# how to use population proportion to determine sample size?

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.

I am studying vaccination pattern among nurses (yes /no). There are three studies where vaccination rate was 47%, 52% and 57% . Now which values should I choose for the proportaion (p)? 0.47 or 0.52 or 0.57 or can I simply go for an intermediate 0.5?

• The proportion (p) of binary data MUST NOT be confused with the p-value from statistical testing. Therefore I edited your post. Otherwise a good question. – Ferdi Dec 22 '16 at 9:25
• I accepted your suggestion , yes some may confuse with p value...........Thanx – gourab Dec 22 '16 at 9:29
• Thank you for accepting. Are the sample sizes of the three samples equal? – Ferdi Dec 22 '16 at 9:30
• It always bothers me that people talk about proportions without the experiment (trial) is Bernoulli. You can have a dichotomous variables without them being independent. Almost always the Bernoulli trial is assumed as I suspect it is here with the three pilot studies. – Michael Chernick Dec 22 '16 at 14:48
• I would suggest looking at the three studies individually. Given the initial sample size in each case what would the new sample size be for each follow-up study. It may well be if the sample sizes in the pilot studies are large enough since all three estimate are "close" to 0.5, that the followup sample sizes N1, N2, and N3 corresponding to 0.47, 0.52 and 0.57 are not much less than the sample size N using 0.5. If that is the case there is little cost to using the conservative value N. – Michael Chernick Dec 22 '16 at 14:56