This is a very simple and very pathological example that's easily ferreted out with a few more summary statistics (median, min, max) but it's a good illustration of the blind application of statistics. Short of visualization, non-parametric statistics really help with such things. Correlation is a fragile, linear measure, and things that are obviously correlated by inspection can easily appear mathematically uncorrelated -- points on a unit circle, for example. Likewise, the mean of any skewed distribution tells you very little, but that's the statistic that's always cited. Quantiles, medians, and non-parametric measures of correlation such as rank correlation are simple and often overlooked. They do a good job screening for pathological data sets like Anscombe's quartet and real world ones.

It's also worth mentioning "dumbbell" data sets. Two clusters of data, each of which have a independent, meaningful correlation in them, can easily leverage a linear regression into a meaningless line passing through the two clusters. That's a pretty common issue with high dimensional data (obviously you can see it in a 2D scatter plot), and it's not easily caught short of looking at regression diagnostic statistics.

I believe the "dumbbell" effect you are referring to is Simpson's paradox: http://en.wikipedia.org/wiki/Simpson's_paradox

As you point out obviously you can see it in a 2D scatter plot, but you have to select the correct two variables.

I think, typically, if you've gone to the trouble of calculating variance and correlation, you would have also calculated the median and mode of these datasets. The differences would have been obvious with those basic analyses.

How do you define the mode of a data set where all the values are different?

Statwing looks great!

Right now I do my data analysis in numpy, but this looks good for my Excel-based colleagues.

What library is doing the statistics?

Thanks, really appreciate it! We use numpy, scipy, and pandas.

EDIT: clarified libraries we use.

So a concept you find in a beginner stats textbook is now 'news'? Definition of blogspam surely...

I would agree with you. Anyways I hope people were not making such errors and if we were, then at least someone would benefit from reading this!

My favourite part of this (aside from the message) is that it links back to this exact discussion page.

An equally common mistake is to visualize without analyzing :-)

who doesn't look at the data range, min, max, mode???

Range and mode won't save you from the quartet, and they're a red herring in any case (you'd need to add statistics until you go blue in the face).