Several days ago, I came across a hilarious experiment - Mark Haub (@Haub_KSU), a human nutrition professor at Kansas State University has lost 27 pounds in 2 months while being on a “convenience store diet”. He ate every 3 hours and two thirds of his food consumption came from junk food, or, as some would say, “empty calories” and heavily processed, sugar-laden foods. Notably, his only limitation was the caloric intake, which he set at 1,800 kCal/day with his projected total daily expenditure (TDEE) being 2,600 kCal/day. His goal was to show that caloric deficit is the main thing that really matters for weight loss.
While I personally stand in awe and applaud this approach, there were lots of criticisms, including many comments claiming that this approach is not truly scientific. Effectively, lots of people said that we need randomized controlled trials with hundreds of participants to prove pretty much anything in medicine and healthcare.
Well, as a researcher who does know statistics well, I beg to differ. N=1 studies, like the one of Mark Haub, are extremely important as they often help us to prove some concepts before we get into more rigorous research, but also, believe it or not, even with one subject you can have all the statistical power in the world to prove certain hypotheses. It really depends on the question you want to answer.
Statistics are based on probability theory - we always talk about sample sizes and power in the context of being able to predict the future or to extrapolate our findings to larger samples or populations with a certain degree of certainty. The higher that sample size (n), the more certain we are - that's the main rule. But there are situations when all we need is just one subject.
Let me illustrate it with the following example. Say, we are studying sprinters and we want to know the typical time it takes for a sprinter to complete a 100-meter dash. Obviously, we need to test multiple subjects running 100-meter dashes and eventually we will end up with some average number, which we will call the mean, and we will also be able to see the spread of the scores, which is called the standard deviation. With these numbers we will be able to predict the outcomes of some random sprinters running the 100-meter dash with certain degree of certainty. Specifically, we will be able to say that given the characteristics of a sprinter we are sure that say in 95% (typical conventional level of certainty) the time will be within a certain interval and the more experiments we conduct (the higher n we have) the more precise and certain our answer will be.
Now, let's assume that we want to answer a different question - we want to show that it's not possible for a human to run a 100-meter dash in less than 10 seconds. How many experiments will we need to perform to prove it? We can obviously start doing multiple tests and having people completing the dash in much longer periods of time, say 14 seconds on average. And no matter how many tests we do, we will still never be 100% sure that the 100-meter dash cannot be beaten in 10 seconds.
But, at the same time, we can have an alternative hypothesis - a person can run the 100-meter dash in less than 10 seconds. And all we have to do in order to prove it is simply have one person (like Jim Hines in 1968) run it in less than 10 seconds. That is the power of one! We don't always need multiple tests and endless rigorous experiments in order to prove the point, it can be made with an n=1 study.
Having said that, I must note, that whereas the n=1 studies are quite underrated and are extremely helpful, adding them up like Dr.Shawn Baker (@SBakerMD) planned to do with his www.nequalsmany.com platform doesn't make much sense from a statistical standpoint, but I find it fascinating too and I will definitely talk about it in another blog.
So, for now, I will simply thank Mark Haub for his experiment and congratulate him on his great weight loss - it's quite an achievement on its own. Meanwhile, if you have questions on this topic, please do not hesitate to contact me either on this site, or on YouTube channel. Also, subscribe to my newsletter so that I can let you know every time I post something new.