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Correlation is a statistical tool used to measure the strength and direction of the relationship between two variables. When statisticians say that two factors are correlated, they are using numerical representation, such as Pearson's correlation coefficient, to indicate how closely the variation in one variable is associated with the variation in another.

For instance, there might be a positive correlation between the number of hours studied and exam scores, suggesting that as one increases, so does the other. However, this correlation does not indicate that studying longer causes better scores; other factors, such as the difficulty of the material or the student's intrinsic understanding of the subject, could also play significant roles.

Confounding variables are external factors that can cause spurious correlations between two seemingly related variables. These are variables that affect both the independent variable (the cause) and the dependent variable (the effect), but are not typically of interest to the researcher.

For example, let's say ice cream sales and shark attacks are positively correlated. A confounding variable, such as hot weather, can explain this correlation since warmer temperatures can increase both the likelihood of people buying ice cream and swimming in the ocean where shark attacks may occur.

Spurious correlations are relationships between two variables that appear to be related to one another but are actually influenced by the presence of one or more external factors. These relationships can be mistakenly interpreted as evidence of causation when, in fact, they're not.

An often-cited, humorous example is the correlation between the number of films Nicolas Cage appeared in a given year and the number of people who drowned in swimming pools. While the data may show a relationship, it is clear that there is no direct causative link between these two variables – their correlation is spurious.

While correlation is an invaluable statistical tool, it has significant limitations that must be recognized. Correlation does not imply causation; it does not determine whether one variable causes changes in another, but merely that they are related in some way. One can't infer the direction of the cause-effect relationship from correlation - whether A causes B, B causes A, or both are affected by an outside variable C is not something correlation can uncover.

Also, outliers can heavily influence the results of a correlation study, leading to misleading conclusions. Thus, careful analysis and thoughtful experimental design are paramount in establishing true causation between variables.