As a follow-up to last week’s post (Beware of geeks bearing gifts), I’m posting four charts known as Anscombe’s Quartet, as an example of how statistical measures can fall short. It is important to understand the data behind a number, as a single numbers can only convey so much information and statistics can be manipulated in a variety of ways.
In the below four charts:
- all of the y-axes have the same mean AND variance
- all of the x-axes have the same mean AND variance
- the correlation between x and y is identical
- all of the charts share the same mean regression
The human mind prefers simplicity and our brain develops heuristics (rules of thumb) as shortcuts to help us process data more quickly. One of the things that I have learned over the years is to look at the data behind various investment numbers. When looking at empirical or projected returns, single numbers are rarely helpful. Annualized returns are simple and easy to understand, but monthly or annual and/or sequential returns are often much more informative. Similarly, an average return number or average volatility number is rarely as telling as the probability distribution behind it.
A few takeaways for me include:
- understand the distribution that is behind a number
- understand what each statistical output represents and does not represent
- visualizing data is often helpful
Full Disclosure: The information provided here is for educational purposes only. Nothing in this article should be construed as a tax advice, solicitation or offer, or recommendation, to buy or sell any security. There is a potential for loss as well as gain. Actual investors may experience different results from the results shown. Past performance is no guarantee of future results.