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In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
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 ...
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 ...
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa). The fallacy is commonly associated ...
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of pointing to individual cases or data that seem to confirm a particular position while ignoring a significant portion of related and similar cases or data that may contradict that position. Cherry picking may be committed intentionally or unintentionally.
Multiple comparisons problem. An example of coincidence produced by data dredging (uncorrected multiple comparisons) showing a correlation between the number of letters in a spelling bee's winning word and the number of people in the United States killed by venomous spiders. Given a large enough pool of variables for the same time period, it is ...
Murphy's law [a] is an adage or epigram that is typically stated as: "Anything that can go wrong will go wrong.".. Though similar statements and concepts have been made over the course of history, the law itself was coined by, and is named after, American aerospace engineer Edward A. Murphy Jr.; its exact origins are debated, but it is generally agreed it originated from Murphy and his team ...