Here is a trap that is easy to fall in to. Confusing correlation as causation. As analysts, it is our job to see the data as it is rather than imply causation that doesn’t exist.
Let’s sample a chart, recently featured in Economist’s graphic detail under the title Measuring well-being.
At the end of the article they show the above chart and say, (emphasis mine)
BCG also compared financial inclusion (the percentage of individuals aged 15 or over with a bank account) against each country’s SEDA score, revealing a clear relationship.The report’s authors found that countries with higher financial inclusion generally had higher well-being than their peers at a similar income level.
Now, it is easy to misunderstand above chart and come to a conclusion that if you provide bank accounts to everyone in a country, then the country’s SEDA score (well-being) would improve.
But this would be wrong.
As an analyst leaning towards awesomeness, you want to ask questions like,
- Is it a coincidence that countries with higher well-being naturally have bank accounts for everyone?
- How does having a bank account impact a person’s well being?
- What other factors can contribute to well being? What about access to education, healthcare and information?
So there you go. Next time you see data or visual analysis that exhibits correlations, do not confuse them as causation. Question the factors first.
More charting principles and guidelines for you
- How to select right chart for your data
- Don’t make your charts heavier than they should be
- Avoid data dumps in your charts
- Understand data to ink ratio to make better charts
Do you often confuse correlation with causation?
Have you seen such misinterpretation of data in your work life? What was it like? Please share your thoughts in the comments section.
7 Responses to “Correlation vs. Causation [Charting Chatter]”
It's the age old question, if there's a positive relationship between church and crime, that is as crime increases there is a corresponding increase in the number of churches, do we blame increases in crime on an increase in the number of churches? Or are churches an outcome of increasing crime?
Correlation and regression CANNOT tell you the answer. In fact there probably are other factors which drive this relationship. The classic example of this is, "When big ships leave harbor, small ships return", but the cause of this paired relationship is dependent upon a 3rd factor, "because the tide rises".
There are other modeling techniques which can model causality, such as Structured Equation Modeling, but as far as I know these are not reproducible in Excel; at least not without a lot of very complicated math.
While you're at it, Chandoo, you should consider doing a series of posts on the Data Analysis toolpak. Excel is somewhat limited in its statistical capability, but you can run quite a few tests with it.
Pearson Correlation (and Spearman Correlation with a data rank helper column)
Single & Multiple Regression
Covariance (correlation of variances, e.g. does the variability in one factor correspond to changes in variability in another?)
ANOVA (Difference of means between multiple factors)
F-Tests (test for differences in variances between two independent samples of, probably, the same factor)
T-Tests to compare two means.
I don't use Z tests generally, because I almost never have a sample of equal size to the population, but it's there. Generally a T-Test is sufficient.
One of the the assumptions of ALL of these data analysis techniques is that the data is normally distributed, which it very rarely is. These are referred to as parametric tests. There are non-parametric equivalent tests for each of these, but Excel doesn't support them, except for Spearman Correlations which I've mentioned above.
I need to use the Excel Data Analysis toolpack and calculate the tests you mention above (6:00 pm). Can you recommend, or do you offer, a 1:1 / remote tutoring? I'm looking for about 1 hour of assistance on a homework problem.
One last thing, and I'll shut up. 🙂
Some good formulas outside of the Data Analysis Toolpak:
=percentile(array,n) which gives you the Nth percentile of an array.
Fire departments in the USA frequently look at the 90th percentile response time for an array of response times.
=correl(array1,array2), which gives you the Pearson correlation between two arrays or factors.
Some folks might also benefit from:
CHISQ.DIST, CHISQ.DIST.RT, CHISQ.INV to compare categorical data.
CONFIDENCE.NORM and CONFIDENCE.T to estimate the value of a population mean between two values, that is the mean of the sample is X, with a confidence interval of between X1 and X2 for the population.
LINEST for regression using formulas, but this technique ignores Beta Coefficients; key for understanding X factor behaviors.
Ok, enough of that. 🙂
The source of the problem is largely the graph.
When a correlation exists, the axes of x and y are normally chosen to support the correlation, X means Y
In this particular case, the axes are reversed.
IMO there's a causation between the two but it's not the bank account that makes people happy. It's having enough money so that you need a bank account, i.e. not living from hand to mouth.
Yesterday I saw an article where some academics have come up with a technique (called the Additive Noise Model) to measure causation for continuous variables using observational data only.
This is a big deal, because this technique can unlock answers to a huge number of questions.
The academic paper, published in the Journal of Machine Learning Research) can be found here: