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An example of Neyman–Pearson hypothesis testing (or null hypothesis statistical significance testing) can be made by a change to the radioactive suitcase example. If the "suitcase" is actually a shielded container for the transportation of radioactive material, then a test might be used to select among three hypotheses: no radioactive source ...
Statistical tests are used to test the fit between a hypothesis and the data. [1] [2] Choosing the right statistical test is not a trivial task. [1]The choice of the test depends on many properties of the research question.
Test statistic is a quantity derived from the sample for statistical hypothesis testing. [1] A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.
Naaman [3] proposed an adaption of the significance level to the sample size in order to control false positives: α n, such that α n = n − r with r > 1/2. At least in the numerical example, taking r = 1/2, results in a significance level of 0.00318, so the frequentist would not reject the null hypothesis, which is in agreement with the ...
In statistical hypothesis testing, there are various notions of so-called type III errors (or errors of the third kind), and sometimes type IV errors or higher, by analogy with the type I and type II errors of Jerzy Neyman and Egon Pearson. Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e ...
An example of Pearson's test is a comparison of two coins to determine whether they have the same probability of coming up heads. The observations can be put into a contingency table with rows corresponding to the coin and columns corresponding to heads or tails.
The closed testing principle allows the rejection of any one of these elementary hypotheses, say H i, if all possible intersection hypotheses involving H i can be rejected by using valid local level α tests; the adjusted p-value is the largest among those hypotheses.
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 .