One Way ANOVA Calculator

One-way ANOVA online. F table, p-value, eta squared and Tukey or Duncan post-hoc with letter grouping. Free, no signup.

When to use it

Use when experimental units are uniform (lab or greenhouse) and treatments are randomly assigned with no blocking. Simplest design for testing whether three or more group means differ. Equal or near-equal sample sizes per group keep the F test most robust to mild assumption violations.

When NOT to use it

Do not use a one-way CRD when units are arranged in natural blocks (field strips, days, batches) since unmodelled block variance inflates the error MS. In that case use RBD. Do not use when residuals are heavily non-normal at small n; use Kruskal-Wallis instead. For two groups only, prefer a t-test.

What you get

An ANOVA table (Source / df / SS / MS / F / p), grand mean, coefficient of variation (CV percent), eta-squared and omega-squared effect sizes, treatment means with standard errors, a residual diagnostic block (Shapiro-Wilk on residuals, Levene on group variances), and your choice of LSD / DMRT / Tukey HSD post-hoc with compact letter display.

Worked example

One-way CRD worked example, three groups of six observations.

a1: 6, 8, 4, 5, 3, 4
a2: 8, 12, 9, 11, 6, 8
a3: 13, 9, 11, 8, 7, 12

Expected output: F = 9.265, p = 0.00240 (df 2, 15)

Source: Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods, 8th ed. Iowa State UP, ch. 12 (one-way completely randomised design). Cross-checked vs R 4.6.0 stats::aov.

How to interpret the output

If p is below your chosen alpha (typically 0.05) the null of equal means is rejected. Read the post-hoc letter display to see which specific groups differ: groups sharing a letter are not significantly different. CV percent under roughly 10 percent is good for cereal-yield trials, under 15 percent for vegetables (Gomez and Gomez 1984). A non-significant F is not proof of equality; report the effect size and consider a TOST equivalence test.

Common pitfalls

Forgetting to check the Shapiro-Wilk p on residuals before reading the F.
Ignoring Levene's test when group sizes are very unequal; switch to Welch ANOVA if Levene is significant.
Reporting only F without the degrees of freedom (write F(2, 15) = 9.27, p = 0.0024).
Choosing DMRT for international journals where Tukey HSD is the expected family-wise control.

Try it in StatVeda

The CRD engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.

Open CRD

References

Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.
Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods, 8th edition. Iowa State University Press, Ames.
Gomez, K. A. and Gomez, A. A. (1984). Statistical Procedures for Agricultural Research, 2nd edition. John Wiley and Sons, New York.