How Chocolate Helped Me Understand Correlations: Part 1

I love chocolate! Even more than Psychology, Neuroscience and wine. So it’s not surprising that I used a chocolate context to help me understand what correlations are, what they mean and what they don’t mean. And guess what, chocolate as it turns out has its benefits!

This blog post is split into two parts; what a correlation means and what do the correlations tell us about chocolate.

Part 1: What is a correlation?

A correlation tells you three things:

  • There’s a relationship or an association between two factors or variables, for instance, eating chocolate and improved brain function

  • The direction of the relationship; if eating chocolate and improved brain function increase together or decrease together (positive correlation), if eating chocolate and improved brain function go in opposite directions, i.e. if one increases the other decreases and vice versa (negative correlation), or if there’s no pattern to be seen (no correlation)

  • The strength of the relationship (the r value), tells us if there is a strong relationship between eating chocolate and improved brain function (r = approx. ±0.7), a weak relationship and therefore it’s likely that there are other factors involved (r = approx. ±0.3), or they’re not related (r = 0)

If a study reported that eating chocolate and improved brain function showed a strong positive correlation, this means:

  1. Eating chocolate and improved brain function are related (a correlation)
  2. The more chocolate you eat the better your brain will function (a positive correlation)
  3. Eating chocolate is very related to a well functioning brain (a strong positive correlation)

On the flip side, if a study reported that eating chocolate and improved brain function showed a weak negative correlation, this means:

  1. Eating chocolate and improved brain function are still related (a correlation)
  2. The more chocolate you eat the worse your brain will function (a negative correlation)
  3. Eating chocolate is a little related to a well functioning brain and there are likely other factors involved (a weak negative correlation)

But a correlation does not mean causal, I repeat, correlation ≠ causation!

This is possibly the most common misinterpretation. Just because one thing is correlated with something else, it does not mean that one is causing the other.

So why report that there’s a causation when there’s only a correlation?

If a theory (sometimes called a hypothesis or model) is based on something tangible, for instance, if there are reports that most of the chocolate-eating population tend to be smarter, then there’s a good reason to test if eating chocolate and improved brain function are correlated. But this needs to be done without any other influencing factors being involved. If chocolate is the only factor being tested (or eaten) and all other factors are controlled for (i.e. they have no influence), and the results show there’s a correlation, two things can be reported:

  1. Chocolate and improved brain function are related
  2. It could be suggested that chocolate can improve brain function

But it’s not always that simple. Sometimes studies are based on weak theories, poor experimental designs or conducting the wrong statistical tests, and still random correlations can be found.

But don’t panic! This is pretty common and science is as much about proving theories as disproving them. When weird results appear, most researchers go back and check and retest what they did. But occasionally there’s the odd ego jumping the gun. A lot of the time the facts are checked and rectified, but the real battle is checking them before the study goes viral…

Are you feeling a little frustrated that correlations don’t provide a definitive answer?

I don’t blame you. But this is how science works and how psychology testing works; test, test and test again until you have enough studies and evidence to support your theory. And at the end of the day, all this testing is worth finding out if chocolate really does make us smarter.

Written by Alison Holland

References

http://www.steekproeven.eu/wp/wp-content/uploads/2013/03/nejmon1211064chocolate.pdf

https://pdfs.semanticscholar.org/34c4/33a22cf59744b130f2597aaf5aa1733768a1.pdf

https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php

http://www.theofficediet.com/health-benefits-of-dark-chocolate/

http://theconversation.com/clearing-up-confusion-between-correlation-and-causation-30761

https://www.skepticalraptor.com/skepticalraptorblog.php/correlation-does-not-imply-causation-except-when-it-does/

http://www.tylervigen.com/spurious-correlations

http://www.dummies.com/education/math/statistics/how-to-interpret-a-correlation-coefficient-r/