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| In [[statistics]], a '''spurious relationship''' (or, sometimes, '''spurious correlation''') is a [[mathematical relationship]] in which two events or variables have no direct causal connection, yet it may be wrongly inferred that they do, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "confounding factor" or "[[lurking variable]]"). Suppose there is found to be a correlation between A and B. Aside from coincidence, there are three possible relationships:
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| : A causes B,
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| : B causes A,
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| : '''OR'''
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| : C causes both A and B.
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| In the last case there is a spurious correlation between A and B. In a regression model where A is regressed on B but C is actually the true causal factor for A, this misleading choice of [[dependent and independent variables|independent variable]] (B instead of C) is called specification error.
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| Because correlation can arise from the presence of a lurking variable rather than from direct causation, it is often said that "[[Correlation does not imply causation]]".{{citation needed|date=April 2013}}
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| A spurious relationship should not be confused with a '''spurious regression''', which refers to a regression that shows significant results due to the presence of a [[unit root]] in both variables.{{citation needed|date=April 2013}}
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| ==General example==
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| An example of a spurious relationship can be illuminated by examining a city's [[ice cream]] sales. These sales are highest when the rate of drownings in city [[swimming pool]]s is highest. To allege that ice cream sales cause drowning, or vice-versa, would be to imply a spurious relationship between the two. In reality, a [[heat wave]] may have caused both. The heat wave is an example of a hidden or unseen variable, also known as a [[confounding variable]].
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| Another popular example is a series of Dutch statistics showing a positive correlation between the number of storks nesting in a series of springs and the number of human babies born at that time. Of course there was no causal connection; they were correlated with each other only because they were correlated with the weather nine months before the observations.<ref>{{cite book |editor1-first=Roger |editor1-last=Sapsford |editor2-first=Victor |editor2-last=Jupp |title=Data Collection and Analysis |publisher=Sage |year=2006 |isbn=0-7619-4362-5 }}</ref> However Höfer et al. (2004) showed the correlation to be stronger than just weather variations as he could show in post reunification Germany that, while the number of clinical deliveries was not linked with the rise in stork population, out of hospital deliveries correlated with the stork population.<ref>{{cite journal|last=Höfer|first=Thomas|coauthors=Hildegard Przyrembel and Silvia Verleger|title=New evidence for the Theory of the Stork|journal=Paediatric and Perinatal Epidemiology|year=2004|volume=18|issue=1|pages=18–22|doi=10.1111/j.1365-3016.2003.00534.x}}</ref>
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| ==Detecting spurious relationships==
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| The term "spurious relationship" is commonly used in [[statistics]] and in particular in [[experimental techniques|experimental research]] techniques, both of which attempt to understand and predict direct causal relationships (X → Y). A non-causal correlation can be spuriously created by an antecedent which causes both (W → X and W → Y). Intervening variables (X → W → Y), if undetected, may make indirect causation look direct. Because of this, experimentally identified [[correlation]]s do not represent [[Causality|causal relationships]] unless spurious relationships can be ruled out. | |
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| ===Experiments===
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| In experiments, spurious relationships can often be identified by controlling for other factors, including those that have been theoretically identified as possible confounding factors. For example, consider a researcher trying to determine whether a new drug kills bacteria; when the researcher applies the drug to a bacterial culture, the bacteria die. But to help in ruling out the presence of a confounding variable, another culture is subjected to conditions that are as nearly identical as possible to those facing the first-mentioned culture, but the second culture is not subjected to the drug. If there is an unseen confounding factor in those conditions, this control culture will die as well, so that no conclusion of efficacy of the drug can be drawn from the results of the first culture. On the other hand, if the control culture does not die, then the researcher cannot reject the hypothesis that the drug is efficacious.
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| ===Non-experimental statistical analyses===
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| Disciplines whose data are mostly non-experimental, such as [[economics]], usually employ observational data to establish causal relationships. The body of statistical techniques used in economics is called [[econometrics]]. The main statistical method in econometrics is multivariate [[regression analysis]]. Typically a linear relationship such as
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| :<math>y = a_0 + a_1x_1 + a_2x_2 + \cdots + a_kx_k + e</math> | |
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| is hypothesized, in which <math>y</math> is the dependent variable (hypothesized to be the caused variable), <math>x_j</math> for ''j'' = 1, ..., ''k'' is the ''j''<sup>th</sup> independent variable (hypothesized to be a causative variable), and <math>e</math> is the error term (containing the combined effects of all other causative variables, which must be uncorrelated with the included independent variables). If there is reason to believe that none of the <math>x_j</math>s is caused by ''y'', then estimates of the coefficients <math>a_j</math> are obtained. If the null hypothesis that <math>a_j=0</math> is rejected, then the alternative hypothesis that <math>a_{j} \ne 0 </math> and equivalently that <math>x_j</math> causes ''y'' cannot be rejected. On the other hand, if the null hypothesis that <math>a_j=0</math> cannot be rejected, then equivalently the hypothesis of no causal effect of <math>x_j</math> on ''y'' cannot be rejected. Here the notion of causality is one of [[Causality#Necessary and sufficient causes|contributory causality]]: If the true value <math>a_j \ne 0</math>, then a change in <math>x_j</math> will result in a change in ''y'' ''unless'' some other causative variable(s), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect; thus a change in <math>x_j</math> is ''not sufficient'' to change ''y''. Likewise, a change in <math>x_j</math> is ''not necessary'' to change ''y'', because a change in ''y'' could be caused by something implicit in the error term (or by some other causative explanatory variable included in the model).
