Caffeine at night does more than keep you up late

You end up limited, as you note, to your population. 5 people won't defeat detractors who believe that this effect is limited within some, e.g., metabolic profile but it ought to give them serious food for thought as to how wide the affected metabolic profile actually is.

If these 5 volunteers were chosen at random, then the potential generality of effect can still be large as a detractor would be fighting, at best, with the notion that the 5 chosen were circumstantially susceptible to this effect (as compared to a study of convenience where one might believe that "college students" or "hospital volunteers" are especially susceptible).

So, in a certain sense, testing every human on earth improves the power of the statement you can make (not really its "accuracy" though maybe its "precision", in a sense), but in many other ways that may be too expensive for the kind of result the author seeks.

I'd be interested to understand why this is?

I replied to cossatot below in more detail. The short version: In studies like this one, N isn't 5, but humans(e.g. the original N) x treatment repetitions x measurement points.

You are right that it would be dangerous to ignore it, that wasn't what I implied.

The problem is that the statistical model (in my field we do a lot of ANOVA and t-tests, along with the occasional chi-square) can only account for what you model. So there could be some kind of systematic error that influences your results in a fashion that is not modeled by the statistics. Having a large-N study makes it harder to have that systematic error (but not impossible - as an example: look at complaints about how much psychological and cognitive science research is only on WEIRD subjects - western, educated, industrial, rich, developed).

The other problem, of course, is that one time in a hundred, you'll get a p < 0.01 significant result by chance. Which is a lot in the long run. Worse, you can induce type two errors by running hundreds of trials (or testing hundreds of variables) and not accounting for that - just pick the one thing that had significant results on a single test. This approach is unscrupulous, but not unheard of in academic circles where you need to publish tons of work to get promoted.

Reproducability indeed is a major problem, but looking at statistical significance alone isn't the cure (especially if applied a posterior).

We should rather look at effect sizes and robust study designs.

In fact, modern studies aiming for causality often calculate the population size needed for statistical significance beforehand. It's a standard formula in most textbooks. You only need the expected effect size and then can calculate the population needed to guarantee significance.

A few points are important to consider.

First, I was only talking about experimental studies searching causal relationships. There are other possible designs, for example field studies (e.g. "school district A gets the new math curriculum, school district B the old one. Which one fares better?") or simple population observations ("people playing golf live longer than the average population."). Each design has advantages and disadvantages regarding generality of the statement one can make, and for each one different statistical considerations apply.

Second, the statistical power does not rely on a high population alone, as that (more or less) only affects the significance tests. Much more important is the effect size. If you can measure a large effect (as this study did), it's pretty hard not to reach significance anyway.

Third, from a statistical point of view, the population isn't 5, but much higher.

Let me explain: There are certain kinds of treatments whose effect is reversable. Caffeine intake is an good example: Once you stop taking caffeine, the effect recedes. While designing the study, you can use that property. One common way is an ABAB design, where A is a phase with treatment and B is a phase without. You can chain as much AB pairs as time permits, and additionally you can measure multiple times per phase. Statistically, the population now is real_humans x number_of_phases x measure_points_per_phase.