# 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

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### 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

**spurious correlationspuriousmisleading results**

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 paradox

**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**

### Down syndrome

**Down's syndrometrisomy 21Downs Syndrome**