Some Pictures are Mental — The Statistics of Graphics and Illustrations

Picture these two scenarios:

1. Imagine throwing a rock from the sun to the earth and hitting within one-third of a mile from the center of your target.

2. Imagine throwing a rock from New York to Los Angeles and hitting the target within two-thirds of an inch of dead center.

Which one is more accurate?

To answer that question, we must question our understanding of the word accuracy. Accuracy and precision–a complementary but different concept–are both terms that statistics attempts to quantify, and their meaning is actually very important.

(I have to interject here–this is not an article about accuracy and precision, so you might consider skipping ahead to the next bold heading.)

Accuracy answers the question “did we hit our target”? The question is so ubiquitous that many images, such as this one, are available to illustrate this important concept.

This image above depicts “bullet holes” that have hit a target near its center–they are accurate.

Precision, illustrated in this second image, indicates that the bullets all hit the target very close to the same point.

Clearly, both of these concepts benefit from a graphical depiction of their meaning.  But that brings us back to our original question…

Which one is more accurate?
You might be surprised to find out that both statements represent the exact same accuracy, as Chip and Dan Heath report in their book, Made to Stick, the source of this illustration. The difference is the scale–from “here to the sun” versus “New York to LA”–the scale we use to communicate about accuracy matters.  You and I can imagine the rock flying from NY to LA, and the idea of hitting a target within 2/3 of an inch is vivid. We have a mental image of what this means. However, we couldn’t even begin to conceptualize what .0001% accuracy means, for example.

We can picture the accuracy when we have a picture, even when it’s just a mental one. It helps us understand how Picture = 1000 Words.

What message have you been trying to communicate, but your words have been painting the wrong picture?

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Where Do We Go From Here

How do we find our way then, when we are exploring the unknown, blazing a trail into uncharted territory? How do we apply elementary statistical principles to transform uncertainty into decisive action? What is to prevent us from making a preposterous application of ATOMs when we deal with very complex situations, those in which our intuition fails?

These questions are not much different from those faced by Chuck Yeager before he ever broke the sound barrier or Neil Armstrong as he took that first step on the moon. Neither of these men, nor anyone around them–with hundreds or thousands of highly educated, very scientific people on these teams–knew what to expect. Or did they…?

ATOMs is a weekly column that introduces analytical tools of mathematics and statistics and illustrates their application. To read more about ATOMs, you can read Where Do We Go From Here, or view the online workbook here.