In statistics, a confounding variable (also confounding factor, lurking variable, a confound, or confounder) is an extraneous variable
Extraneous variable
Extraneous variables are variables other than the independent variable that may bear any effect on the behavior of the subject being studied. This only affects the people in the experiment, not the place the experiment is taking place in...

 in a statistical model
Statistical model
A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...

 that correlates (positively or negatively) with both the dependent variable and the independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...

. The methodologies of scientific studies therefore need to account for these variables - either through experimental design, in which case, one achieves control
Scientific control
Scientific control allows for comparisons of concepts. It is a part of the scientific method. Scientific control is often used in discussion of natural experiments. For instance, during drug testing, scientists will try to control two groups to keep them as identical and normal as possible, then...

, or through statistical means, in which case we are said to account for them - to avoid a false positive (Type I) error; an erroneous conclusion that the dependent variables are in a causal
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

 relationship with the independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...

. Such a relation between two observed variables is termed a spurious relationship
Spurious relationship
In statistics, a spurious relationship 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 In statistics, a spurious relationship...

. Thus, confounding is a major threat to the validity of inferences made about cause and effect, i.e. internal validity
Internal validity
Internal validity is the validity of inferences in scientific studies, usually based on experiments as experimental validity.- Details :...

, as the observed effects should be attributed to the independent variable rather than the confounder.

In the case of risk assessments evaluating the magnitude and nature of risk to human health, it is important to control for confounding to isolate the effect of a particular hazard such as a food additive, pesticide, or new drug. For prospective studies, it is difficult to recruit and screen for volunteers with the same background (age, diet, education, geography, etc.), and in historical studies, there can be similar variability. Due to the inability to control for variability of volunteers and human studies, confounding is a particular challenge.


For example, consider possible statistical relationships between ice cream consumption and number of drowning deaths for a given period. These two variables have a positive, and potentially statistically significant
Statistical significance
In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. The phrase test of significance was coined by Ronald Fisher....

, correlation with each other.
  • At first sight, an evaluator might be tempted to infer a causal relationship in one direction or the other (either that ice cream causes drowning or that drowning causes ice cream consumption):
    • On one hand, the evaluator might attribute the entirety of the correlation to the causal chain "Since a) a nonzero fraction of people who eat ice cream go swimming shortly thereafter, b) swimming after eating causes cramps in a nonzero fraction of that fraction of people, and c) those cramps cause the inability to swim and the subsequent drowning of a nonzero fraction of the latter fraction, an increase in ice cream sales will cause an increase in drowning deaths."
    • On the other, the evaluator might attribute the entirety of that correlation to the causal chain "Since a) drowning deaths cause bereavement among almost all of the deceased's loved ones and b) some nonzero fraction of grieving persons console themselves with ice cream, an increase in drowning deaths will cause an increase in ice cream consumption."
    • In turn, if both of these patterns hold true, they will amplify each other, although that amplification is bounded at a horizontal asymptote: Some of the people who eat ice cream and then drown will leave behind grieving loved ones who console themselves with ice cream, some of those ice-cream-eating loved ones will go swimming after eating their ice cream, and some of those ice-cream-eating-and-then-swimming loved ones will drown, etc., but even in a world where these two factors are the only ones in play, the small percentages at issue quickly reduce the amplification at each successive iteration to almost nil.
  • In the world in which these observations are made, however, although either or both of these causal relationships might hold true in some minute fraction of cases, and although an accordingly minute fraction of the correlation may be attributable to either or both of them, the evaluator will vastly overstate the force of these relationships if s/he does not account for a confounding — and indeed far more influential — variable, namely the season: An increase in average temperature causes both an increase in ice cream consumption (observed event 1) and an increase in the number of people swimming; furthermore, if the fraction of swimmers who drown remains constant
    Ceteris paribus
    or is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...

    , an increase in the number of people swimming will cause an increase in the number of people who drown (observed event 2). This causal structure is by far the greatest contributor to the observed correlation, and since the season's being summer is by far the greatest contributor to warm weather, summertime is the root cause of an overwhelming majority of each observed increase.
  • Since the "branches" of the causal "event tree
    Event tree
    Error tree is an inductive analytical diagram in which an event is analyzed using Boolean logic to examine a chronological series of subsequent events or consequences...

