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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.
Type I errors which consist of rejecting a null hypothesis that is true; this amounts to a false positive result. Type II errors which consist of failing to reject a null hypothesis that is false; this amounts to a false negative result.
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.
Here the null hypothesis is by default that two things are unrelated (e.g. scar formation and death rates from smallpox). [7] The null hypothesis in this case is no longer predicted by theory or conventional wisdom, but is instead the principle of indifference that led Fisher and others to dismiss the use of "inverse probabilities". [8]
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.
Pr(y) is the probability under the null hypothesis of a potentially observed outcome y, T(y) is the value of the test statistic for an outcome y, with larger values of T representing cases which notionally represent greater departures from the null hypothesis,
The p-value is not the probability that the null hypothesis is true, or the probability that the alternative hypothesis is false. [2] A p -value can indicate the degree of compatibility between a dataset and a particular hypothetical explanation (such as a null hypothesis).