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Probabilities and proportions: which one is the chart showing

The New York Times showed this chart (link):






Here's a picture:












Rick Wicklin

Nice discussion of an important topic. Those who communicate statistical ideas should clearly state whether they are presenting conditional probabilities. There would be less confusion if the graph had a title such as "Vaccination Status for Participants in Various Activities." In other words, of the people who participated in these activities, here is a breakdown of their vaccination status.

To get the best of both worlds, we could include the proportion of people who do each activity. For example, 20% of people surveyed dined out, 15% of people surveyed gathered outside, and so forth. Then you could figure out the proportions in the population.

Richard Krablin

Rick points out the biggest problem with the chart, one must first understand that these proportions are of the people who answered yes to each question. No information is given to assess the proportions of those who answered yes versus no. Presumably the data are available.

It is also interesting to note that the half vaccinated proportion is half or more of the fully vaccinated, implying a surge in vaccinations in the approximately two weeks before the survey. That says people are rapidly acting on their perceived "protected" status.


Nice discussion, though I'm not sure I misread the chart (I read past it to the discussion without fully analysing it, but I think I read it correctly first time, though adding the values down to 100 probably helped). Are you suggesting that the rows & columns should have been transposed? I'd have probably done this first since the labels are so much longer, and you'd have less columns. But can you explain "Most survey charts plot probabilities not proportions." in a little more detail pls? Thanks!


Antro: Thanks for raising this important point. It is not just a transpose. The calculations are different because the base of the proportions is different. In the NYT chart, the base is the subset of population that has undertaken an activity, and then it shows the proportion of that subset who are vaccinated and unvaccinated. In the alternative - more typical - presentation, the base is the subset of population with a specific vaccination status, and then it shows the proportion of that subset who has undertaken an activity. The first thing is notice is that 20% of the former base is not the same as 20% of the latter base since the base population are different.

Here's a current example to illustrate the difference (numbers are made up but directionally correct): maybe 60% of those who died from Covid-19 are 65 and above but we can't just transpose and say 60% of 65 and above have died from Covid-19... that is clearly way too high a proportion.

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