# Causation and causal relationship between

### Why correlation does not imply causation? – Towards Data Science

There's quite a bit of confusion about the meanings of statistical terms like correlation, association, and causality. I wrote this post to clear up the confusion, but. Reverse causation or reverse causality or wrong direction is an informal fallacy of . Once emergent data tests positively for validity and reliability, you would consider the extent of the existential relationship as an indicator of causality.

Hence, we have alternate reasoning issue in this case. We can reject hypothesis based on inverse causality. For instance, higher mental stress can actually influence a person to smoke. Once again, we can reject hypothesis based on inverse causality. Higher age leads to both, having kids and higher maturity levels.

Causal relation does exist. We definitely know that inverse causality is not possible. Also alternate reasoning or mutual independence can be rejected.

If you were able to answer all the 4 scenarios correctly, you are ready for the next concept. In case you got any of the scenario wrong, you probably need more practice on finding cause-effect pairs.

## Australian Bureau of Statistics

What are the keypoints in establishing causation? Sometimes X and Y might just be correlated and nothing else. In such cases we reject hypothesis based on mutual independence.

In fields like pharma, it is very important to establish cause-effect pairs. An experiment is often defined as random assignment of observational units to different conditions, and conditions differ by the treatment of observational units. Treatment is a generic term, which translates most easily in medical applications e. If we do not have the luxury to do a randomized experiment, we are forced to work on existing data sources.

These events have already happened without any control. Hence, the selection is not random. Deriving out causality from Observational data is very difficult and non-conclusive. For a conclusive result on causality, we need to do randomized experiments. Why are observational data not conclusive?

We can never conclude individual cause-effect pair. There are multiple reason you might be asked to work on observational data instead of experiment data to establish causality. First is, the cost involved to do these experiments.

For instance, if your hypothesis is giving free I-phone to customers, this activity will have an incremental gain on sales of Mac. Doing this experiment without knowing anything on causality can be an expensive proposal.

Second is, not all experiments are allowed ethically. Correlation does not mean causality or in our example, ice cream is not causing the death of people.

### Statistical Language - Correlation and Causation

When 2 unrelated things tied together, so these can be either bound by causality or correlation. In Majority of the cases correlation, are just because of the coincidences.

So the less the information we have the more we are forced to observe correlations. Similarly the more information we have the more transparent things will become and the more we will be able to see the actual casual relationships. Weather is actually causing the rise in ice cream sales and homicides.

As in summer people usually go out, enjoy nice sunny day and chill themselves with ice creams. There is no causal relationship between the ice cream and rate of homicide, sunny weather is bringing both the factors together. And yes, ice cream sales and homicide has a causal relationship with weather. One making an argument based on these two phenomena must however be careful to avoid the fallacy of circular cause and consequence.

## What’s the difference between Causality and Correlation?

Poverty is a cause of lack of education, but it is not the sole cause, and vice versa. Third factor C the common-causal variable causes both A and B[ edit ] Main article: Spurious relationship The third-cause fallacy also known as ignoring a common cause [6] or questionable cause [6] is a logical fallacy where a spurious relationship is confused for causation.

It is a variation on the post hoc ergo propter hoc fallacy and a member of the questionable cause group of fallacies. All of these examples deal with a lurking variablewhich is simply a hidden third variable that affects both causes of the correlation.

Example 1 Sleeping with one's shoes on is strongly correlated with waking up with a headache. Therefore, sleeping with one's shoes on causes headache.

• Correlation does not imply causation
• Correlation vs Causation: Understand the Difference for Your Business
• Why correlation does not imply causation?

The above example commits the correlation-implies-causation fallacy, as it prematurely concludes that sleeping with one's shoes on causes headache. A more plausible explanation is that both are caused by a third factor, in this case going to bed drunkwhich thereby gives rise to a correlation.

So the conclusion is false. Example 2 Young children who sleep with the light on are much more likely to develop myopia in later life. Therefore, sleeping with the light on causes myopia. This is a scientific example that resulted from a study at the University of Pennsylvania Medical Center. Published in the May 13, issue of Nature[7] the study received much coverage at the time in the popular press.

It did find a strong link between parental myopia and the development of child myopia, also noting that myopic parents were more likely to leave a light on in their children's bedroom. Example 3 As ice cream sales increase, the rate of drowning deaths increases sharply. Therefore, ice cream consumption causes drowning.

This example fails to recognize the importance of time of year and temperature to ice cream sales. Ice cream is sold during the hot summer months at a much greater rate than during colder times, and it is during these hot summer months that people are more likely to engage in activities involving water, such as swimming. The increased drowning deaths are simply caused by more exposure to water-based activities, not ice cream.

The stated conclusion is false. This suggests a possible "third variable" problem, however, when three such closely related measures are found, it further suggests that each may have bidirectional tendencies see " bidirectional variable ", abovebeing a cluster of correlated values each influencing one another to some extent.