# Correlation and causal relationship

### Difference Between Causality And Correlation? | Business Analytics Tool

What is the difference between correlation and causality? However, many people tend to mix up these two relationship,often causing incorrect conclusions. However, there is a difference between cause and effect (causation) and relationship (correlation). Sometimes these areas can be confused. This animation explains the concept of correlation and causation. of the other event; i.e. there is a causal relationship between the two events.

Causality lets you change the future. What pizza and the germ theory of disease have in common A correlation is a relationship that you observe between two variables that appear to be related. Until the late 19th century, it was believed by scientists and laypeople alike that bad odors caused disease.

The sick and dying tended to smell unpleasant so the two phenomena were correlated. However, it was only in that the germ theory of disease became accepted.

### Correlation does not imply causation - Wikipedia

With this, it became clear that while bad smells and disease often appeared together, both were caused by a third, hitherto unknown variable—the microscopic organisms we know as germs. Correlations are often mistaken for causation because common sense seems to dictate that one caused the other. After all, bad smells and disease are both unpleasant, and always seem to appear at the same time and in the same places.

But you can have a foul odor without a disease. To prove causation, you need to find a direct relationship between variables. You need to show that one relies on the other, not just that the two appear to move in concert. 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.

The medical thermometer had not yet been invented, so this increase in temperature was rarely noticed. Noticeable symptoms came later, giving the impression that the lice left before the person got sick.

One making an argument based on these two phenomena must however be careful to avoid the fallacy of circular cause and consequence. 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. 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.

### Correlation and Causation

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.

Correlation vs. Cause and Effect

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. Therefore, the simple conclusion above may be false.

Example 5 Since the s, both the atmospheric CO2 level and obesity levels have increased sharply.