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That is, a misuse of statistics occurs when an argument uses statistics to assert a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. Often, when the statistics are false or misapplied, this constitutes a statistical fallacy.
The philosophy of statistics is the study of the mathematical, conceptual, and philosophical foundations and analyses of statistics and statistical inference. For example, Dennis Lindely argues for the more general analysis of statistics as the study of uncertainty . [ 1 ]
Logical Fallacies, Literacy Education Online; Informal Fallacies, Texas State University page on informal fallacies; Stephen's Guide to the Logical Fallacies (mirror) Visualization: Rhetological Fallacies, Information is Beautiful; Master List of Logical Fallacies, University of Texas at El Paso; Fallacies, Internet Encyclopedia of Philosophy
A formal fallacy, deductive fallacy, logical fallacy or non sequitur (Latin for "it does not follow") is a flaw in the structure of a deductive argument that renders the argument invalid. The flaw can be expressed in the standard system of logic. [ 1 ]
In statistics, it may involve basing broad conclusions regarding a statistical survey from a small sample group that fails to sufficiently represent an entire population. [1] [6] [7] Its opposite fallacy is called slothful induction, which consists of denying a reasonable conclusion of an inductive argument (e.g. "it was just a coincidence").
The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]
These include statistical tests: Popper is aware that observation statements are accepted with the help of statistical methods and that these involve methodological decisions. [21] When this distinction is applied to the term "falsifiability", it corresponds to a distinction between two completely different meanings of the term.
As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting conclusion is false. Statistical methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping.