ANOVA Visualizer

Drag each group's mean, and the spread shared by all groups, and watch the F statistic respond in real time.

Groups

Number of groups

Group 1 mean = 6.0

Group 2 mean = 8.0

Group 3 mean = 10.0

Within-group spread = 1.2

Each group has 8 points. Move the means apart or the spread down to raise F; move the means together or the spread up to lower it.

Group data, with group means (dashes) and the grand mean (dotted line)

F statistic

61.25

p-value

< 0.0001

2, 21

SS between = 64, SS within = 10.971, SS total = 74.971

MS between = 32, MS within = 0.522

F = MS between ÷ MS within = 61.25

At the 5% level, the group means are significantly different (F = 61.25, p < 0.0001). The variation between the groups is large relative to the variation within them. Drag the spread slider up with the means fixed, and watch F fall even though the means themselves have not moved — ANOVA compares distance between groups against noise within them, not just the raw gap between the means.

How to use this tool

Choose 3 or 4 groups.
Drag each group's mean slider to move its data up or down the chart.
Drag the spread slider to make each group's points tighter or more scattered.
Watch the F statistic and p-value update, and read the sum-of-squares breakdown underneath.

Formula Reference

Between-groups sum of squares

SSbetween = Σ nᵢ(x̄ᵢ − x̄)²

Within-groups sum of squares

SSwithin = Σ Σ(xᵢⱼ − x̄ᵢ)²

F statistic

F = MSbetween ÷ MSwithin

ArticleANOVA: Comparing Three or More Group Means ArticleThe F-Distribution ArticleTukey's HSD Post-Hoc Test CalcANOVA Calculator TableF-Table GlossaryGlossary: ANOVA

Frequently Asked Questions

Why does F fall when I increase the spread, even if the means do not move?+

ANOVA judges the gap between group means against the amount of random variation inside each group. Increasing the spread inflates the within-group variance, so the same gap between means becomes less remarkable, and F falls.

Why does F rise when I pull the means apart?+

A bigger gap between group means increases the between-groups sum of squares while the within-groups variance stays the same, so F rises and the groups become easier to tell apart statistically.

What does the F statistic actually measure?+

It is the ratio of the average squared distance of the group means from the grand mean (adjusted for group size) to the average squared distance of individual points from their own group mean. A large F means the groups differ more than random noise alone would explain.

Why do all the points sit at the same relative positions within a group?+

To isolate the effect of the sliders, the visualizer uses a fixed pattern of eight offsets per group and shifts them by the mean and spread you choose, rather than redrawing new random data on every change.