BYTETOOLS

One-Way ANOVA Calculator

Build a complete one-way ANOVA table from pasted groups: sums of squares, degrees of freedom, mean squares, the F statistic, an exact p-value and eta squared.

9.26471
F statistic
2, 15
df (between, within)
0.002399
p-value
3.6823
Critical F (α = 0.05)

ANOVA table

SourceSSdfMSFp
Between groups842429.264710.002399
Within groups (error)68154.53333——
Total15217———

Reject the null hypothesis (p ≤ α = 0.05)

0.5526
η² (eta squared)
0.4787
ω² (omega squared)
8
Grand mean

Group summary

GroupnSumMeanSD
Group 163051.78885
Group 265492.19089
Group 3660102.36643

SSB = Σ nⱼ(x̄ⱼ − x̄)², SSW = Σ Σ (x − x̄ⱼ)², F = MSB / MSW, and p is the upper tail of the F distribution from the regularized incomplete beta function. A significant F says at least one group mean differs — it does not say which, so follow up with a post-hoc test.

Assumes independent observations, roughly normal residuals and similar variances between groups (6.0 values per group on average).

What is the One-Way ANOVA Calculator?

The ByteTools One-Way ANOVA Calculator compares the means of two or more groups in a single test. Paste one group per line, and the tool builds the standard ANOVA table: between-groups and within-groups sums of squares, degrees of freedom, mean squares, the F ratio and the p-value read from the F distribution.

  • Full ANOVA table with SS, df, MS, F and p
  • Handles unbalanced designs with different group sizes
  • Exact p-value from the F distribution, not a rounded table
  • Eta squared and omega squared effect sizes
  • Per-group n, sum, mean and standard deviation
  • 100% local — your data is never uploaded

How to use the One-Way ANOVA Calculator

  1. 1

    Paste your data with one group per line, values separated by spaces, commas or tabs.

  2. 2

    Add as many groups as you need — they can be different sizes.

  3. 3

    Pick your significance level alpha.

  4. 4

    Read the ANOVA table: SS, df, MS, F and the p-value.

  5. 5

    Check eta squared and the group summary below, then click Copy table.

About the One-Way ANOVA Calculator

The ByteTools One-Way ANOVA Calculator compares the means of two or more groups in a single test. Paste one group per line, and the tool builds the standard ANOVA table: between-groups and within-groups sums of squares, degrees of freedom, mean squares, the F ratio and the p-value read from the F distribution.

Group sizes do not have to match, so unbalanced designs work fine. Underneath the table you get eta squared and omega squared as effect sizes, the critical F at your chosen alpha, and a per-group summary of n, sum, mean and standard deviation so you can see which group is pulling the result.

All of the statistics are computed in your browser using a hand-written regularized incomplete beta function for the F tail, so the p-value agrees with R or SPSS rather than a rounded table. Nothing is uploaded, unpublished data stays on your own machine, and the page continues to work with no connection.

Frequently asked questions

What does a significant ANOVA result actually tell me?

It tells you that at least one group mean differs from the others, but not which one. That is why a significant F is normally followed by a post-hoc comparison such as Tukey's HSD, which tests the individual pairs while controlling the overall error rate.

Why not just run several t-tests instead of an ANOVA?

Every extra t-test adds another chance of a false positive, so comparing four groups pairwise means six tests and a real error rate far above 5%. ANOVA asks the whole question in one test at your stated alpha, which is why it is the standard first step.

What assumptions does one-way ANOVA make?

It assumes the observations are independent, the residuals are roughly normal and the groups have similar variances. It copes reasonably well with mild departures, especially when group sizes are close to equal, but strongly unequal variances call for Welch's ANOVA instead.

What is the difference between eta squared and omega squared?

Both describe how much of the total variation the group differences explain. Eta squared is simply SSB divided by SST and is slightly optimistic, while omega squared subtracts the variation you would expect by chance and is a less biased estimate, especially with small samples.

How do I read the F statistic?

F is the between-groups mean square divided by the within-groups mean square, so it compares variation between the group means with variation inside the groups. An F near 1 means the groups look no more different than random noise; the larger F gets, the stronger the evidence of a real difference.

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