Statistics

== Misuse ==
{{main|Misuse of statistics}}

[[Misuse of statistics]] can produce subtle but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.

Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The [[statistical significance]] of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance. The set of basic statistical skills (and skepticism) that people need to deal with information in their everyday lives properly is referred to as [[statistical literacy]].

There is a general perception that statistical knowledge is all-too-frequently intentionally [[Misuse of statistics|misused]] by finding ways to interpret only the data that are favorable to the presenter.<ref name=Huff>Huff, Darrell (1954) ''[[How to Lie with Statistics]]'',  WW Norton & Company, Inc. New York.  {{isbn|0-393-31072-8}}</ref> A mistrust and misunderstanding of statistics is associated with the quotation, "[[Lies, damned lies, and statistics|There are three kinds of lies: lies, damned lies, and statistics]]". Misuse of statistics can be both inadvertent and intentional, and the book ''[[How to Lie with Statistics]]'',<ref name=Huff/> by [[Darrell Huff]], outlines a range of considerations. In an attempt to shed light on the use and misuse of statistics, reviews of statistical techniques used in particular fields are conducted (e.g. Warne, Lazo, Ramos, and Ritter (2012)).<ref>{{cite journal | last1 = Warne | first1 = R. Lazo | last2 = Ramos | first2 = T. | last3 = Ritter | first3 = N. | year = 2012 | title = Statistical Methods Used in Gifted Education Journals, 2006–2010 | journal = Gifted Child Quarterly | volume = 56 | issue = 3| pages = 134–149 | doi = 10.1177/0016986212444122 | s2cid = 144168910 }}</ref>

Ways to avoid misuse of statistics include using proper diagrams and avoiding [[Bias (statistics)|bias]].<ref name="Statistics in Archaeology">{{cite book | chapter = Statistics in archaeology | pages = [https://archive.org/details/encyclopediaarch00pear/page/n2072 2093]–2100 | first1 = Robert D. | last1 = Drennan | title =  Encyclopedia of Archaeology | url = https://archive.org/details/encyclopediaarch00pear | url-access = limited | year = 2008 | publisher = Elsevier Inc. | editor-first = Deborah M. | editor-last = Pearsall | isbn = 978-0-12-373962-9 }}</ref> Misuse can occur when conclusions are [[Hasty generalization|overgeneralized]] and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlooking sampling bias.<ref name="Misuse of Statistics">{{cite journal |last=Cohen |first=Jerome B. |title=Misuse of Statistics |journal=Journal of the American Statistical Association |date=December 1938 |volume=33 |issue=204 |pages=657–674 |location=JSTOR |doi=10.1080/01621459.1938.10502344}}</ref> Bar graphs are arguably the easiest diagrams to use and understand, and they can be made either by hand or with simple computer programs.<ref name="Statistics in Archaeology" /> Most people do not look for bias or errors, so they are not noticed. Thus, people may often believe that something is true even if it is not well [[Sampling (statistics)|represented]].<ref name="Misuse of Statistics" /> To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole.<ref name="Modern Elementary Statistics">{{cite journal|last=Freund|first=J.E.|author-link = John E. Freund|title=Modern Elementary Statistics|journal=Credo Reference|year=1988}}</ref> According to Huff, "The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism."<ref>{{cite book|last=Huff|first=Darrell|title=How to Lie with Statistics|year=1954|publisher=Norton|location=New York|author2=Irving Geis |quote=The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism.}}</ref>

To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case:<ref name=Huff/>
* Who says so? (Does he/she have an axe to grind?)
* How does he/she know? (Does he/she have the resources to know the facts?)
* What's missing? (Does he/she give us a complete picture?)
* Did someone change the subject? (Does he/she offer us the right answer to the wrong problem?)
* Does it make sense? (Is his/her conclusion logical and consistent with what we already know?)

[[File:Simple Confounding Case.svg|upright=0.9|thumb|right|The [[confounding variable]] problem: ''X'' and ''Y'' may be correlated, not because there is causal relationship between them, but because both depend on a third variable ''Z''. ''Z'' is called a confounding factor.]]

===Misinterpretation: correlation===
{{See also|Correlation does not imply causation}}
The concept of [[correlation]] is particularly noteworthy for the potential confusion it can cause. Statistical analysis of a [[data set]] often reveals that two variables (properties) of the population under consideration tend to vary together, as if they were connected. For example, a study of annual income that also looks at age of death, might find that poor people tend to have shorter lives than affluent people. The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or [[confounding variable]]. For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables.