# Causation and causal relationship math

### Correlation does not imply causation - Wikipedia

When two variables are related, we say that there is association between Causality can only be determined by reasoning about how the data. The point means that, when A and B both cause C, observing a correlation between A and B in cases where C is true, does not mean there is a. A causal relation between two events exists if the occurrence of the first causes the other. The first event is called the cause and the second event is called the.

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.

How Ice Cream Kills! Correlation vs. Causation

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.

## Correlation does not imply causation

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.

### causality - Relationships between correlation and causation - Cross Validated

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. The groups are not on the same footing: We would therefore expect them to be significant healthier than office workers, on average, and should rightly be concerned if they were not. This is also known as the Will Rogers effect, after the US comedian who reportedly quipped: When the Okies left Oklahoma and moved to California, they raised the average intelligence level in both states.

If diagnostic methods improve, some very-slightly-unhealthy patients may be recategorised — leading to the health outcomes of both groups improving, regardless of how effective or not the treatment is.

### What Are Causal Relationships Pertaining to Algebra? | Sciencing

Picking and choosing among the data can lead to the wrong conclusions. The skeptics see period of cooling blue when the data really shows long-term warming green. This is bad statistical practice, but if done deliberately can be hard to spot without knowledge of the original, complete data set.

• Association VS. Causal relationships
• Australian Bureau of Statistics

Consider the above graph showing two interpretations of global warming data, for instance. Or fluoride — in small amounts it is one of the most effective preventative medicines in history, but the positive effect disappears entirely if one only ever considers toxic quantities of fluoride.

For similar reasons, it is important that the procedures for a given statistical experiment are fixed in place before the experiment begins and then remain unchanged until the experiment ends.

Consider a medical study examining how a particular disease, such as cancer or Multiple sclerosis, is geographically distributed. If the disease strikes at random and the environment has no effect we would expect to see numerous clusters of patients as a matter of course. If patients are spread out perfectly evenly, the distribution would be most un-random indeed! So the presence of a single cluster, or a number of small clusters of cases, is entirely normal.

Sophisticated statistical methods are needed to determine just how much clustering is required to deduce that something in that area might be causing the illness. Unfortunately, any cluster at all — even a non-significant one — makes for an easy and at first glance, compelling news headline. One must always be wary when drawing conclusions from data! Randall MunroeCC BY-NC Statistical analysis, like any other powerful tool, must be used very carefully — and in particular, one must always be careful when drawing conclusions based on the fact that two quantities are correlated.

Instead, we must always insist on separate evidence to argue for cause-and-effect — and that evidence will not come in the form of a single statistical number.