# Confounding

confounding factorconfounding variableconfounding variablesconfoundconfounderconfoundedconfoundersconfounding factorslurking variableconfounds
In statistics, a confounder (also confounding variable, confounding factor, or lurking variable) is a variable that influences both the dependent variable and independent variable, causing a spurious association.wikipedia
232 Related Articles

### Dependent and independent variables

dependent variableindependent variableexplanatory variable
In statistics, a confounder (also confounding variable, confounding factor, or lurking variable) is a variable that influences both the dependent variable and independent variable, causing a spurious association.
Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect.

### Spurious relationship

In statistics, a confounder (also confounding variable, confounding factor, or lurking variable) is a variable that influences both the dependent variable and independent variable, causing a spurious association.
In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but not causally related, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "common response variable", "confounding factor", or "lurking variable").

### Causality

causalcause and effectcausation
Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations.
One very practical result of this theory is the characterization of confounding variables, namely, a sufficient set of variables that, if adjusted for, would yield the correct causal effect between variables of interest.

### Experiment

experimentalexperimentationexperiments
For these reasons, experiments offer a way to avoid most forms of confounding.
An experiment must also control the possible confounding factors—any factors that would mar the accuracy or repeatability of the experiment or the ability to interpret the results.

### Collider (statistics)

colliderCollider (epidemiology)conditioning on a collider
A typical counterexample occurs when Z is a common effect of X and Y, a case in which Z is not a confounder (i.e., the null set is Back-door admissible) and adjusting for Z would create bias known as "collider bias" or "Berkson's paradox."
Colliders are sometimes confused with confounder variables.

### Quasi-experiment

quasi-experimentalQuasi-experimental designquasi-experiments
This is particularly true if there are confounding variables that cannot be controlled or accounted for.

### Random assignment

randomly assignedrandomizationassignment of treatments to units
Randomized trials are not affected by confounding by indication due to random assignment.
Random assignment, blinding, and controlling are key aspects of the design of experiments, because they help ensure that the results are not spurious or deceptive via confounding.

### Epidemiology

epidemiologistepidemiologicalepidemiologists
Formal conditions defining what makes certain groups "comparable" and others "incomparable" were later developed in epidemiology by Greenland and Robins (1986) using the counterfactual language of Neyman (1935) and Rubin (1974). In epidemiology, one type is "confounding by indication", which relates to confounding from observational studies.
Confounding has traditionally been defined as bias arising from the co-occurrence or mixing of effects of extraneous factors, referred to as confounders, with the main effect(s) of interest.

### Cohort study

cohort studiescohortcohorts
This minimizes the chance that results will be influenced by confounding variables, particularly ones that are unknown.

### Observational study

observational studiesobservationalobservational data
In epidemiology, one type is "confounding by indication", which relates to confounding from observational studies.
One common approach is to use propensity score matching in order to reduce confounding.

### Randomized controlled trial

randomized controlled trialsrandomized clinical trialrandomized control trial
Such practices introduce selection bias and confounders (both of which should be minimized by randomization), possibly distorting the results of the study.

### Conditional probability

conditional probabilitiesconditionalconditioned
for all values X = x and Y = y, where P(y \mid x) is the conditional probability upon seeing X = x.

### Bayesian network

Bayesian networkshierarchical Bayes modelhierarchical Bayesian model
This is done by simulating an intervention do(X = x) (see Bayesian network) and checking whether the resulting probability of Y equals the conditional probability P(y \mid x).

Berkson's fallacy
A typical counterexample occurs when Z is a common effect of X and Y, a case in which Z is not a confounder (i.e., the null set is Back-door admissible) and adjusting for Z would create bias known as "collider bias" or "Berkson's paradox."

### Medieval Latin

LatinMiddle LatinMediaeval Latin
According to Morabia (2011), the word derives from the Medieval Latin verb "confudere", which meant "mixing", and was probably chosen to represent the confusion (from Latin: con=with + fusus=mix or fuse together) between the cause one wishes to assess and other causes that may affect the outcome and thus confuse, or stand in the way of the desired assessment.

### Ronald Fisher

R.A. FisherR. A. FisherFisher
Fisher used the word "confounding" in his 1935 book "The Design of Experiments" to denote any source of error in his ideal of randomized experiment.

### Leslie Kish

Kish, LeslieKishKish, L.
According to Vandenbroucke (2004) it was Kish who used the word "confounding" in the modern sense of the word, to mean "incomparability" of two or more groups (e.g., exposed and unexposed) in an observational study.

### Jerzy Neyman

NeymanJerzy Spława-NeymanNeyman, Jerzy
Formal conditions defining what makes certain groups "comparable" and others "incomparable" were later developed in epidemiology by Greenland and Robins (1986) using the counterfactual language of Neyman (1935) and Rubin (1974).

### Donald Rubin

Don RubinRubinDonald B. Rubin
Formal conditions defining what makes certain groups "comparable" and others "incomparable" were later developed in epidemiology by Greenland and Robins (1986) using the counterfactual language of Neyman (1935) and Rubin (1974).

### Judea Pearl

PearlPearl, JudeaProf. Dr. Judea Pearl
These were later supplemented by graphical criteria such as the Back-Door condition (Pearl 1993; Greenland, Pearl and Robins, 1999).

### Risk assessment

risk assessmentsassessmentacceptable risk
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.

### Human

humanshuman beinghuman beings
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.

### Health

human healthphysical healthwellness
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.

### Pesticide

pesticidescrop sprayingchemical pesticides
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.

### Down syndrome

Down's syndrometrisomy 21Downs Syndrome