Hula-Hoops, Confidence Intervals, and Invisible Men

In addition to doing statistical analysis, a big part of my job is explaining the meaning of the results. I am privileged to work with a lot of really smart people on all manner of biomedical and translational research. However, "really smart" does not always mean that everyone is highly numerate; some people just are not good at expressing themselves that way. That's OK too, not everyone can be expected to be good at everything, but it does present a special challenge sometimes when I need to explain something statistical to someone who has difficulty understanding. Somewhat surprisingly, the toughest questions are not about the most complex mathematics. Instead, the hardest questions to answer are often on the most basic concepts.

Case in point, a few days ago I was asked to define a confidence interval for a client who needed to be able it explain the concept to yet another colleague who was asking her. Here I have someone not-too-numerate needing to explain it to someone else likely not-too-numerate, and it's important, so I needed to give a clear and simple definition for her to understand and pass on.

A bit of background before I give my definition; this was relating to an observational study on clinical data, and we have a large number of means, standard errors, and confidence intervals to report. All intervals presented at at a 95% confidence level.

A confidence interval (CI) is a range of values that is likely to contain the actual value we want to know. For the purposes of this paper we have made a lot of single value estimates, or point estimates, of the means and slopes in which we are interested. Although this is not a random sample, we hope that this patient sample is an unbiased representation of a larger group of similar patients. If we were to repeat the study with another group, we would hope to get similar results, as opposed to very different findings. Confidence intervals represent a reasonable range of values that might be the true value that represents the entire population, and not just the single sample we happen to have. The confidence level is the probability, here 95%, that the true value we are trying to determine is actually within the interval.

To make sure I got the full meaning across, I added a bit about how to interpret confidence intervals.

Confidence intervals are very useful for interpreting the clinical importance of a finding. If the low and low ends of the interval are both clinically meaningful and not too far apart, then we can be fairly certain of a sound result even though we have some uncertainty due to sampling error. If the CI is “wide” there might be a lot of room for interpretation of what the result really means. The width of a confidence interval is directly related to the statistical significance. There is also a matter of “clinical significance” – not everything that is statistically significant is clinically meaningful, and vice-versa.

I wrote that up and fired it off in an email, but I felt like I still hadn't gotten it simple enough. I needed an easy non-technical example, and a moment of inspiration hit me; the Hula-Hoop as an analogy to a confidence interval, and an invisible man as the population the interval is trying to capture:

A simpler/sillier definition: You are throwing a hula-hoop at an invisible man. You can be pretty sure that you have actually caught the invisible man inside the hoop (95%), but you can’t be certain. If it is a big hula-hoop, you still don’t know exactly where he is. If the hula-hoop is small enough then you know almost exactly where he is, or close enough that you don’t care.


Now think about throwing “statistical hula-hoops” at the values you want to know about the general population to report in your study. You have captured most of them inside the hoops (95%), but you still don’t know precisely where they are.

Perhaps not the finest hour of statistical science, but if it gets the point across I'll still be happy with it.

[image - 100 hula hoops]