Final answer:
Correlation between two variables does not indicate causation because it could be influenced by a third, confounding variable. Correlation coefficients only measure the strength and direction of a relationship. Controlled experiments are needed to establish causation, not observational studies that only show correlation.
Step-by-step explanation:
When two variables are correlated, it means there is a relationship between them such that changes in one variable are associated with changes in the other. However, this does not mean that one variable causes the other to change. The main reason why we cannot conclude causation from correlation is due to c) The possibility of a third variable. This third variable, often called a confounding variable, may influence both variables of interest, thus explaining the correlation.
For example, the observed correlation between ice cream sales and crime rates might lead one to presume that ice cream consumption drives crime rates up, but in reality, higher temperatures might increase both. Likewise, early correlational research indicated a relationship between smoking and cancer, but without experimental evidence, we could not claim causation. It’s important to understand that correlation coefficients, r, merely tell us about the strength and direction of a relationship, not causality.
Only controlled experiments, where variables are manipulated and confounding factors are controlled, can establish a cause-and-effect relationship. In observational studies, the inability to control for all variables is why correlations observed do not guarantee causation.