Visualizing Complex Relationships

minard_napoleonThe graphic above has been called the best statistical graphic ever drawn. It is Charles Minard’s infographic of Napoleon’s failed invasion of Russia in 1812-1813. It is ultimately a map overlaid with key facts about the campaign. Amazingly, it was published in 1869 – well before the term ‘infographic’ was created.

The beige line is Napoleon’s advance to Moscow and the black line is his retreat. The thickness of the beige and black lines indicate the number of troops that were part of the army at each location. The line chart at the bottom shows the temperatures at various points along the army’s retreat (the temperatures are listed in the Réaumur scale, but the coldest temperature equates to -35.5 degrees fahrenheit).

Here’s what I love about this graphic, and the potential for using visualization in analysis: Minard is able to display 6 different variables in a single, two-dimensional picture in a way that can be analyzed and is communicated in a human way. It is simply a visual representation of a multi-dimensional dataset that allows anyone to interact, analyze, and draw conclusions about the underlying data. No, we cannot draw statistical inference directly from this visual, but we can sure create better hypotheses and be more collaborative in the process.

Let’s consider a more business-focused scenario like time to product failure. If we had a table showing the number of products failing at each point in time along with a number of other key variables like hours of use, software updates, etc., it could be possible to construct a similar graphic. Hard-core engineers and OR analysts will still like interacting directly with the raw data, but think how much easier it would be to have discussions with product managers and other decision-makers about product failures. Think how many more people can be included in analyzing and hypothesizing about the data.

As business-to-business relationships become more and more complex, we need to find ways to include more people, more non-analysts, in the process of looking for insights in our data. I believe the best way to do this is to find ways to visualize our data, not just our findings. That’s what this graphic inspires in me. Bon travail, M. Minard, bon travail!


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