Interactive F-Statistic Visualization

An interactive tool for visualizing F-statistics and ANOVA concepts through draggable group clusters

This interactive visualization helps you understand the F-statistic and ANOVA (Analysis of Variance) by allowing you to manipulate group means, sample sizes, and variances in real-time.

How to Use

• Drag the colored circles to move group centers and see how this affects the F-statistic
• Adjust sample sizes (N) and variances (σ²) using the input controls
• Add or remove groups using the buttons in the left panel
• Watch how the F-statistic and p-value change as you modify the data

Key Concepts

The F-statistic measures the ratio of between-group variance to within-group variance:

• Higher F-values indicate greater differences between groups relative to variation within groups
• Lower p-values (< 0.05) suggest statistically significant differences between groups
• The visualization shows the grand mean (overall average) and dashed lines connecting each group to it

Interactive F-Statistic Visualization

Drag the colored circles to move clusters. Adjust sample size (N) and variance (σ²) with the inputs below.

Groups

ANOVA Statistics

SS Between: 0.00

SS Within: 0.00

SS Total: 0.00

df Between: 1

df Within: 18

MS Between: 0.00

MS Within: 0.00

F = 0.00

p = 0.000

This visualization demonstrates several important statistical concepts:

• Sum of Squares (SS): Between-group and within-group variation
• Degrees of Freedom (df): Used in calculating the F-statistic
• Mean Squares (MS): Average variation between and within groups
• F-statistic: The test statistic for ANOVA
• p-value: The probability of observing this F-statistic by chance