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The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis, or a statement of 'no effect' or 'no difference'. [2] It is often symbolized as H 0.
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 ...
More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; [4] and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. [5]
This is why the hypothesis under test is often called the null hypothesis (most likely, coined by Fisher (1935, p. 19)), because it is this hypothesis that is to be either nullified or not nullified by the test. When the null hypothesis is nullified, it is possible to conclude that data support the "alternative hypothesis" (which is the ...
In null-hypothesis significance testing, the p-value [note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
In statistical hypothesis testing, a null result occurs when an experimental result is not significantly different from what is to be expected under the null hypothesis; its probability (under the null hypothesis) does not exceed the significance level, i.e., the threshold set prior to testing for rejection of the null hypothesis. The ...
Thus, the null hypothesis is rejected if >, (where , is the upper tail critical value for the distribution). Bartlett's test is a modification of the corresponding likelihood ratio test designed to make the approximation to the χ k − 1 2 {\displaystyle \chi _{k-1}^{2}} distribution better (Bartlett, 1937).
The Shapiro–Wilk test tests the null hypothesis that a sample x 1, ..., x n came from a normally distributed population. The test statistic is = (= ()) = (¯), where with parentheses enclosing the subscript index i is the ith order statistic, i.e., the ith-smallest number in the sample (not to be confused with ).