Simply put, correlation is about understanding potential relationships between data variables. For example, temperature is frequently correlated with ice cream sales, and exercise frequency is also commonly known to be associated with health outcomes. Several correlation measures exist to quantify the magnitude and direction of these relationships: Pearson’s correlation for linear relationships, Spearman’s rank for monotonic relationships, and Kendall’s tau for ordinal data, to name a few.

Despite its consolidated theoretical foundations, there are some common myths and misunderstandings around correlation that propagate like wildfire. Let’s dismantle some of them in this article.

Myth 1: Pearson Correlation as a One-Fits-All Approach

A very common misconception is taking for granted that the very popular Pearson correlation coefficient is a one-fits-all solution, suitable for identifying any relationships between data variables. Pearson’s correlation is only suitable for linear relationships between continuous variables and assumes both variables are normally distributed. Therefore, since many real-world data don’t abide by these assumptions, it may fail to capture or realistically measure the strength of relationships that are non-linear, monotonic, or influenced by outliers.

Recall that the Pearson correlation coefficient is measured as a value ranging between -1 and 1, and calculated as follows:

One real-world use case where this becomes evident is in analyzing the relationship between age and income. While income often increases with age early in a person’s career, it often tends to reach a plateau or even may decrease later in life, resulting in a relationship of a non-linear nature. Pearson’s correlation might suggest a weak or no relationship close to 0, failing to capture the actual, nuanced trend. In this situation, using Spearman’s rank correlation or data visualization with scatterplots would provide clearer clues about the true nature of the relationship.

Myth 2: Highly Correlated Variables Visually Look Like This…

Let’s talk about data visualizations and scatter plots, and start with this question for you: which of the following two scatterplots show more highly correlated variables: the left-hand side one or the right-hand side one?

More than a few think that, when variables visually appear moderately to strongly correlated, a steeper slope indicates a higher correlation. The steepness of the slope reflects the relative magnitude or units of measurement of the two variables, not the strength of their correlation. A strong correlation coefficient is visually reflected by data points tightly clustered around a line, but the slope of that line-like visual pattern is just related to the data values. For this reason, the plot on the left-hand side above is the one where data variables are more strongly correlated.

A real-world situation leading to the left-hand side plot (high correlation, low slope) occurs when visualizing years of education vs. income growth rate: while more education generally leads to higher income growth, the increase is subtle and gradual. Meanwhile, a moderate correlation, high slope plot like the right-hand side one mimics real-world scenarios like representing price vs. demand for a luxury product. Small price variations can significantly impact demand in luxury retail, but the correlation between the two is not that strong, as demand is influenced also by other socioeconomic factors.

Myth 3: No Correlation Means Independent Variables

This myth is easier to debunk. When correlation coefficients are closer to 0, they indicate low or no correlation between two variables. Does this mean the two variables are independent? Not necessarily.

A clear real-world example of this is the relationship between a person’s shoe size and their age. While the correlation coefficient between shoe size and age might be close to zero for adults (no linear relationship), this does not mean that shoe size and age are totally independent. In fact, both variables are dependent in the specific context of childhood growth, where children’s shoe sizes increase with age. Therefore, even though the correlation coefficient may be close to zero for adults, the two variables are still dependent if we consider earlier stages of life.

Myth 4: Correlation Implies Causation

There is no better way to describe the last of the myths in this article than revisiting a classic even among the classics: correlation implies causation. As little as you have been exposed to data science and data analysis communities, chances are you heard about this myth. In a nutshell, just because two variables are correlated does not imply one causes the other. Remember: correlation simply measures the strength and direction of the relationship between two variables: it cannot be used to account for underlying factors or causative mechanisms.

A classic example of the correlation vs. causation myth — more examples are further elaborated upon in this article — is the relationship between ice cream sales and drowning incidents in the sea. While both tend to rise in summer, this doesn’t mean eating more ice cream causes more chances of drowning. The actual cause for both is (at least partly) warmer weather, which drives both increased open-air swimming and higher ice cream sales.

Wrapping Up

Besides the four myths and example scenarios illustrated around correlation, we wrap up this article with another interesting related reading that unveils another scientifically studied phenomenon: the Simpson Paradox, which states that aggregated data may distort the “original” relationship between variables. Happy reading!