Common Examples of Positive Correlations. The more time you spend running on a treadmill, the more calories you will burn. Taller people have larger shoe sizes and shorter people have smaller shoe sizes. The longer your hair grows, the more shampoo you will need.

Why is it unwise to conclude that if two variables are correlated, one must have caused the other? A. Variables can never be measured with complete accuracy. It is impossible to conclude that two variables are related unless one can measure them perfectly.

An example of positive correlation would be height and weight. Taller people tend to be heavier. A negative correlation is a relationship between two variables in which an increase in one variable is associated with a decrease in the other.

There are several statistical reasons for unexpected correlations: Non-linear relationships — Correlation coefficients assume that the relationship between two variables is linear. Outliers — The strength of a correlation coefficient can be deflated or inflated by outliers.

Correlation is symmetric, so shoe size and age are correlated. But it would be absurd to say that shoe size causes age. In other words, even when there is a causal relationship, the causality typically only goes one way. (Of course, it could go both ways, as in a feedback loop.)

Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For example, height and weight are related; taller people tend to be heavier than shorter people. Correlation can tell you just how much of the variation in peoples’ weights is related to their heights.

Causation can occur without correlation when a lack of change in the variables is present. There’s no correlation. If I hit a glass with a hammer once, we have a clear, obvious causative effect, but because I did it once, there’s no correlation because there’s no other variable to compare it against.