When determining sample size we require population proportion (p) for a dichotomous outcome that to be measured (at 95% CI , 3% error ).
If the proportion (p) is unknown a conservative estimate of .5 assumed. sometimes pilot study conducted to find a value for the proportion (p). If there is previous study we can take values for the proportion (p) from there.
One wants to study vaccination pattern among nurses (yes /no). There are three studies where vaccination rate was 47%, 52% and 57% . Now which values should be chosen for the proportion (p)? 0.47 or 0.52 or 0.57 or can one simply go for an intermediate 0.5?
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your sample size will be proportional to the variance p(1-p)
i would use the value giving the maximum variance in the reasonable range according to previous knowledge
given the values you have from previous research, i would go for 0.5 (maximum variance for p ranging between 0.47 and 0.57)
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I would recommend p = .50 because it yields the most conservative values (which is why it is the default assumption) -- plus it is easily within the range of your observed values.
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