# Non causal correlation is the relationship

### Elements of Research

The two variables aren't related at all, but correlate by chance. The more things are examined. In non-causal relationships, the relationship that is evident between the two The positive correlation between the number of churches and the number of. Jan 28, A correlation raises the possibility of a cause-and-effect relationship, but no more or less than it raises the possibility of a non-causal.

A relationship between variables, however, does not necessarily mean that a causal relationship exists.

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

Remember, correlation does not necessarily mean, or guarantee, causation. In other words, the observed relationship may be a coincidence.

As a reminder, the direction of a relationship refers to positive or negative relations between variables. A positive relation means that as values of one variable increase, or decrease, values of the other variable also increase, or decrease. A negative relationship means that as values of one variable increase, or decrease, values of the other variable change in the opposite direction.

The magnitude of a relationship between variables is also important when considering causality. The magnitude of a relationship is the extent to which variables change together in one direction or 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.

### Association VS. Causal relationships

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.

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!

• Correlations
• Judging correlations

Researchers usually want to detect causal relationships. 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. 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.

## Australian Bureau of Statistics

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. The real reason however is that lice are extremely sensitive to body temperature. A small increase of body temperature, such as in a feverwill make the lice look for another host. 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.

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