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Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores.
This test procedure is based on the statistic whose sampling distribution is approximately a Chi-Square distribution with (k − 1) degrees of freedom, where k is the number of random samples, which may vary in size and are each drawn from independent normal distributions. Bartlett's test is sensitive to departures from normality.
For example, for = 0.05 and m = 10, the Bonferroni-adjusted level is 0.005 and the Šidák-adjusted level is approximately 0.005116. One can also compute confidence intervals matching the test decision using the Šidák correction by computing each confidence interval at the ⋅ {\displaystyle \cdot } (1 − α) 1/ m % level.
A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test making use of the proof by contradiction. A permutation test involves two or more samples. The null hypothesis is that all samples come from the same distribution : =.
A very simple equivalence testing approach is the ‘two one-sided t-tests’ (TOST) procedure. [11] In the TOST procedure an upper (Δ U) and lower (–Δ L) equivalence bound is specified based on the smallest effect size of interest (e.g., a positive or negative difference of d = 0.3).
A proof procedure for a logic is complete if it produces a proof for each provable statement. The theorems of logical systems are typically recursively enumerable, which implies the existence of a complete but usually extremely inefficient proof procedure; however, a proof procedure is only of interest if it is reasonably efficient.
A standard proof (or certificate), as used in the verifier-based definition of the complexity class NP, also satisfies these requirements, since the checking procedure deterministically reads the whole proof, always accepts correct proofs and rejects incorrect proofs. However, what makes them interesting is the existence of probabilistically ...
Neyman–Pearson lemma [5] — Existence:. If a hypothesis test satisfies condition, then it is a uniformly most powerful (UMP) test in the set of level tests.. Uniqueness: If there exists a hypothesis test that satisfies condition, with >, then every UMP test in the set of level tests satisfies condition with the same .