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| Regression analysis controls for other relevant variables by including them as regressors (explanatory variables). This helps to avoid mistaken inference of causality due to the presence of a third, underlying, variable that influences both the potentially causative variable and the potentially caused variable: its effect on the potentially caused variable is captured by directly including it in the regression, so that effect will not be picked up as a spurious effect of the potentially causative variable of interest. In addition, the use of multivariate regression helps to avoid wrongly inferring that an indirect effect of, say ''x''<sub>1</sub> (e.g., ''x''<sub>1</sub> → ''x''<sub>2</sub> → ''y'') is a direct effect (''x''<sub>1</sub> → ''y'').
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| Just as an experimenter must be careful to employ an experimental design that controls for every confounding factor, so also must the user of multiple regression be careful to control for all confounding factors by including them among the regressors. If a confounding factor is omitted from the regression, its effect is captured in the error term by default, and if the resulting error term is correlated with one (or more) of the included regressors, then the estimated regression may be biased or inconsistent (see [[omitted variable bias]]).
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| ==See also==
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| *[[Causality]]
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| *[[Correlation does not imply causation]]
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| *[[Omitted-variable bias]]
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| *[[Post_hoc_ergo_propter_hoc#Pattern|Post hoc fallacy]]
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| *[[Specification (regression)]]
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| ==Footnotes==
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| {{Reflist}}
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| ==References==
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| *{{cite book |last=Pearl |first=Judea |title=Causality: Models, Reasoning and Inference |publisher=Cambridge University Press |year=2000 |isbn=0521773628 }}
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| *{{cite journal |last=Yule |first=G. U. |year=1926 |title=Why do we sometimes get nonsense correlations between time series?—A study in sampling and the nature of time series |journal=[[Journal of the Royal Statistical Society]] |volume=89 |issue=1 |pages=1–64 |jstor=2341482 }}
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| ==External links==
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| * Burns, William C., "''[http://www.burns.com/wcbspurcorl.htm Spurious Correlations]''", 1997.
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| * [http://bayes.cs.ucla.edu/LECTURE/lecture_sec1.htm "The Art and Science of Cause and Effect"]: a slide show and tutorial lecture by Judea Pearl
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| [[Category:Logical fallacies]]
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| [[Category:Logic and statistics]]
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| [[Category:Statistical dependence]]
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All of the trophies from all for this members in your clan get added up and as well , divided by 2 identify your clans overall awards. Playing many different kinds of games gets your gaming time more enjoyable. and your league also determines your primary battle win bonus. 5 star rating and she is known to be ach addictive as players frequently devote several hours experiencing the game. She focuses on beauty salon business manufacturing and client fascination.
When you are locating that handle system tough to successfully use, optimize the places within your activity. The default manage course of action might not be needed for everyone. Some people prefer a better express screen, a set including more sensitive management also known as perhaps an inverted pecking order. In several on the net gaming, you may mastery these from the setting's area.
Pay attention to a game's evaluation when purchasing an existing. This evaluation will allow you to discover what age level clash of clans hack tool is ideal for and will make it known when the sport is violent. It figure out whether you should buy the sport.
The entire acceptable abatement for the lack of best stretches of electrical energy is essential. Who have'nt experienced it prices would bound developed to be prohibitive and cipher would unquestionably purchase them.
Sensei Wars, the feudal Japan-themed Clash of Clans Secrets attacker from 2K, holds aloof accustomed its aboriginal agreeable amend again his barrage on iOS aftermost 12 ,.
In are playing a dressing in game, and you don't any experience with it, set the difficulty even to rookie. If you have any questions pertaining to where and the best ways to utilize clash of clans gem generator no survey, you could call us at our own internet site. This is considered help you pick moving up on the unique has of the game in addition to the learn your way around the field. In the case when you set it much better than that, you commonly tend to get frustrated and thus not have any fun.
Nearly as your village grows, the to explore uncharted territories for Gold and Woodworking which are the 5 key resources you may want to expect to require at start of the video games ( addititionally there is just Stone resource, that owners discover later inside the game ). As a result of your exploration, you will likely expect to stumble with many islands whereby this villages happen to stay held captive under BlackGuard slavery and you boost from free Gold choices if they are vacant.