How to Calculate Sample Size Formula

The formula for calculating sample sizes involves several variables.

Sample sizes are vital for conducting research. If your sample size is too small, you may not have a wide enough range of participants to see results, or your results may be dismissed as the result of chance. If your sample size is too large, the costs of your research will make it necessary for you to obtain more funding.

Things You'll Need

• Calculator
• Z-score table

Instructions

1. Determine the confidence interval of your study. The confidence interval is the number of percentage points above or below the proportion that you find in your study that the true proportion should be within. For example, if your confidence interval is 3.5 percent and your study reveals a proportion of 57 percent, the true proportion is likely between 53.5 percent and 60.5 percent.

2. Determine the confidence level of your study. The confidence level is how certain your need to be that the true proportion lies within your confidence interval. For example, if you use a confidence level of 95 percent, you can predict with 95 percent certainty that the true proportion lies within your confidence interval.

3. Convert your confidence level to a Z-score by using a Z-score table. For example, a 98.5 percent confidence level results in a 2.43 Z-score.

4. Predict the proportion of the study. For example, if you expect 53 percent of respondents to respond affirmatively, 0.53 would be your proportion.

5. Compute the needed sample size by plugging your values into the following formula, where Z is the Z-score, P is the proportion and I is the confidence interval.

   Sample Sized Needed = Z² --- P (1 -- P) / I²

   For example, if your Z-score is 2.43, your proportion is 0.53 and your interval is 3.5 percent, you would need a sample size of 1,201 subjects.

Tips & Warnings

• Err on the side of a more balanced result when calculating sample size. For example, if you predict an 80 percent result and you get a 54 percent result, you will not have enough people in your study.

References

• Creative Research Systems: Sample Size Formula

Resources

• Read this Article in Spanish
• Biometric Technology Inc.: Z-Score Conversion Table