What is sample size?

In a precision-based calculation the aim is, for example, to estimate a prevalence with a chosen precision. Naing et al. (2006) give n = Z² · P · (1 − P) / d² for a single proportion, where Z is the value for the confidence level (1.96 for 95%), P the expected proportion and d the half-width of the confidence interval. According to the same authors n is inversely proportional to the square of the precision (d); on that relationship, halving the half-width quadruples n.

A power-based calculation needs α, the target power, the target difference and, for continuous outcomes, the standard deviation (CONSORT 2010 explanation document). Bland (2009) argues that, if results are presented as confidence intervals, sample size should also rest on confidence interval width rather than power; DELTA2 (2018) notes that precision-based approaches were not then commonly applied.

Whitley and Ball (2002) state that the calculation rests on the number needed in the final analysis, so more subjects must be approached; in their example, 10% refusal and a final sample of 52 require about 58 people, which fits n / (1 − q) for a refusal or drop-out proportion q. Naing et al. advise oversampling by 10% to 20% for non-response, and note that cluster or multistage sampling needs the design effect as a multiplier. CONSORT asks for the attrition allowance to be reported.