You improve the precision of anything you observe from your sample of subjects by having a larger sample. The central limit theorem (or CLT, one of the foundations of probability theory) describes how random fluctuations behave when a bunch of random variables are added (or averaged) together. Among many other things, the CLT describes how the precision of a sample statistic depends on the sample size.

The precision of any sample statistic increases (that is, the SE decreases) in proportion to the square root of the sample size. So, if Trial A has four times as many subjects as Trial B, then the results from Trial A will be twice as precise as (that is, have one-half the SE of) the results from Trial B, because the square root of four is two.

You can also get better precision (and smaller SEs) by setting up your experiment in a way that lessens random variability in the population. For example, if you want to compare a weight-loss product to a placebo, you should try to have the two treatment groups in your trial as equally balanced as possible with respect to every subject characteristic that can conceivably influence weight loss.

Identical twins make ideal (though hard-to-find) subjects for clinical trials because they're so closely matched in so many ways. Alternatively, you can make your inclusion criteria more stringent. For example, you can restrict the study groups to just males within a narrow age, height, and weight range and impose other criteria that eliminate other sources of between-subject variability (such as history of smoking, hypertension, nervous disorders, and so on).

But although narrowing the inclusion criteria makes your study sample more homogeneous and eliminates more sources of random fluctuations, it also has some important drawbacks:

• It makes finding suitable subjects harder.

• Your inferences (conclusions) from this study can now only be applied to the narrower population (corresponding to your more stringent inclusion criteria).