ANOVA calculator

Paste three or more groups to test whether their means differ, then see exactly which pairs are different, with every step of the working.

  • Free, no sign-up
  • Step-by-step working
  • Runs in your browser

Not sure this is the right tool? Find the right one

  1. 1 Copy and paste your data
  2. 2 Choose an option
  3. 3 Click “Run ANOVA”
  4. 4 Read the result

Tip: No need to type: copy your numbers from Excel, Google Sheets or a CSV file and paste them straight into the box.

This is example data so you can see how the tool works. Replace it with your own: copy your numbers from Excel or Google Sheets and paste them in, or type them.

Paste your groups

Paste columns from a spreadsheet (names in the first row), or type one group per line: Morning: 72, 68, 75

Significance level (if unsure, keep 0.05)

Your result

How to use the ANOVA calculator

  1. In Excel or Google Sheets, select your groups, one column per group with the names in the first row, and copy them.
  2. Paste them into the box. Columns can have different numbers of values. You can also type one group per line.
  3. Keep the significance level at 0.05 unless your course says otherwise, then click Run ANOVA.
  4. Read the p-value and the ANOVA table, then the Tukey comparisons to see which groups differ.
  5. Check the chart of group means and the equal-variance check before reporting the result.

One-way ANOVA formulas

ANOVA splits the total variation into variation between the group means and variation within the groups:

SSbetween = Σni(xi − x)2 , SSwithin = Σ(ni − 1)si2

Each is divided by its degrees of freedom to give a mean square, and their ratio is the F statistic:

F = MSbetweenMSwithin = SSbetween / (k − 1)SSwithin / (N − k)

k
The number of groups
ni, N
The size of group i, and the total number of values
xi, si
The mean and standard deviation of group i
x
The grand mean of all the values together
MS
Mean square: a sum of squares divided by its degrees of freedom
F
The test statistic, compared with an F distribution with k − 1 and N − k degrees of freedom

Worked example

Three groups of 3 students each scored: A: 4, 5, 6; B: 7, 8, 9; C: 5, 6, 7. Do the group means differ?

  1. Group means and the grand mean
    means 5, 8, 6; grand mean = 57 / 9 = 6.333
  2. Between groups: each group's size times its mean's squared distance from the grand mean
    SSbetween = 3(5 − 6.333)² + 3(8 − 6.333)² + 3(6 − 6.333)² = 14
  3. Within groups: squared distances from each group's own mean
    SSwithin = (1 + 0 + 1) + (1 + 0 + 1) + (1 + 0 + 1) = 6
  4. Mean squares with k − 1 = 2 and N − k = 6 degrees of freedom, then F
    F = 14 / 26 / 6 = 71 = 7 , p = 0.027

What it means: p = 0.027 is below 0.05, so the group means are not all equal. Tukey's test would then show that B differs from A, the pair furthest apart. With only three values per group, a real study would want more data.

How to interpret ANOVA results

  • The p-value answers one question: are the group means all equal? Below α, at least one differs.
  • Tukey comparisons say which pairs differ, with p-values adjusted for making several comparisons.
  • η² (eta squared) gives the size of the effect: the share of the variation explained by the groups.
  • The chart shows each group's mean and 95% confidence interval. Groups whose intervals barely overlap tend to differ.
  • Check the assumptions: similar spreads in each group, and no extreme outliers. Draw a box plot of the groups to see both.

Comparing just two groups? Use the t-test calculator. For counts in categories rather than measurements, use the chi-square test.

Frequently asked questions

What does ANOVA tell you?

One-way ANOVA tests whether the means of three or more groups are all equal. A small p-value says that at least one group mean differs from the others, but not which one. That’s what the Tukey post hoc comparisons below the ANOVA table are for: they test every pair of groups while keeping the overall chance of a false alarm at your significance level.

Why not just run several t-tests?

Each t-test has a 5% chance of a false alarm. With three groups you’d run three tests, and the chance of at least one false alarm rises to about 14%; with five groups (ten tests) it’s about 40%. ANOVA tests all the groups at once at 5%, and Tukey’s test then compares pairs with that error rate controlled. With only two groups, ANOVA gives the same p-value as a pooled t-test (F = t²).

What are the assumptions of ANOVA?

The observations are independent, each group comes from a roughly normal population, and the groups have similar variances. ANOVA is fairly robust to non-normal data when groups have similar sizes and about 15 or more values each. For equal variances, a common rule of thumb is that the largest standard deviation is less than twice the smallest; the calculator also runs Levene’s test (Brown-Forsythe version) and warns you if it fails.

What is the F statistic?

F is the ratio of the variation between the group means to the variation within the groups: F = MSbetween / MSwithin. If the groups really have the same mean, F should be around 1. A large F means the group means are further apart than the natural scatter inside the groups would explain.

What is eta squared (η²)?

η² is the share of the total variation in the data that is explained by which group a value is in: SSbetween / SStotal. Common rough guidelines are 0.01 for a small effect, 0.06 for medium and 0.14 for large. Unlike the p-value, it doesn’t grow just because the sample is bigger.

How do I run ANOVA in Excel?

Turn on the Analysis ToolPak (File → Options → Add-ins), then choose Data → Data Analysis → Anova: Single Factor, select your columns and click OK. It gives the same ANOVA table as this calculator, but no post hoc tests. In Google Sheets there is no built-in ANOVA; paste your columns here instead.

Last reviewed November 13, 2026