[kibibu]

The paper includes a section on power analysis which justifies the sample size (although the justification is for a sample of 20, they recruited 25 eligible participants and lost 6 in screening).

Some points though:

- A within-participants study has inherently more power than a between-subjects study. Trying two different diets with the same person removes a lot of variables that you'd need to control for in between-subjects studies (and yes, they randomized the order of intervention and found no difference based on order)

- It looks like this was conducted in a way that supported compliance with the protocol, and using analysis techniques that would be unwieldy for a much larger sample size.

Even with N=19, the reported significance is very compelling.