One-Sample Equivalence Test

Power and Sample Size
Power Analysis - Difference

  

If you specify your sample size and the power that you want to achieve, then Minitab calculates the maximum difference allowed. For larger sample sizes, the difference can be closer to your equivalence limits.

Example Output

1-Sample Equivalence Test

 

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: 0.732

 

 

Sample

  Size  Power  Difference

    28    0.9           *

    40    0.9   -0.071272

    40    0.9    0.071272

    60    0.9   -0.140212

    60    0.9    0.140212

   100    0.9   -0.204306

   100    0.9    0.204306

Interpretation

The snack bag analysis shows that, with 28 observations, you cannot achieve a power of 0.9 to claim equivalence, regardless of the difference. The analysis also shows the following:

·    With 40 observations, your power is at least 0.9 if the difference is between approximately  -0.07 and 0.07.

·    With 60 observations, your power is at least 0.9 if the difference is between approximately -0.14 and 0.14.

·    With 100 observations, your power is at least 0.9 if the difference is between approximately -0.20 and 0.20.

The power curve is a useful way to visualize the relationship between the sample size and the difference that you can accommodate and still be able to claim equivalence.