    " reintersect in only a vanishingly few cases, for all practical purposes, each of the two observed increases merely coincides with, rather than causing or being caused by, the other.

Confounding in Risk Assessments

In risk assessments, factors such as age, gender, and educational levels often have impact on health status and so should be controlled. Beyond these factors, researchers may not consider or have access to data on other causal factors. An example is on the study of smoking tobacco on human health. Smoking, drinking alcohol, and diet are lifestyle activities that are related. A risk assessment that looks at the effects of smoking but does not control for alcohol consumption or diet may overestimate the risk of smoking. Smoking and confounding are reviewed in occupational risk assessments such as the safety of coal mining. When there is not a large sample population of non-smokers or non-drinkers in a particular occupation, the risk assessment may be biased towards finding a negative effect on health.

Experimental controls

There are various ways to modify a study design to actively exclude or control confounding variables:
  • Case-control studies assign confounders to both groups, cases and controls, equally. For example if somebody wanted to study the cause of myocardial infarct and thinks that the age is a probable confounding variable, each 67 years old infarct patient will be matched with a healthy 67 year old "control" person. In case-control studies, matched variables most often are the age and sex. Drawback: Case-control studies are feasible only when it is easy to find controls, i.e., persons whose status vis-à-vis all known potential confounding factors is the same as that of the case's patient: Suppose a case-control study attempts to find the cause of a given disease in a person who is 1) 45 years old, 2) African-American, 3) from Alaska, 4) an avid football player, 5) vegetarian, and 6) working in education. A theoretically perfect control would be a person who, in addition to not having the disease being investigated, matches all these characteristics and has no diseases that the patient does not also have — but finding such a control would be an enormous task.
  • Cohort studies
    Cohort study
    A cohort study or panel study is a form of longitudinal study used in medicine, social science, actuarial science, and ecology. It is an analysis of risk factors and follows a group of people who do not have the disease, and uses correlations to determine the absolute risk of subject contraction...

    : A degree of matching is also possible and it is often done by only admitting certain age groups or a certain sex into the study population, creating a cohort of people who share similar characteristics and thus all cohorts are comparable in regard to the possible confounding variable. For example, if age and sex are thought to be confounders, only 40 to 50 years old males would be involved in a cohort study that would assess the myocardial infarct risk in cohorts that either are physically active or inactive. Drawback: In cohort studies, the overexclusion of input data may lead researchers to define too narrowly the set of similarly situated persons for whom they claim the study to be useful, such that other persons to whom the causal relationship does in fact apply may lose the opportunity to benefit from the study's recommendations. Similarly, "over-stratification" of input data within a study may reduce the sample size in a given stratum to the point where generalizations drawn by observing the members of that stratum alone are not statistically significant
    Statistical significance
    In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. The phrase test of significance was coined by Ronald Fisher....

  • Double blinding: conceals from the trial population and the observers the experiment group membership of the participants. By preventing the participants from knowing if they are receiving treatment or not, the placebo effect
    Placebo effect
    Placebo effect may refer to:* Placebo effect, the tendency of any medication or treatment, even an inert or ineffective one, to exhibit results simply because the recipient believes that it will work...

     should be the same for the control and treatment groups. By preventing the observers from knowing of their membership, there should be no bias from researchers treating the groups differently or from interpreting the outcomes differently.
  • Randomized controlled trial
    Randomized controlled trial
    A randomized controlled trial is a type of scientific experiment - a form of clinical trial - most commonly used in testing the safety and efficacy or effectiveness of healthcare services or health technologies A randomized controlled trial (RCT) is a type of scientific experiment - a form of...

    : A method where the study population is divided randomly in order to mitigate the chances of self-selection by participants or bias by the study designers. Before the experiment begins, the testers will assign the members of the participant pool to their groups (control, intervention, parallel), using a randomization process such as the use of a random number generator. For example, in a study on the effects of exercise, the conclusions would be less valid if participants were given a choice if they wanted to belong to the control group which would not exercise or the intervention group which would be willing to take part in an exercise program. The study would then capture other variables besides exercise, such as pre-experiment health levels and motivation to adopt healthy activities. From the observer’s side, the experimenter may choose candidates who are more likely to show the results the study wants to see or may interpret subjective results (more energetic, positive attitude) in a way favorable to their desires.
  • Stratification: As in the example above, physical activity is thought to be a behaviour that protects from myocardial infarct; and age is assumed to be a possible confounder. The data sampled is then stratified by age group – this means, the association between activity and infarct would be analyzed per each age group. If the different age groups (or age strata) yield much different risk ratios, age must be viewed as a confounding variable. There exist statistical tools, among them Mantel–Haenszel methods, that account for stratification of data sets.

