Sample size is the first question in most thesis vivas. You do not need to be a statistician; you need to know which of four situations you are in and where your assumed values came from.
Estimating a prevalence
n = Z²·p·(1−p)/d². With 95% confidence (Z = 1.96), an expected prevalence of 30% and absolute precision of 5%, n = 323. Cite the study your 30% came from.
Comparing two means
n per group = 2·(Zα + Zβ)²·σ²/Δ². Use a previous study for the standard deviation and a clinically meaningful difference for Δ, not the largest difference you can find.
Comparing two proportions
n per group = (Zα + Zβ)²·[p1(1−p1) + p2(1−p2)]/(p1 − p2)². State power (usually 80%) and alpha (5%) explicitly.
Diagnostic accuracy
Use the expected sensitivity (or specificity), the disease prevalence in your setting and the desired precision. Buderer's formula is the one usually cited for this design.
- Always add 10% for attrition in prospective studies
- Write the formula, the values, the source and the final number in the synopsis
- If the department's patient load cannot reach the number, change the design or the duration, not the precision