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Concept
Misuse of statistics
Summary
Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. 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 false statistics trap can be quite damaging for the quest for knowledge. For example, in medical science, correcting a falsehood may take decades and cost lives.
Misuses can be easy to fall into. Professional scientists, even mathematicians and professional statisticians, can be fooled by even some simple methods, even if they are careful to check everything. Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardization of their tests.
One usable definition is: "Misuse of Statistics: Using numbers in such a manner that – either by intent or through ignorance or carelessness – the conclusions are unjustified or incorrect." The "numbers" include misleading graphics discussed elsewhere. The term is not commonly encountered in statistics texts and no authoritative definition is known. It is a generalization of lying with statistics which was richly described by examples from statisticians 60 years ago.
The definition confronts some problems (some are addressed by the source):
Statistics usually produces probabilities; conclusions are provisional
The provisional conclusions have errors and error rates. Commonly 5% of the provisional conclusions of significance testing are wrong
Statisticians are not in complete agreement on ideal methods
Statistical methods are based on assumptions which are seldom fully met
Data gathering is usually limited by ethical, practical and financial constraints.
How to Lie with Statistics acknowledges that statistics can legitimately take many forms.
Official source
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