Determine the estimated proportion of your study. For example, if you take a poll for which of the two finalists would win American Idol and you expect 56 percent of respondents to vote for Contestant A, the proportion would be 0.56.
Determine the confidence interval for your study. The confidence interval is how precise you want the results of the study to be. For example, if you wanted the actual proportion to be within 2 percent of your study, the confidence interval would be 0.02.
Determine the confidence level for your study. This is how sure you want to be that the true proportion is within the range of your study. For example, if your confidence level is 95 percent and the confidence interval is 0.02, you are saying that there is a 95 percent probability that the true proportion lies between two percentage points above and two percentage points below the proportion you got from your study.
Use a table to convert the confidence level from a percentage to a Z-score (see Resources). For example, a 90 percent confidence level would translate to a 1.645 Z-score.
Use the values found in the prior steps in the following formula to calculate the minimum sample size when Z is the Z-score, P is the proportion and I is the confidence interval.
Minimum Sample Size = (Z^2 * (1 - P) * (P)) / I ^ 2
For example, if you wanted to find the minimum sample size needed for a study you wanted to be within 2 percent of the actual value with 90 percent confidence and you expected the proportion to be 56 percent, you would need at least 1,667 people.