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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] Type I errors can be thought of as errors of commission, in which the status quo is ...
Testing a hypothesis suggested by the data can very easily result in false positives (type I errors). If one looks long enough and in enough different places, eventually data can be found to support any hypothesis. Yet, these positive data do not by themselves constitute evidence that the hypothesis is correct. The negative test data that were ...
If the null hypothesis is valid, the only thing the test person can do is guess. For every card, the probability (relative frequency) of any single suit appearing is 1/4. If the alternative is valid, the test subject will predict the suit correctly with probability greater than 1/4. We will call the probability of guessing correctly p. The ...
Consider the following example. Given the test scores of two random samples, one of men and one of women, does one group score better than the other? 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 ...
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Naaman [3] proposed an adaption of the significance level to the sample size in order to control false positives: α n, such that α n = n − r with r > 1/2. At least in the numerical example, taking r = 1/2, results in a significance level of 0.00318, so the frequentist would not reject the null hypothesis, which is in agreement with the ...
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.
For example, if one test is performed at the 5% level and the corresponding null hypothesis is true, there is only a 5% risk of incorrectly rejecting the null hypothesis. However, if 100 tests are each conducted at the 5% level and all corresponding null hypotheses are true, the expected number of incorrect rejections (also known as false ...