When I posted before with the title “An Economist Reads The Newspaper”, I had no idea that it would be a theme…nor did I envision the theme taking a turn for the creepy this soon. Regardless, I was walking in the Harvard Science Center the other day and saw a poster that said the following:
“50-75% of people who have chlamydia have no symptoms.”
This poster clearly achieved it marketing goal, at least in the short term, since it immediately made me think two things. First, it made me think that *obviously* I must have chlamydia, since I am exhibiting no symptoms (at least not to my knowledge). Second, as a corollary, it made me think that maybe I’ve been doing it with too many models. *rim shot*
Luckily, as a skeptical economist, I quickly saw the error in my initial train of thought. The fallacy in my thought process was a misapplication of Bayes’ Rule. (I suggest scrolling down to the examples on that link, since your brain might explode otherwise.) I don’t want to get too technical on you here, so suffice it to say that I was mistaken to make an inference before stopping to say to myself “wait a minute, this all depends on how likely it is for someone to have chlamydia in the first place.” (Sidenote: I can only imagine what I’m going to see now for search terms that people use to get to my site.) Like any true geek, I looked up statistics on the prevalence of chlamydia, and I determined that a reasonable infection rate to use is about 1 percent. I also figured that I would make the middle of the road approach regarding the data from the poster and assume that 62.5 percent of people who have chlamydia don’t have any symptoms…even though that clearly doesn’t have the same ring to it.
To do the math, we need to consider the following:
- The conditional probability of one thing happening (let’s call it A) given that another thing happened (let’s call it B) is given by “the probability that both A and B happened divided by the probability that B happened.”
- The probablity that one has chlamydia and no symptoms is 1% times 62.5%, or 0.625%.
- The probability that one has chlamydia and does have symptoms is 1% times (1-62.5%), or 0.375%.
- The probability that one doesn’t have chlamydia yet exhibits symptoms…well, let’s just assume that this is zero. (This should logically be zero unless chlamydia shares exact symptoms with another disease.)
- The probability that one doesn’t have chlamydia and doesn’t exhibit symptoms is then 1-1%, or 99%.
Why this is information is helpful is summarized by the following:
Lesson learned: in a lot of cases, no news is most likely good news. Note, however, that if chlamydia were more prevalent in the population overall, this number would be higher. Revised lesson learned: no news is most likely good news when the news is that you don’t have burn marks from getting struck by lightning. (Hint: you probably didn’t get struck by lightning, but you already knew that.)