Example of Power and Sample Size for 1-Sample Equivalence Test

A packaging engineer wants to test a new method to seal snack bags. The force that is required to open the bags should be within 10% of the target value of 4.2 N (Newtons). Before collecting the data for a 1-sample equivalence test, the engineer uses a power and sample size calculation to determine how large the sample must be to obtain a power of 80% (0.8). From previous samples, the engineer estimates the standard deviation of the population is 0.332.

  1. Choose Stat > Power and Sample Size > Equivalence Tests > 1-Sample.
  2. From What do you want to determine? (Alternative hypothesis), choose Lower limit < test mean - target < upper limit.
  3. In Lower limit, enter –0.42. In Upper limit, enter 0.42.
  4. In Differences (within the limits), enter 0 0.1 0.2 0.3.
  5. In Power values, enter 0.8.
  6. In Standard deviation, enter 0.332.
  7. Click OK.

Interpret the results

If the difference is 0 (the mean force is on target), then the engineer needs a sample size of 7 to achieve a power of 0.8. If the engineer uses a sample size of 9, the power of the test is over 0.9 for a difference of 0.

When the difference is closer to the upper equivalence limit (0.42), the engineer needs a larger sample size to achieve the same power. For example, for a difference of 0.3, the engineer needs a sample size of 49 to achieve a power of 0.8.

For any sample size, as the difference approaches the lower equivalence limit or the upper equivalence limit, the power of the test decreases and approaches α (alpha, which is the risk of claiming equivalence when it is not true).

Power and Sample Size

1-Sample Equivalence Test Method Power for difference: Test mean - target Null hypothesis: Difference ≤ -0.42 or Difference ≥ 0.42 Alternative hypothesis: -0.42 < Difference < 0.42 α level: 0.05 Assumed standard deviation: 0.332
Results Sample Target Difference Size Power Actual Power 0.0 7 0.8 0.805075 0.1 9 0.8 0.834590 0.2 16 0.8 0.811465 0.3 49 0.8 0.802154
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