Example of Power and Sample Size for Paired t

A manager at a fitness facility wants to determine whether a weight-loss program is effective. The manager wants to be able to detect a difference of at least 3 pounds. In an earlier study, the manager determined that the standard deviation of the paired differences is 3. Before collecting the data for a paired t-test, the manager uses a power and sample size calculation to determine what the power of the test will be with different sample sizes.

  1. Choose Stat > Power and Sample Size > Paired t.
  2. In Sample sizes, enter 10 20 50.
  3. In Differences, enter 3.
  4. In Standard deviation of paired differences, enter 5.
  5. Click OK.

Interpret the results

To detect a difference of 3 pounds in the weight-loss program, the manager can obtain a power value of approximately 0.4 with a sample size of 10, a power value of approximately 0.72 with a sample size of 20, and a power value of approximately 0.99 with a sample size of 50. A sample size of 20 or fewer does not give the test adequate power to detect a difference of 3, and a sample size of 50 may give the test too much power.

Power and Sample Size

Paired t Test Testing mean paired difference = 0 (versus ≠ 0) Calculating power for mean paired difference = difference α = 0.05 Assumed standard deviation of paired differences = 5
Results Sample Difference Size Power 3 10 0.395918 3 20 0.721005 3 50 0.986031

Power Curve for Paired t Test

By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy