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In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false. [1] Type I error: an innocent person may be convicted. Type II error: a guilty person may be not convicted.
The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H 1, H 2, ..., H m. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant.
This is the most popular null hypothesis; It is so popular that many statements about significant testing assume such null hypotheses. Rejection of the null hypothesis is not necessarily the real goal of a significance tester. An adequate statistical model may be associated with a failure to reject the null; the model is adjusted until the null ...
At a significance level of 0.05, a fair coin would be expected to (incorrectly) reject the null hypothesis (that it is fair) in 1 out of 20 tests on average. The p-value does not provide the probability that either the null hypothesis or its opposite is correct (a common source of confusion). [36]
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.
As a particular example, if a null hypothesis states that a certain summary statistic follows the standard normal distribution (,), then the rejection of this null hypothesis could mean that (i) the mean of is not 0, or (ii) the variance of is not 1, or (iii) is not normally distributed. Different tests of the same null hypothesis would be more ...
The null hypothesis is rejected if the F calculated from the data is greater than the critical value of the F-distribution for some desired false-rejection probability (e.g. 0.05). Since F is a monotone function of the likelihood ratio statistic, the F -test is a likelihood ratio test .
The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H 1, H 2, ..., H m. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant.