F test for equal variances
Definition taught in Hypothesis tests, part of Statistical inference
F test for equal variances
| Type | Definition |
| Taught in | Hypothesis tests |
| Part | Statistical inference |
| Properties | 1 |
For two independent normal samples, F=s_1^2/s_2^2 has the F_{n_1-1,n_2-1} distribution when \sigma_1^2=\sigma_2^2. Against \sigma_1^2\neq\sigma_2^2 at level \alpha, reject when F\ge F_{n_1-1,n_2-1;1-\alpha/2} or F\le1/F_{n_2-1,n_1-1;1-\alpha/2}.
Properties
Variance-ratio F pivot
Main article: Variance-ratio F pivot
For two independent normal samples,
\frac{s_1^2/\sigma_1^2}{s_2^2/\sigma_2^2}
has the F distribution with (n_1-1,\,n_2-1) degrees of freedom.
Used in
- Taught in Hypothesis tests, where the derivation and examples are.
- All 6 questions on Hypothesis tests
See also
Null and alternative hypotheses · Critical region · p-value · Type I and type II errors · Neyman–Pearson approach · Power function · One-sample t test · Two-sample t test