Communicating Uncertainty/Making Numbers easy to interpret
Making Numbers (and Statistical Analyses) Easy to Interpret
When dealing with very large or very small numbers, it is a good idea to round these up/down to make it easier for people to picture.
If something has a 4,427-1 chance of happening, it’s fine to tell people that there is ‘roughly a 4,500-1 chance.’ However, if something has an 8.3/1 chance of happening, telling someone that there is ‘roughly a 10/1 chance,’ is misleading because there is actually a reasonably large difference between the two.
Watch out for related contingencies (e.g. when one thing affects another, make sure you state the chance based on the combined likelihood, as well as the individual ones). For example, if I have a 10% chance of winning a regional award based on my grades, and then a 20% chance of winning a national award, it should be made clear that I only have a 2% chance of winning the national one (0.1 x 0.2 = 0.02).
It is also important to avoid framing bias when working with numbers. Framing bias can cause people to home in on the wrong message, and is often linked to your choice of wording, or even in the order that you introduce things.
Suppose there is a 10/1 chance that people will have a reaction to a new immunization that will make you feel very poorly for a few days, but that it is important to have the jab as catching the disease without immunization could be much worse.
If you tell people that ‘anyone having a reaction will feel very poorly and 1 in 11 of you will have this reaction,” you are focusing on the negative possibility and could dissuade people from having the immunization.
You should instead say something like ‘being able to protect ourselves from this disease is very important, so although there is a 10% chance that you might have a reaction that could make you feel poorly for a few days, medical staff are recommending this jab.’