As is well known, the expression “correlation does not equal causation” is a fundamental principle in statistics. It means that solely because two variables are observed to be correlated or change in tandem, it does not necessarily mean that one variable causes the other to change. The presence of a correlation between two variables does not have to imply a cause-and-effect relationship all the time.
In order to explain correlations without addressing causation, there may appear several alternative possibilities for that. Coincidence, common cause, and reverse causation are among the most commonly used concepts (Salkind & Frey, 2019). The first alternative defines the moment of two variables showing a correlation by chance or coincidence, without any prior causal relationship. The second one is the occurrence of two variables influenced by a common underlying factor or cause, which is the opposite of coincidence. Finally, reverse causation refers to specific cases in which the second variable causes changes in the first, rather than the other way around.
A correlation can be considered significant when the relationship between two variables is unlikely to be entirely due to chance. It means that the connection between the variables is not a result of random variation in the data, but rather that there is a structured relationship between the two given variables (Salkind & Frey, 2019). It is essential to remember that the significance of a correlation does not necessarily imply that meaningful conclusions can be drawn based solely on statistical results.
Several notions may explain this, such as causal inference and confounding variables (Salkind & Frey, 2019). In the first one, significance testing in correlation analysis only estimates whether the correlation differs from zero and, thus, does not establish causality. The presence of confounding variables, in turn, can influence correlations, making them appear significant even when there is no actual causal relationship.
Reference
Salkind, N. J. & Frey, B. B. (2019). Statistics for people who (think they) hate statistics (7th ed.). SAGE Publications.