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The sign test is a special case of the binomial test where the probability of success under the null hypothesis is p=0.5. Thus, the sign test can be performed using the binomial test, which is provided in most statistical software programs. On-line calculators for the sign test can be founded by searching for "sign test calculator".
The procedure works by assessing whether the observed departure, measured by the test statistic, is larger than a value defined, so that the probability of occurrence of a more extreme value is small under the null hypothesis (usually in less than either 5% or 1% of similar data-sets in which the null hypothesis does hold).
Region of rejection / Critical region: The set of values of the test statistic for which the null hypothesis is rejected. Power of a test (1 − β) Size: For simple hypotheses, this is the test's probability of incorrectly rejecting the null hypothesis. The false positive rate. For composite hypotheses this is the supremum of the probability ...
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 ...
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.
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, the null distribution is the probability distribution of the test statistic when the null hypothesis is true. [1] For example, in an F-test, the null distribution is an F-distribution. [2] Null distribution is a tool scientists often use when conducting experiments.
In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test ...