# 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).