Peer review
Peer review
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...

 is a process that can assist in reducing instances of confounding. It is a process of evaluating the provision, work process, or output of an individual or collective operating in the same field as the reviewer(s). While not an experimental control of confounding because peer review happens after the completion of the experiment, peer review can unearth cases of confounding ex post facto, by testing for the ability to reproduce the results and assessing for chance.
  • Controlling for confounding by measuring the known confounders and including them as covariate
    In statistics, a covariate is a variable that is possibly predictive of the outcome under study. A covariate may be of direct interest or it may be a confounding or interacting variable....

    s in multivariate analyses; however, multivariate analyses reveal much less information about the strength of the confounding variable than do stratification methods.

All these methods have their drawbacks:
  1. The best available defense against this possibility is often to dispense with efforts at stratification and instead conduct a randomized study
    Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....

     of a sufficiently large
    Law of large numbers
    In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times...

     sample taken as a whole, such that all confounding variables (known and unknown) will be distributed by chance across all study groups.
  2. Ethical considerations: In double blind and randomized controlled trials, participants are not aware that they are recipients of sham treatments and may be denied effective treatments. There is resistance to randomized controlled trials in surgery because patients would agree to invasive surgery which carry risks under the understanding that they were receiving treatment.

Types of confounding

Confounding by indication:
Evaluating treatment effects from observational data is problematic. Prognostic factors may influence treatment
decisions, producing a type of bias referred to as "confounding by indication". Controlling for known prognostic
factors may reduce this problem, but it is always possible that a forgotten or unknown factor was not included
or that factors interact complexly. Confounding by indication has been described as the most important limitation
of observational studies of treatment effects. Randomized trials are not affected by confounding by

Confounding variables may also be categorised according to their source: the choice of measurement instrument (operational compound), situational characteristics (procedural confound), or inter-individual differences (person confound).
  • An operational confound is a type of confound that can occur in both experiment
    An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

    al and nonexperimental research designs. This type of confound occurs when a measure designed to assess a particular construct inadvertently measures something else as well.
  • A procedural confound is a type of confound that can occur in a laboratory experiment or a quasi-experiment
    A quasi-experiment is an empirical study used to estimate the causal impact of an intervention on its target population. Quasi-experimental research designs share many similarities with the traditional experimental design or randomized controlled trial, but they specifically lack the element of...

    . This type of confound occurs when the researcher mistakenly allows another variable to change along with the manipulated independent variable.

Decreasing the Likelihood of Confounding Factors in Ecological Risk Assessments

Diminishing the effect of confounding factors can be obtained by increasing the types and numbers of comparisons performed in the analysis. Confounding variables are unlikely to occur and act similarly at multiple times and locations. Also, the environment can be characterized in detail at the study sites to ensure sites are ecologically similar and therefore less likely to have confounding variables. Lastly, the relationship between the environmental variables that possibly confound the analysis and the measured parameters can be studied. The information pertaining to environmental variable can then be used in site-specific models to identify residual variance that may be due to real effects.

See also

  • Anecdotal evidence
    Anecdotal evidence
    The expression anecdotal evidence refers to evidence from anecdotes. Because of the small sample, there is a larger chance that it may be true but unreliable due to cherry-picked or otherwise unrepresentative of typical cases....

  • Joint effect
  • Simpson's paradox
    Simpson's paradox
    In probability and statistics, Simpson's paradox is a paradox in which a correlation present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics, and it occurs when frequencydata are hastily given causal...

  • Procedural confound
  • Operational confound

External links

These sites contain descriptions or examples of confounding variables:

This textbook has a nice overview of confounding factors and how to account for them in design of experiments:
  • Design and Analysis of Experiments, D. C. Montgomery, see Section 7-3 in 6th edition (2005, John Wiley & Sons)
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