hypothesize (version 0.11.0)

intersection_test: Intersection Test (AND)

Description

Combines hypothesis tests using the AND rule: rejects only when ALL component tests reject.

Usage

intersection_test(...)

Value

A hypothesis_test of subclass intersection_test with fields n_tests and component_pvals.

Arguments

...

hypothesis_test objects or numeric p-values.

Use Case --- Bioequivalence

Bioequivalence requires showing a drug's effect is both "not too low" AND "not too high". This is naturally an intersection test.

Boolean Algebra

Together with complement_test() (NOT) and union_test() (OR), this forms a complete Boolean algebra. De Morgan's law holds by construction: union_test(a, b) = complement_test(intersection_test(complement_test(a), complement_test(b)))

Details

The p-value is \(\max(p_1, \ldots, p_k)\) — the intersection rejects at level \(\alpha\) if and only if every component p-value is below \(\alpha\).

This is the intersection-union test (IUT; Berger, 1982). No multiplicity correction is needed — the max is inherently conservative.

See Also

union_test(), complement_test(), fisher_combine()

Examples

# All must reject for intersection to reject
intersection_test(0.01, 0.03, 0.04)  # significant
intersection_test(0.01, 0.80)         # not significant