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The misuse of Statistics can trick the observer who does not understand them into believing something other than what the data shows or what is really 'true'. That is, a misuse of statistics occurs when an argument uses statistics to assert a falsehood. In some cases, the misuse may be accidental.
Statistical assumptions can be put into two classes, depending upon which approach to inference is used. Model-based assumptions. These include the following three types: Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. [5]
The observational interpretation fallacy is the cognitive bias where associations identified in observational studies are misinterpreted as causal relationships.This misinterpretation often influences clinical guidelines, public health policies, and medical practices, sometimes to the detriment of patient safety and resource allocation.
Persuasive definition – purporting to use the "true" or "commonly accepted" meaning of a term while, in reality, using an uncommon or altered definition. (cf. the if-by-whiskey fallacy) Ecological fallacy – inferring about the nature of an entity based solely upon aggregate statistics collected for the group to which that entity belongs. [27]
On the basis that it is always assumed, by statistical convention, that the speculated hypothesis is wrong, and the so-called "null hypothesis" that the observed phenomena simply occur by chance (and that, as a consequence, the speculated agent has no effect) – the test will determine whether this hypothesis is right or wrong.
By comparison, a jingle fallacy is the assumption that two measures which are called by the same name capture the same construct. [4] [5] [6] An example of the jangle fallacy can be found in tests designed to assess emotional intelligence. Some of these tests measure merely personality or regular IQ-tests. [7]
In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously [1] or estimates a subset of parameters selected based on the observed values. [2] The larger the number of inferences made, the more likely erroneous inferences become.
Research dating back to Émile Durkheim suggests that predominantly Protestant localities have higher suicide rates than predominantly Catholic localities. [3] According to Freedman, [4] the idea that Durkheim's findings link, at an individual level, a person's religion to their suicide risk is an example of the ecological fallacy.