How to Determine Sample Size in Empirical Experiments

Statistical analysis is used for a variety of scientific experiments, including clinical trials for medications and social science research. A sample size refers to the number of observations in an empirical study. For example, a clinical trial for a new drug that includes 100 participants has a sample size of 100. Larger sample sizes typically lead to more accurate results. However, increasing the sample size within an experience leads to higher cost for the experiment. Ideally, a sample size will be large enough to provide accurate, generalizable results but small enough that the experiment is manageable and not too costly.

Instructions

1. Determine the largest sample size that can be used for the experiment given the research budget and other constraints.

2. Obtain an estimate of standard deviation within the population by reviewing similar studies that have been conducted in the past. For example, if the experiment is a clinical trial for a new antidepressant medication, obtain standard deviation estimates from previous clinical trials for related antidepressant medications. Note the sample size used in the study that the standard deviation estimate was obtained from. Set the standard deviation estimate to "O" and the sample size used for the standard deviation estimate to "Y."

3. Determine an acceptable confidence level for the experiment. Typically, a 95 percent confidence level is used for experiments, which basically means that the experiment has a 1 in 20 chance of giving unreliable results.

4. Use a standard normal curve areas table to obtain the "z value" for your given confidence level. If your given confidence level is 95 percent, need to look for the z value associated with "0.95." Set this value equal to "z."

5. Calculate the tolerable error using the following equation: (Z * O) / (square root of Y). Set this value to "E."

6. Calculate the sample size for this experiment by solving the following equation: (Z^2 * O^2) / (E^2).

7. Estimate the number of participants who will fail to follow through with the requirements of the experiment (for example, by failing to attend the sessions or not completing necessary assessments) if the study is using human subjects. This estimate can be obtained by reviewing previously conducted clinical trials.

8. Increase the sample size value obtained in Step 6 to account for the estimated number of subjects that will drop out of the study.

9. Compare the sample size obtained in Step 8 to the sample size in Step 1. If the sample size in Step 8 is less than the sample size in Step 1, use the sample size in Step 8 for your study. If the sample size in Step 8 is greater than the sample size in Step 1, consider whether the largest sample size that can be supported for the experiment will yield reliable data from the study.

References

• Interactive Mathematics: The z-Table
• "An Introduction to Statistical Methods & Data Analysis"; R. Lyman Ott and Michael T. Longnecker; 2001