One-Sample Equivalence Test

Power and Sample Size
Power Analysis - Sample Size

  

Increasing the sample size increases the power of your test. (See Power for equivalence tests for further discussion.) You want enough observations in your sample to achieve adequate power, but not so many that you waste time and money on unnecessary sampling.

If you specify the power that you want to achieve and the difference that you want to accommodate and still be able to claim equivalence, Minitab calculates how large your sample must be. (Because sample sizes are given in integer values, the actual power may be slightly greater than your target value.)

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  Target

Difference    Size   Power  Actual Power

       0.0      35     0.9      0.907219

       0.1      47     0.9      0.903687

       0.2      97     0.9      0.902206

       0.3     321     0.9      0.900788

Interpretation

The snack bag analysis shows that, if the difference is 0, then you need at least 35 observations to achieve a power of 0.9. A sample size of 35 gives you a power of approximately 0.91.

If the difference is closer to your lower equivalence or your upper equivalence limit (-0.42 or 0.42), you need more observations to achieve the same power. For example, if the difference is 0.3, you need at least 321 observations to achieve a power of 0.9.

The power curve is a useful way to visualize the relationship between power and sample size.