Research Methods · Simplified
ANOVA F-Ratio Visualiser
F is one variance estimate divided by another. Three separate things move it, and only one of them is the effect.
The simulator
Three groups, one ratio
Each sample is generated from three normal populations and then analysed for real. Move a control and a fresh sample is drawn, so the numbers are an actual analysis rather than a formula being displayed.
Key terms
- Between-groups variance
- How far the three group means sit from the overall mean. It picks up any real difference between the populations, and also ordinary sampling noise.
- Within-groups variance
- How spread out people are inside their own group. It picks up noise only, which is why it works as the yardstick.
- F
- Between-groups variance divided by within-groups variance. When the populations are identical both estimate the same thing, so F wanders around 1.
- Share of variance
- The proportion of the total variation that lies between the groups. Unlike F it does not grow with the sample size.
One mark per person. The heavy tick on each row is that group's mean, and the bar beneath spans the three means: that reach is what the numerator measures, and the scatter within each row is what the denominator measures.
What this shows
F is a ratio, and three things move it
Set the separation to zero and draw a few samples. F does not settle on zero, it wanders around 1, because both parts of the ratio are then estimating the same thing.
Key idea: The numerator asks how far apart the group means are; the denominator asks how spread out people are inside their groups. When the populations are identical both estimate the same quantity and their ratio hovers near 1. Separation raises F, spread lowers it, and sample size raises it without the populations changing at all. That last one is why F is not a measure of how large a difference is: the share of variance beside it is, and it barely moves when you add people.
Every figure here is computed from one generated sample, so it moves when you redraw. That is the point rather than a defect. The simulation assumes normal populations, equal spreads and independent observations, which is what makes the reference distribution for F correct; real data satisfy those to varying degrees. A significant F says the three means are unlikely to be this far apart under identical populations. It does not say which groups differ, by how much, or whether the difference matters.
The longer version adds a second experiment on what F cannot carry, worked-example presets, a browse-then-commit identification task and a select-all challenge on interpretation. It is at ANOVA F-Ratio Visualiser in the main collection.