# What is a causal relationship between two variables

### Causal and non-causal relationships

A relationship, or correlation, in research broadly refers to any relationship between two or more variables. A causal relationship is a relationship between. For instance, evidence supporting causation might be very different if we're Correlation is just a linear association between two variables. For example, for the two variables "hours worked" and "income earned" there is a relationship between the two if the increase in hours worked.

### Statistical Language - Correlation and Causation

The packaging material might influence shelf life, but the shelf life cannot influence the packaging material used. The relationship is therefore causal. A bank manager is concerned with the number of customers whose accounts are overdrawn. Half of the accounts that become overdrawn in one week are randomly selected and the manager telephones the customer to offer advice.

Any difference between the mean account balances after two months of the overdrawn accounts that did and did not receive advice can be causally attributed to the phone calls. If two variables are causally related, it is possible to conclude that changes to the explanatory variable, X, will have a direct impact on Y. Non-causal relationships Not all relationships are causal.

## Types of Relationships

In non-causal relationships, the relationship that is evident between the two variables is not completely the result of one variable directly affecting the other. In the most extreme case, Two variables can be related to each other without either variable directly affecting the values of the other.

The two diagrams below illustrate mechanisms that result in non-causal relationships between X and Y. If two variables are not causally related, it is impossible to tell whether changes to one variable, X, will result in changes to the other variable, Y.

When we talk about types of relationships, we can mean that in at least two ways: The Nature of a Relationship While all relationships tell about the correspondence between two variables, there is a special type of relationship that holds that the two variables are not only in correspondence, but that one causes the other.

This is the key distinction between a simple correlational relationship and a causal relationship. A correlational relationship simply says that two things perform in a synchronized manner. For instance, there has often been talk of a relationship between ability in math and proficiency in music. In general people who are good in one may have a greater tendency to be good in the other; those who are poor in one may also tend to be poor in the other.

If this relatioship is true, then we can say that the two variables are correlated. But knowing that two variables are correlated does not tell us whether one causes the other.

### Elements of Research

We know, for instance, that there is a correlation between the number of roads built in Europe and the number of children born in the United States. Does that mean that if we want fewer children in the U. Or, does it mean that if we don't have enough roads in Europe, we should encourage U.

At least, I hope not. While there is a relationship between the number of roads built and the number of babies, we don't believe that the relationship is a causal one.

This leads to consideration of what is often termed the third variable problem. In this example, it may be that there is a third variable that is causing both the building of roads and the birthrate, that is causing the correlation we observe. For instance, perhaps the general world economy is responsible for both.

When the economy is good more roads are built in Europe and more children are born in the U. The key lesson here is that you have to be careful when you interpret correlations.