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That is, once the confounding variable (hospital's incidence of UTI) was included in the analysis, it became clear that antibiotic prophylaxis was associated with a higher incidence of UTIs.Īppleton et al. (2000) presented an example of Simpson's paradox from a study of urinary tract infections (UTIs) in which the association between antibiotic prophylaxis and UTIs had a relative risk (RR) 1 within each stratum. Although these were not experimental studies, the deleterious consequences of overlooking confounding variables are demonstrated. Four of these articles address studies from the health care literature, two of which are described here. A number of examples of Simpson's paradox have been described in the literature ( Appleton, French, & Vanderpump, 1996 Julious & Mullee, 1994 Perera, 2006 Reintjes, de Boer, van Pelt, & Mintjes-de Groot, 2000 Wagner, 1982). If there is inconsistency in the relationship between an outcome and treatment across studies, then it may be that confounding has occurred in at least some of those studies. One way to investigate this matter is to examine findings across studies. The extent to which Simpson's paradox is likely to occur in experimental research is difficult to determine because what has not been tested and reported in a publication can not be detected easily by a reader. (For further reading on Simpson's paradox, see Neutel, 1997 and Rücker & Schumacher, 2008.) Key to the occurrence of this paradox is the combination of these two conditions, because unequal sample sizes alone generally are not a problem as long as they are not coupled with other internal validity issues, such as power. The effect size of the confounding variable has to be strong enough to reverse the zero-order association between the independent and dependent variables ( Cornfield et al., 1959), and the imbalance in the groups on the confounding variable has to be large ( Hsu, 1989).
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This erroneous conclusion can lead to the ineffective intervention being implemented and to investigators building further studies on the erroneous conclusions, with concomitant waste of time, effort, and other resources.įor this paradox to occur, two conditions must be present: (a) an ignored or overlooked confounding variable that has a strong effect on the outcome variable and (b) a disproportionate distribution of the confounding variable among the groups being compared ( Hintzman, 1980 Hsu, 1989).
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In experimental research, a spurious relationship can lead to an erroneous conclusion that an intervention is effective, when in fact it is not. A spurious association is one that cannot be inferred to be causal because a third factor functions as a cause of the correlation among the variables. With Simpson's paradox, in the collapsed table the marginal correlation between cause and effect would be considered spurious. Simpson (1951) demonstrated how, when two or more 2 × 2 contingency tables are collapsed into one table, the findings from the collapsed table can be contradictory to the findings from the original tables. Simpson's paradox is an extreme condition of confounding in which an apparent association between two variables is reversed when the data are analyzed within each stratum of a confounding variable. This paper comprises three sections-a description of Simpson's paradox, a hypothetical example, and a discussion of ways to avoid Simpson's paradox.
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The purpose of this paper is to raise awareness of the potentially devastating effects of Simpson's paradox in experimental studies. Given the enormous investment in time and cost in testing an intervention and the potential impact it could have on health outcomes, it is incumbent upon investigators to determine an intervention's effects as accurately as possible. The impact of Simpson's paradox often has been discussed in relation to descriptive studies, but rarely has it received attention in the context of experimental studies. Simpson (1951) demonstrated how differential analyses of contingency tables (i.e., analysis in which the confounding variable is excluded or included) can lead to different conclusions. Simpson's paradox arises from the combination of an ignored confounding variable and a disproportionate allocation of the variable, and it can lead to a conclusion about an intervention effect that is the opposite of the correct inference (hence a paradox). One threat that has received inadequate attention in the nursing literature is Simpson's paradox. It is important to be reminded of potential threats to internal validity that can arise in experimental studies. Given that such experiments are intended to determine whether interventions should be used in practice, rigor is critical in study design. Over the past 20 years, nursing investigators have turned increasingly toward conducting experimental tests of innovative interventions.