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A possible null hypothesis is that the mean male score is the same as the mean female score: H 0: μ 1 = μ 2. where H 0 = the null hypothesis, μ 1 = the mean of population 1, and μ 2 = the mean of population 2. A stronger null hypothesis is that the two samples have equal variances and shapes of their respective distributions.
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.
If the probability of obtaining a result as extreme as the one obtained, supposing that the null hypothesis were true, is lower than a pre-specified cut-off probability (for example, 5%), then the result is said to be statistically significant and the null hypothesis is rejected.
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 ).
In science, a null result is a result without the expected content: that is, the proposed result is absent. [1] It is an experimental outcome which does not show an otherwise expected effect. This does not imply a result of zero or nothing, simply a result that does not support the hypothesis .
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 ...
It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and is therefore a nuisance ...
Assuming H 0 is true, there is a fundamental result by Samuel S. Wilks: As the sample size approaches , and if the null hypothesis lies strictly within the interior of the parameter space, the test statistic defined above will be asymptotically chi-squared distributed with degrees of freedom equal to the difference in dimensionality of and . [14]