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 consequences of such misinterpretations can be quite severe. For example, in medical science, correcting a falsehood may take decades and cost lives; likewise, in democratic societies, misused statistics can distort public understanding, entrench misinformation, and enable governments to implement harmful policies without accountability. Misuses can be easy to fall into. Professional scientists, mathematicians and even 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.
Definition, limitations and context 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 in other sources. The term is not commonly encountered in statistics texts and there is no single authoritative definition. 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. Whether the statistics show that a product is "light and economical" or "flimsy and cheap" can be debated whatever the numbers. Some object to the substitution of statistical correctness for moral leadership (for example) as an objective. Assigning blame for misuses is often difficult because scientists, pollsters, statisticians and reporters are often employees or consultants. An insidious misuse of statistics is completed by the listener, observer, audience, or juror. The supplier provides the "statistics" as numbers or graphics (or before/after photographs), allowing the consumer to draw conclusions that may be unjustified or incorrect. The poor state of public statistical literacy and the non-statistical nature of human intuition make it possible to mislead without explicitly producing faulty conclusion. The definition is weak on the responsibility of the consumer of statistics. A historian listed over 100 fallacies in a dozen categories including those of generalization and those of causation. A few of the fallacies are explicitly or potentially statistical including sampling, statistical nonsense, statistical probability, false extrapolation, false interpolation and insidious generalization. All of the technical/mathematical problems of applied probability would fit in the single listed fallacy of statistical probability. Many of the fallacies could be coupled to statistical analysis, allowing the possibility of a false conclusion flowing from a statistically sound analysis. An example use of statistics is in the analysis of medical research. The process includes experimental planning, the conduct of the experiment, data analysis, drawing the logical conclusions and presentation/reporting. The report is summarized by the popular press and by advertisers. Misuses of statistics can result from problems at any step in the process. The statistical standards ideally imposed on the scientific report are much different than those imposed on the popular press and advertisers; however, cases exist of advertising disguised as science, such as Australasian Journal of Bone & Joint Medicine. The definition of the misuse of statistics is weak on the required completeness of statistical reporting. The opinion is expressed that newspapers must provide at least the source for the statistics reported.
Simple causes Many misuses of statistics occur because
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