The most consequential statistics in a study happen before any data exists. An underpowered study wastes the participants it recruited and answers nothing; an oversized one wastes resources and, in a clinical setting, exposes people to risk for no gain. This guide covers sizing a study for whichever question you are actually asking.
There are two ways to size a study, and they answer different questions. Powering for *significance* asks "how many do I need to detect an effect of size Δ, if it is real?" — you supply the smallest effect worth detecting, not the effect you hope to see. Sizing for *precision* asks "how many do I need for my confidence interval to be no wider than W?" — the better frame whenever you are estimating a quantity (a rate, a limit of agreement, a reference limit) rather than testing a hypothesis.
Two conventions keep the result honest: pre-specify the primary endpoint and the analysis before you look at the data (ICH E9), and register the plan where your field expects it. Post-hoc "observed power" computed from your own result adds nothing — it is a restatement of the p-value, not evidence about the design.
Pick the calculator that matches the primary endpoint and design. Each solves for whichever quantity you leave blank — sample size from a target power, or power from a sample size you are stuck with.
A diagnostic study is sized on the AUC, and a survival trial on the number of *events* rather than the number of patients — which is why follow-up length trades off against recruitment.
When the goal is to *estimate* something — a prevalence, a bias, a reference limit — power is the wrong frame. Size the study so the confidence interval is narrow enough to be useful, by naming the half-width you can live with.
A non-significant difference is not evidence of no difference — absence of evidence is not evidence of absence. To claim two treatments are interchangeable you must pre-specify a margin Δ and show the whole confidence interval falls inside it. Choosing that margin is a clinical judgement, not a statistical one, and it belongs in the protocol.