S Z 2 P Q E 2. Over the years researchers have grappled with the problem of finding the perfect sample size for statistically sound results. Its equation can be derived by using population size the critical value of the normal distribution sample proportion and margin of error.
Fill the N and e values into the formula n N 1 Ne 2.
N z 2 p 1 - p e 2 where z 1645 for a confidence level a of 90 p proportion expressed as a decimal e margin of error. Thus if there is no information available to approximate p 1 and p 2 then 05 can be used to generate the most conservative or largest sample sizes. When you want to identify the sample size for a larger population one can use the following formula. The values of p 1 and p 2 that maximize the sample size are p 1 p 2 05.