ANOVA Calculator
Run a one-way or two-way ANOVA (with or without replication) to compare means, or a one-sample z-test.
About the ANOVA Calculator
One-way ANOVA tests whether three or more groups share the same mean by comparing variation between groups with variation within them. A large F (small p) means at least one mean differs; a post-hoc test then shows which. It assumes independent samples, roughly normal data and similar variances. The z-test compares a mean with a known population SD against a hypothesised value.
The formula
F = [SSB ÷ (k − 1)] ÷ [SSW ÷ (N − k)]; z = (x̄ − μ₀) ÷ (σ ÷ √n)
- Two-way
- SST = SSA + SSB (+ SSAB) + SSE, each sum of squares from the row, column (and cell) totals with the correction factor T²/N
Worked example
Example: F statistic = 15.75
- Inputs: Test: One-way ANOVA; Groups (one group per line): 10, 12, 11, 13; 14, 15, 13, 16; 9, 10, 11, 10; α: 0.05.
- Formula: F = [SSB ÷ (k − 1)] ÷ [SSW ÷ (N − k)]; z = (x̄ − μ₀) ÷ (σ ÷ √n)
- Result: F statistic = 15.75
Questions people ask
What does two-way ANOVA add?
It tests two factors at once (say, machine and operator): one F for the rows, one for the columns. With more than one value in each cell it also tests their interaction, whether the effect of one factor depends on the other.
Why not several t-tests?
Each extra test raises the chance of a false positive; ANOVA tests all groups at once.
Which group is different?
Use a post-hoc test such as Tukey's HSD after a significant ANOVA.