Howell: insect sprays
Compare sprays with unequal variation.
Kruskal–Wallis test: ozone by month
Compare skewed ozone measurements by month.
Dunnett’s test: blanket recovery vs standard
Compare treatments with the standard blanket.
From mean, SD and n: warp breaks by tension
Calculate from summary statistics.
ANOVA bar graph with stars: vitamin C dose
Show dose comparisons as a bar graph.
Kruskal–Wallis with small groups: mucociliary clearance
Compare three small samples by rank.
How to run a one-way ANOVA
From group values to a figure and report.
1Paste your groups
Enter raw values or mean, SD and n.
2Choose a test
Select one-way ANOVA, Welch or Kruskal–Wallis.
3Read the comparisons
Choose a post hoc test and review the results.
4Export your figure
Choose brackets or letters and download your figure.
Which ANOVA and post hoc test should I use?
Choose a test that matches your data and comparison.
| Data situation | Test | Post hoc | Effect | Default labels |
|---|---|---|---|---|
| Similar group variances | One-way ANOVA | Tukey (all pairs) | η² / ω² | Brackets |
| Compare treatments with a control | One-way ANOVA | Dunnett (vs control) | η² / ω² | Brackets |
| Different group variances | Welch ANOVA | Games–Howell | η² / ω² | Brackets |
| Ranked or strongly skewed data | Kruskal–Wallis | Dunn | ε² | Brackets |
Welch's ANOVA when SDs differ
Welch’s ANOVA allows unequal variances; Games–Howell provides all-pair comparisons without assuming a common variance.
Normality and equal variances
Independent observations and suitable residual distributions matter. Median-centered Levene is the Brown–Forsythe test; use checks as context, not as an automatic gate.
Brackets or letters
Brackets show individual comparisons. Groups sharing a letter have not been separated by the selected post hoc test at the chosen alpha.
References: Tukey (1953) · Kramer (1956) · Dunnett (1955) · Games & Howell (1976) · Dunn (1964) · Delacre et al. (2019) · Brown & Forsythe (1974) · Piepho (2004)
One-way ANOVA formulas
The table partitions variation within and between groups.
One-way ANOVA
SSbetween = Σ ni(x̄i − x̄)2 · SSwithin = Σ(ni − 1)si2
F = (SSbetween / (k − 1)) / (SSwithin / (N − k))
η² = SSbetween / SStotal · ω² = (SSbetween − (k − 1)MSwithin) / (SStotal + MSwithin)
Welch ANOVA
wi = ni / si² · F = [Σwi(x̄i − x̄w)² / (k − 1)] / [1 + 2(k − 2)B / (k² − 1)]
B = Σ (1 − wi / Σw)2 / (ni − 1)
Tukey
q = |x̄i − x̄j| / √[MSwithin(1/ni + 1/nj)/2]
For PlantGrowth, F = 1.883 / 0.389 = 4.85.
Rank tests
H = [12ΣniR̄i² / (N(N + 1)) − 3(N + 1)] / C
C = 1 − Σ(t³ − t) / (N³ − N) · z = (R̄i − R̄j) / √[(N(N + 1)/12 − Σ(t³ − t)/(12(N − 1)))(1/ni + 1/nj)]
References: Fisher (1925) · Welch (1951) · Kruskal & Wallis (1952)
ANOVA calculator FAQ
When should I use ANOVA instead of a t test?
Use ANOVA for three or more independent groups; a t test is often suitable for two. Multiple t tests inflate the family-wise error rate. For two groups, the ordinary ANOVA F equals Student’s t squared. t-test calculator.
Do I need a significant ANOVA before post hoc tests?
No. These procedures adjust the pairwise comparisons; report planned comparisons when only a few pairs matter.
What is the non-parametric alternative to one-way ANOVA?
Kruskal–Wallis compares rank distributions and can be followed by Dunn comparisons. Its p value here uses a chi-square approximation.
What are the assumptions of one-way ANOVA?
Observations should be independent, with approximately normal residuals and similar variances. Levene and Shapiro–Wilk checks provide context; Welch accommodates unequal variances. Power analysis calculator.
Should I report eta squared or omega squared?
Both describe effect size. Omega squared has less small-sample bias, while eta squared is commonly reported and equals R squared in one-way ANOVA. Effect size calculator.
How do I report one-way ANOVA results?
Report F with its degrees of freedom, the p value and an effect size, followed by the post hoc method and relevant comparisons.
Can I use this for repeated measures?
No. Repeated observations on the same participant require a repeated-measures analysis or a Friedman test; two time points may use a paired t test. t-test calculator.
Can I run a two-way ANOVA here?
No. This tool tests one factor. Two-factor designs require a model that includes the interaction.
Do the results match R and other software?
The one-way, Welch, Tukey and Kruskal–Wallis calculations follow the corresponding R methods. Levene variants can differ by their choice of center. Your data stay in your browser.