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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. For example, an innocent person may be convicted. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false. For example: a guilty person may be not convicted.
Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e. when the correct hypothesis is rejected but for the wrong reason. Since the paired notions of type I errors (or "false positives") and type II errors (or "false negatives") that were introduced by Neyman and Pearson are now widely used ...
For composite hypotheses this is the supremum of the probability of rejecting the null hypothesis over all cases covered by the null hypothesis. The complement of the false positive rate is termed specificity in biostatistics. ("This is a specific test. Because the result is positive, we can confidently say that the patient has the condition.")
That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy. The consequences of such misinterpretations can ...
FWER control limits the probability of at least one false discovery, whereas FDR control limits (in a loose sense) the expected proportion of false discoveries. Thus, FDR procedures have greater power at the cost of increased rates of type I errors, i.e., rejecting null hypotheses that are actually true.
This strategy is an example of a heuristic: a reasoning shortcut that is imperfect but easy to compute. [63] Klayman and Ha used Bayesian probability and information theory as their standard of hypothesis-testing, rather than the falsificationism used by Wason. According to these ideas, each answer to a question yields a different amount of ...
Statistical significance. Appearance. In statistical hypothesis testing, 1 [ 2 ] a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. 3 More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis ...
An example of the base rate fallacy is the false positive paradox (also known as accuracy paradox). This paradox describes situations where there are more false positive test results than true positives (this means the classifier has a low precision). For example, if a facial recognition camera can identify wanted criminals 99% accurately, but ...