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In statistical hypothesis testing, a type I error, or a false positive, is the erroneous rejection of a true null hypothesis. A type II error, or a false negative, is the erroneous failure in bringing about appropriate rejection of a false null hypothesis. [1]
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 ...
In that case, the null hypothesis was that she had no special ability, the test was Fisher's exact test, and the p-value was / = /, so Fisher was willing to reject the null hypothesis (consider the outcome highly unlikely to be due to chance) if all were classified correctly. (In the actual experiment, Bristol correctly classified all 8 cups.)
The null hypothesis is that the mean value of X is a given number μ 0. We can use X as a test-statistic, rejecting the null hypothesis if X − μ 0 is large. To calculate the standardized statistic Z = ( X ¯ − μ 0 ) s {\displaystyle Z={\frac {({\bar {X}}-\mu _{0})}{s}}} , we need to either know or have an approximate value for σ 2 , from ...
The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other. Multiple-comparison testing is conducted using needed data in already completed F-test, if F-test leads to rejection of null hypothesis and the factor under study has an impact on the dependent variable. [1]
Low values of the likelihood ratio mean that the observed result was much less likely to occur under the null hypothesis as compared to the alternative. High values of the statistic mean that the observed outcome was nearly as likely to occur under the null hypothesis as the alternative, and so the null hypothesis cannot be rejected.
Statistical hypothesis testing is based on rejecting the null hypothesis when the likelihood of the observed data would be low if the null hypothesis were true. If multiple hypotheses are tested, the probability of observing a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., making a Type I ...
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.