# Negative correlation and causal relationship

### Statistical Language - Correlation and Causation

Correlation and Causation – a simple guide the relationships between them and put everything again together in order to draw general conclusions. increases (a positive correlation) or decreases (a negative correlation). An example of a negative correlation is latitude and temperature; as latitude increases, It is often a very difficult matter to distinguish true causal relationship . Correlation does not imply causation, just like cloudy weather does not imply be a genuine cause-and-effect relationship (such as rainfall levels and . Positives in negative results: when finding 'nothing' means something.

## Fundamentals: Correlation and Causation

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. Seemingly compelling correlations, say between given genes and schizophrenia or between a high fat diet and heart disease, may turn out to be based on very dubious methodology.

### Clearing up confusion between correlation and causation

We are perhaps as a species cognitively ill prepared to deal with these issues. The bad news is that our evolution equipped us to live in small, stable, hunter-gatherer societies. We are Pleistocene people, but our languaged brains have created massive, multicultural, technologically sophisticated and rapidly changing societies for us to live in.

In consequence, we must constantly resist the temptation to see meaning in chance and to confuse correlation and causation. This article is part of a series on Understanding Research. The follow-up question has to be: What is the exact underlying physiological mechanism behind this connection? While this research is helpful in first place, we should only take it as a starting point to discover the true mechanisms if there are any. Without doing that, our interventions will be less effective because we are not targeting the actual cause.

These figures show increased risk of obesity with greater antibiotic use, particularly for children with 4 or more exposures to antibiotics. Increased BMI seems to be associated with an increased risk of several cancers in adults Renehan et al.

Again, we might be misled by this. It would be erroneous to conclude that simply being overweight causes cancers.

CRITICAL THINKING - Fundamentals: Correlation and Causation

Instead, we need to consider other potential variables that might explain the relationship between increased BMI and increased risk of cancers.

In non-causal relationships, the relationship that is evident between the two variables is not completely the result of one variable directly affecting 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.

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!