Correlation and Causation Correlation

Correlation and Causation

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Definitions

Correlation

In statistics, when two or more variables have a statistical relationship, they are said to be correlated. For example, let’s consider the variables “sunscreen sales” and “ice cream sales”; both these variables experience an increase in value in the summers because people purchase more ice cream and sunscreen as the temperature rises. Therefore, both these variables have a statistical relationship as when there is a change in one, there is also a change in the other. 

Causation 

Causation goes beyond defining the extent of the relationship between variables and also defines the type of relationship between them. It implies that a change in one variable causes a change in the other, meaning that the two variables have a causal relationship. In a causal relationship, also referred to as a cause-and-effect relationship, there is an independent variable (the cause) and a dependent variable (the effect); a change in the independent variable influences, or causes, a change in the dependent variable.

For example, let’s consider “temperature” and “ice cream sales”. As the temperature rises, more people purchase ice cream; the change in temperature has caused a change in the sales of ice creams and, therefore, the two variables have a causal relationship. In this relationship, “temperature” is the independent variable (the cause), and “ice cream sales” is the dependent variable (the effect).

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Understanding Correlation

Correlation implies a statistical association between variables. Scatterplots are often used to display variables on an xy-plane to determine the existence and type of correlation between the variables. If the pattern illustrated on the scatterplot can be approximated with a straight line, the correlation between the variables is ‘linear’. If not, the correlation is ‘non-linear’. 

There are three main types of correlations:

  • Positive Correlation: Variables have a positive correlation when they both change in the same direction; when one increases, the other increases too and when one decreases, the other decreases too. 
  • Negative Correlation: Variables have a negative correlation when they both change in opposite directions; when one increases, the other decreases and when one decreases, the other increases. 
  • No Correlation: When two variables are completely unrelated, they are said to have ‘no correlation’; an increase or decrease in one leads to no changes in the other. 

 

Understanding Causation

Causation implies that there is a cause-and-effect relationship between the variables; a change in one causes a change in the other. It is important to keep in mind that correlation does not always imply causation and that a causal relationship can only be established using conclusive and reliable data. 

How to Derive a Cause-and-Effect Relationship

The causal relationship between two variables can be proven using the following approaches: 

  • Randomized Experimental Data: Experiments that use random assignment to distribute test subjects into a control group and a treatment group to study the influence of the independent variable. 
  • Observational Data: There are certain circumstances when randomized experiments cannot be carried out, usually due to ethical reasons of feasibility. In such situations, observational data is used by conducting research with data extracted from existing data sources. This approach is less reliable and not as conclusive in establishing causality when compared to randomized experiments. 

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The Difference between Correlation and Causation

‘Correlation’ and ‘causation’ are two distinct concepts that must not be confused. Correlation simply indicates the existence of a statistical relationship, or association, between two variables; it does not say that one variable influences the other. Causation, on the other hand, does indicate that one variable influences the other and that a change in one ‘causes’ a change in the other. 

Causation always implies correlation, but correlation does not imply causation. Let’s understand why.

Correlation does not Imply Causation

There are two main reasons why correlation does not imply causation: 

  • Third/Confounding Variable: Confounding variables are variables that influence the variables being studied, making them appear to be causally related even though they are not. For instance, although it may seem as though ice cream sales and sunscreen sales are closely related, a change in one is not the reason for the change in the other. A third variable, “temperature” is causally related to both these variables separately, resulting in their correlation. 
  • Directionality Issues: Sometimes variables may actually have a causal relationship but directionality issues make it difficult to determine which variable is independent and which is dependent.

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FAQs on Correlation and Causation

Correlation is a term used to describe the existence of a statistical association, or relationship, between two variables.

 Correlation simply implies a statistical association between variables while causation implies that a change in one variable causes a change in the other. 

 Correlation does not imply causation for the following reasons; 

  1. Directionality issues make it difficult or impossible to distinguish between the independent and dependent variables.
  2. The existence of confounding variables could be the reason for the correlation.

There are three main types of correlation, namely; 

  1. Positive Correlation: Exists when variables change in the same direction
  2. Negative Correlation: Exists when variables change in opposite directions
  3. No Correlation: Exists when there is no association between the variables

Causation is a term used to describe cause-and-effect relationships that exist when a change in one variable can influence a change in the other.

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Hindol Basu 
GM, Voxco Intelligence

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