Association: We observe that as the temperature increases, ice cream sales also tend to increase. We also see that as temperature rises, the number of people visiting the beach increases. Here, we are simply stating an observed relationship, not quantifying it or implying causation. These are examples of associations.
Correlation: We calculate a correlation coefficient for temperature and ice cream sales, and find it's 0.85. This is a strong positive correlation, meaning that as the temperature increases, ice cream sales tend to increase as well. However, this doesn't necessarily mean that the increase in temperature causes the increase in ice cream sales. It's also possible that a third variable is influencing both (such as holiday periods, where both temperature and ice cream sales might be higher).
Causation: To establish causation, we need to rule out potential confounding factors and show that changes in temperature directly lead to changes in ice cream sales. This might involve an experiment or careful observation over time. If, for instance, we observe that irrespective of the day of the week, the specific month, or any special events, the rise in temperature consistently leads to increased ice cream sales, then we might start to argue that higher temperatures cause an increase in ice cream sales.
An additional hypothetical experiment to establish causation could involve manipulating the temperature (like having temperature controlled rooms), and observing the impact on ice cream sales. If all other factors are kept constant and a higher temperature still leads to an increase in ice cream sales, then it is reasonable to conclude a causal relationship: temperature increases cause ice cream sales to increase.