The F-Test and F-Distribution › Assumptions and Limitations
Michael BrenndoerferJanuary 4, 20261 min read
Machine Learning from ScratchAll chapters Part 2 of 9Hypothesis Testing
The F-Test and F-Distribution › Assumptions and LimitationsOne section · Sections in this chapter7 / 10 ↓
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Assumptions of F-Tests
1. Independence: Observations must be independent within and between groups
2. Normality: The underlying populations should be normally distributed
- The F-test for variances is highly sensitive to non-normality
- The regression F-test is less sensitive, especially with larger samples
3. Random sampling: Data should come from random samples of the populations of interest
Sensitivity to Non-Normality
| Application | Sensitivity to Non-Normality |
|---|---|
| Comparing two variances | Poor - Use Levene's test instead |
| Overall regression significance | Moderate - OK with n > 30 |
| Nested model comparison | Moderate - OK with larger samples |
| ANOVA (covered next) | Moderate - OK if groups have similar sizes |