Sample Size Calculation

Hello all,

I just recently came across this website and was hoping an intelligent mind could help me calculate the sample size required for a study.

The study is comparing BMI and proximity to fast-food outlets.

Specifically comparing those <1km to >1km
Expected BMI difference considered significant >5

Accepted Power = 0.8 or 0.9+
Accepted Type 1 error = 0.05
Population size = 1,200,000
Population BMI = 25

Anything else that I need to know to figure this problem out?

I've had a look at a number of online calculators and videos to no avail. Most of it passes straight over my head.

If someone could send me some links / forumulas, or point me in the right direction that would be much appreciated.



New Member
Hi there,

What you need is an estimate for the standard deviation of the BMI. If the standard deviation is high, an effect is harder to detect.

I'm not quite sure what you mean by "Expected BMI difference considered significant >5". Is it your expectation that people living within 1 km have 5 BMI-points more than those living outside 1 km? To me, that sounds pretty incredible. Although I'm no expert, I would expect the effect to be much, much smaller.

You may use a calculator like this one,, to calculate a sample size. Note that most people do two-sided tests as default, even though in your case a one-sided test seems to be defensible.

But, there's an important methodological caveat! If you find that people living within 1 km are heavier, this does in no way imply that this is due to the fast-food place. For that, there are just way too many confounding variables. To actually pry out this effect would require a very complex model with many controlled variables. And even then you can never be sure.