If you want your study to be meaningful, you must make sure your sample size is large enough to be statistically significant. However, larger studies are more expensive because of the extra cost of additional participants. To limit expenses and maximize the results, you need to effectively estimate the sample size you need. One part of that estimation is being able to predict the proportion of people that will choose either option.
Instructions
1. Determine the confidence level you want for your study. The confidence level is the probability that the true proportion will be within the confidence interval for your study. For example, you might want to be 98 percent sure that the true proportion is within the interval.
2. Find the Z-score that corresponds to the confidence interval using a Z-score table. For example, if you wanted a confidence level of 98 percent, you would use 2.326 as the Z-score.
3. Determine your confidence interval. This is the span between the minimum and maximum values that the true proportion could lie between based on your study. For example, if you set your confidence interval to be plus or minus 4 percent, you would be saying that the real proportion is somewhere between four percentage points above and four percentage points below the result from your study, and you would use 0.04 as the value for the confidence interval.
4. Predict the proportion of subjects that will respond to one of the two answers. For example, if you were asking if Babe Ruth or Hank Aaron is the best home run hitter, you would predict that 62 percent of people would say Babe Ruth. This is your predicted proportion.
5. Use the numbers found in Steps 1 through 4 in the formula below, where Z is the Z-score, P is the predicted proportion, and CI is the confidence interval.
Sample Size Needed = (Z^2 * P * (1 - P)) / CI^2
For example, if you had a Z-score of 2.326, estimated proportion of 0.62, and confidence interval of 0.04, you would need at least 797 people for your study.
