hypothesis-testing

Law 8b removal test: remove statistical inference and hypothesis testing has no framework in which to operate.

Hypothesis-testing requires null-hypothesis to operate: the practice of testing hypotheses against a null is constitutive of hypothesis-testing as a statistical concept. Remove null-hypothesis and hypothesis-testing has no defined operation — there is no 'test' without a null to test against.

Hypothesis testing is a specific kind of statistical method: a formal procedure for evaluating evidence using test statistics, p-values, and decision thresholds.

Removal test (Law 8): remove hypothesis-testing and statistical-power ceases to operate — power is defined as the probability of correctly rejecting a false null within a hypothesis test framework. No test framework, no power concept.

Multiple comparisons is the problem of inflated false-positive rates when performing many hypothesis tests simultaneously. Remove hypothesis-testing now and multiple-comparisons stops operating — it has no independent existence outside the framework of testing hypotheses. This is object-level, not meta-level: the concept's operative mechanism IS statistical inference within hypothesis testing.

Bayes factor is a statistic used to compare the evidence for two competing hypotheses. It is built and maintained for the sake of hypothesis testing — its entire purpose is to quantify relative evidence between H1 and H2. Law 8d: the servant (bayes-factor) points at the master (hypothesis-testing).

Rényi divergence quantifies the difference between probability distributions. It is built for the sake of hypothesis testing — serving as a test statistic and divergence measure for comparing distributions in detection theory and statistical decision making.