F-Ratio Demonstration
Explore how the F-ratio changes based on between-group differences and within-group variability.
The F-Ratio Formula
Between-Group Differences
↑ Spread means apart to increase F
Within-Group Variability
↓ Reduce variability to increase F
Group Distributions
F Distribution
SS Between
df =
SS Within
df =
F Ratio
p-value
Between-Group Variance (Signal)
Measures how far each group mean is from the grand mean. When groups are truly different, this value is large. It represents the systematic effect of your independent variable.
Within-Group Variance (Noise)
Measures how much individuals vary within their own group. This represents random variability or error—differences not explained by group membership.
Key Insight: Signal-to-Noise Ratio
The F-ratio is essentially a signal-to-noise ratio. A large F means the differences between groups (signal) are large relative to the variability within groups (noise). When F > 1, between-group differences exceed what we'd expect from random variation alone. The larger F gets, the more confident we are that the groups are truly different.