Here is the first paragraph from the introduction in a paper on headaches: “In the general population 4% have never experienced a headache.” Of course, such a precise number caught my interest. How do we know that 4% of people have never experienced a headache? Luckily, the paper provides some insights, namely that when asked the question “Do you think that you never ever in your whole life have had a headache”, 4% of people say yes (p. 598).
Oh no, survey data. Oh no, 4%. Why does the number combined with the fact that it is survey data give me a headache? Because the Lizardman’s Constant is 4%. Here is my description of the issue from a post a few years ago: “As a rule of thumb, expect that for any response category, 4% of the respondents will pick even the most crazy category. Scott Alexander calls this the Lizardman’s Constant, because four percent of Americans, in a survey on conspiracy theories, believed lizardmen are running the Earth.”
For that reason, I do not believe that, in the general population, 4% have never experienced a headache. It might very well be true, and it certainly sounds credible. The point here is that I am skeptical towards the 4% answer when taking measurement error into account. The number could be 4%, but it could also very well not be 4%.
The reference to the 4% is from another study with the following results (from the abstract): “The prevalence of headache-free individuals was 4.1% (n = 1362) with a female-male ratio of 1:2.2.” I am skeptical towards 4%, so do not get me started on 4.1%. It reminds me of the joke about how you can tell an economist having a sense of humour. (That is, because they use decimal points.)
I have a few issues with the data at hand. First, it could look like that we are here tapping into survey response style rather than actual headache frequencies. For example, the people who report to never have had a headache are also more likely to say that they consume alcohol every day. While it could be the case that you would take advantage of never having a headache by binge drinking, I find it just as likely that we are dealing with a survey artefact.
Second, this is not a number that is representative of any national population. Specifically, the data is from the Danish Blood Donor Study, and as it is formulated in the study of interest: “Our study population of Danish blood donors might be influenced by selection bias, so that it is not completely representative of the whole Danish population.” For that reason, even if we were to take the 4% at face value, there is no reason to believe that this number is representative for the Danish population, the American population or any other population than Danish blood donors.
So how many people have never had a headache? I went to Wikipedia to hopefully get a reliable estimate, and here is what it says: “However, the prevalence of headache varies widely depending on how the survey was conducted, with studies finding lifetime prevalence of as low as 8% to as high as 96%.” So, it could be 4%, but that is the lower bound estimate, and it could also be substantially higher. I do not know what the actual percentage is, but I am confident that people who have never had a headache have never worked with survey data.