Having confidence in confidence intervals

An epidemiology teaching resource

When epidemiologists teach precision & accuracy, they often use images of a target, like these from the Wikipedia article.

This is a great analogy for accuracy and precision. And it also makes a great analogy for thinking about the relationship between your estimate and your target effect (or estimand). The number we estimate in our study is the arrow, and we are shooting it at a target — the center of that target is the ‘true’ value we are hoping to find in our study.

But this analogy can lead to confusion once we get to interpreting the confidence interval. I’ve often heard students mis-use the target analogy to describe their confidence interval as if it were the fixed target, and the “true” value was the arrow that may or may not land on the target 95% of the time.

But, a confidence interval isn’t fixed — the “true” value is the part they should view as fixed. To avoid this misunderstanding, I like to explain confidence intervals with ring toss. The “truth” is in a fixed place, and it’s the confidence interval ring that may or may not land where you want it to.

A side benefit: this analogy can help students see why a 99% confidence interval would be wider than a 95% interval — the bigger the ring, the easier the game of ring toss!

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