Interpret the key results for Power and Sample Size for 1-Sample Equivalence Test

Complete the following steps to interpret power and sample size for a 1-sample equivalence test. Key output includes the difference, the sample size, the power, and the power curve.

Step 1: Examine the calculated values

Difference
If you enter the sample size and the power of the test, then Minitab calculates the difference that the test can accommodate at the specified power and sample size. For larger sample sizes, the difference can be closer to your equivalence limits. This value represents the difference between the population mean and the target.
Sample size
If you enter a difference and a power value for the test, then Minitab calculates how large your sample must be. If you increase the sample size, the power of the test also increases. You want enough observations in your sample to achieve adequate power. But you don't want a sample size so large that you waste time and money on unnecessary sampling or detect unimportant differences to be statistically significant.
Note

Because sample sizes are whole numbers, the actual power of the test might be slightly greater than the power value that you specify.

Power
If you enter a sample size and a difference, then Minitab calculates the power of the test. A power value of 0.9 is usually considered adequate. A power of 0.9 indicates that you have a 90% chance of demonstrating equivalence when the population difference is actually within the equivalence limits. If an equivalence test has low power, you might fail to demonstrate equivalence even when the population mean and the target are equivalent. Usually, when the sample size is smaller or the difference is closer to an equivalence limit, the test has less power to claim equivalence.
Note

The definitions and interpretation in this topic apply to a standard equivalence test that uses the default alternative hypothesis (Lower limit < test mean - target < upper limit).

Power and Sample Size

1-Sample Equivalence Test Method Power for difference: Test mean - target Null hypothesis: Difference ≤ -0.3 or Difference ≥ 0.3 Alternative hypothesis: -0.3 < Difference < 0.3 α level: 0.05 Assumed standard deviation: 0.165
Results Sample Difference Size Power 0.2 25 0.902911
Key Results: Difference, Sample Size, Power

These results show that if the sample size is 25 and the difference is 0.2, then the power of the equivalence test is approximately 0.9. Therefore, using a sample size of 25 provides adequate power for a difference of 0.2.

Step 2: Examine the power curve

Use the power curve to assess the appropriate sample size or power for your test.

The power curve represents every combination of power and difference for each sample size when the significance level and the standard deviation are held constant. Each symbol on the power curve represents a calculated value based on the values that you enter. For example, if you enter a sample size and a power value, Minitab calculates the corresponding difference and displays the calculated value on the graph.

Examine the values on the curve to determine the difference between the mean and the target that can be accommodated at a certain power value and sample size. A power value of 0.9 is usually considered adequate. However, some practitioners consider a power value of 0.8 to be adequate. If an equivalence test has low power, you might fail to demonstrate equivalence even when the mean is equivalent to the target. If you increase the sample size, the power of the test also increases. You want enough observations in your sample to achieve adequate power. But you don't want a sample size so large that you waste time and money on unnecessary sampling or detect unimportant differences to be statistically significant. Usually, differences that are closer to the equivalence limits require more power to demonstrate equivalence.

In this graph, the power curve for a sample size of 30 shows that the test cannot achieve a power of 0.9 for any size difference. The power curve for a sample size of 40 shows that the test has a power of approximately 0.9 for a difference of 0.0. The power curve for a sample size of 100 shows that the test has a power of approximately 0.9 for a difference of ±0.2. For each curve, as the difference approaches the lower equivalence limit or 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).

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