# Causal relationship between variables

### Causal and non-causal relationships

The first step in establishing causality is demonstrating association; simply put, is there a relationship between the independent variable and the dependent. This animation explains the concept of correlation and causation. If you are unable to access the video a Transcript .doc 26kb) has been. I want to re-emphasize that there are NO techniques that enable you definitely determine if a correlation between variables is causal. The only way to do this is to.

That is "if circumstance p is true, then q follows. Where there is causation, there is a likely correlation. Indeed, correlation is often used when inferring causation; the important point is that correlation is not sufficient.

For any two correlated events, A and B, the different possible relationships include[ citation needed ]: A causes B direct causation ; B causes A reverse causation ; A and B are consequences of a common cause, but do not cause each other; A and B both cause C, which is explicitly or implicitly conditioned on; A causes B and B causes A bidirectional or cyclic causation ; A causes C which causes B indirect causation ; There is no connection between A and B; the correlation is a coincidence.

Thus there can be no conclusion made regarding the existence or the direction of a cause-and-effect relationship only from the fact that A and B are correlated. Determining whether there is an actual cause-and-effect relationship requires further investigation, even when the relationship between A and B is statistically significanta large effect size is observed, or a large part of the variance is explained. Examples of illogically inferring causation from correlation[ edit ] B causes A reverse causation or reverse causality [ edit ] Reverse causation or reverse causality or wrong direction is an informal fallacy of questionable cause where cause and effect are reversed.

### The relationship between variables - Draw the correct conclusions

The cause is said to be the effect and vice versa. Example 1 The faster windmills are observed to rotate, the more wind is observed to be.

Therefore wind is caused by the rotation of windmills. In this example, the correlation simultaneity between windmill activity and wind velocity does not imply that wind is caused by windmills.

Wind can be observed in places where there are no windmills or non-rotating windmills—and there are good reasons to believe that wind existed before the invention of windmills.

Therefore, high debt causes slow growth.

## Australian Bureau of Statistics

This argument by Carmen Reinhart and Kenneth Rogoff was refuted by Paul Krugman on the basis that they got the causality backwards: Children that watch a lot of TV are the most violent.

Clearly, TV makes children more violent. This could easily be the other way round; that is, violent children like watching more TV than less violent ones.

Example 4 A correlation between recreational drug use and psychiatric disorders might be either way around: Gateway drug theory may argue that marijuana usage leads to usage of harder drugs, but hard drug usage may lead to marijuana usage see also confusion of the inverse.

Indeed, in the social sciences where controlled experiments often cannot be used to discern the direction of causation, this fallacy can fuel long-standing scientific arguments. Example 5 A historical example of this is that Europeans in the Middle Ages believed that lice were beneficial to your health, since there would rarely be any lice on sick people.

The reasoning was that the people got sick because the lice left. In the most extreme case, Two variables can be related to each other without either variable directly affecting the values of the other.

### Statistical Language - Correlation and Causation

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.

• Correlation does not imply causation

For example, the scatterplot below shows data from a sample of towns in a region. The positive correlation between the number of churches and the number of deaths from cancer is an example of a non-causal relationship -- the size of the towns is a lurking variable since larger towns have more churches and also more deaths.

Clearly decreasing the number of churches in a town will not reduce the number of deaths from cancer! Researchers usually want to detect causal relationships.

13-1 Relationships Between Variables

When it comes to your business, it is imperative that you make the distinction between what actions are related and what caused them to happen. How correlation gets mistaken for causation Picture this: Thirty days into the new app being out, you check your retention numbers.

Users who joined at least one community are being retained at a rate far greater than the average user. This seems like a massive coup.

## Relationship Between Variables

All you know is that the two are correlated. You have no idea what other factors are at play, what other behaviors those users took part in besides joining a community. Once you lay out the variables, you can control and change them to meet your needs.

Look at each of your variables, change one and see what happens.