# Enter your data for Power and Sample Size for Equivalence Test with Paired Data

Stat > Power and Sample Size > Equivalence Tests > Paired

1. From Hypothesis about, indicate how you want to express the equivalence criteria.
• Test mean - reference mean (Difference)

Define equivalence in terms of a difference between the mean of the test population and the mean of the reference population.

• Test mean / reference mean (Ratio, by log transformation)

Define equivalence in terms of the ratio of the mean of the test population to the mean of the reference population, as modeled with a log transformation of the original data. For this option, all observations must be greater than 0.

2. From What do you want to determine? (Alternative hypothesis), select the alternative hypothesis that you are trying to prove or demonstrate.
• If your hypothesis is about Test mean - reference mean (Difference), select one of the following options.
• Lower limit < test mean - reference mean < upper limit

Test whether the difference between the population means is within the limits that you specify.

For example, an analyst measures blood glucose levels twice in the same group of patients, using two different devices. The analyst wants to determine whether the mean glucose reading for the new device is within ± 20% of the mean glucose reading of the currently approved device.

• Test mean > reference mean

Test whether the mean of the test population is greater than the mean of the reference population.

For example, an analyst wants to determine whether a new blade cuts samples of leather better than the currently used blade.

• Test mean < reference mean

Test whether the mean of the test population is less than the mean of the reference population.

For example, an analyst wants to demonstrate that a new medication takes effect in less time, on average, than the current medication.

• Test mean - reference mean > lower limit

Test whether the difference between the population means is greater than a lower limit.

For example, a researcher wants to determine whether the mean reduction in diastolic blood pressure induced by an experimental drug is more than 3 mm Hg greater than the mean reduction induced by the current medication.

• Test mean - reference mean < upper limit

Test whether the difference between the population means is less than an upper limit.

For example, researchers develop a new formulation of a popular medication. The new formulation is less expensive, but requires more time to achieve maximum effect. Researchers want to ensure that the mean difference in time to maximum effect does not exceed that of the current medication by more than 2 minutes.

• If your hypothesis is about Test mean / reference mean (Ratio, by log transformation), select one of the following options.
• Lower limit < test mean / reference mean < upper limit

Test whether the ratio of the population means is within the limits that you specify. Both limits must be greater than zero. A ratio of 1 indicates that the two means are equal.

For example, an analyst needs to demonstrate that the mean bioavailability of a test formulation is within 80% (0.8) and 125% (1.25) that of the reference formulation, using log transformed data.

• Test mean / reference mean > lower limit

Test whether the ratio of the population means is greater than a lower limit.

For example, an analyst needs to demonstrate that the mean bioavailability of a test formulation is greater than 80% (0.8) that of the reference formulation, using log transformed data.

• Test mean / reference mean < upper limit

Test whether the ratio of the population means is less than an upper limit.

For example, an analyst needs to demonstrate that the mean bioavailability of a test formulation is less than 125% (1.25) that of the reference formulation, using log transformed data.

3. Enter a value for each equivalence limit included in the alternative hypothesis.
• Lower limit

Enter the lowest acceptable value for the difference or ratio. You want to demonstrate that the difference (or ratio) between the mean of the test population and the mean of the reference population is not lower than this value.

• Upper limit

Enter the highest acceptable value for the difference or ratio. You want to demonstrate that the difference (or ratio) between the mean of the test population and the mean of the reference population does not exceed this value.

4. Specify values for two of the following power function variables. Leave the variable that you want to calculate blank.
###### Tip

If you enter multiple values into a field, separate the values with a space. You can also use shorthand notation to indicate multiple values. For example, you can enter 10:40/5 to indicate sample sizes from 10 to 40 in increments of 5.

• Sample sizes: Enter a sample size of interest. To assess the effect of different sample sizes, enter multiple values. Larger sample sizes give the test more power to demonstrate equivalence.

• Differences (or Ratios): Enter one or more values to specify the difference (or ratio) between the test mean and the reference mean. The values that you enter must be within the equivalence limits. Differences (or ratios) that are close to an equivalence limit require larger sample sizes to achieve adequate power.

• Power values: Enter one or more values to specify the probability that the test shows equivalence when the population difference (or ratio) is within the equivalence limits.Common values are 0.8 and 0.9. For example, an analyst enters 0.9 to indicate a 90% chance that the test will demonstrate equivalence between the mean of the test treatment and the mean of the reference treatment when the means actually are equivalent.
5. In Standard deviation of paired differences, enter one of the following:
• For a hypothesis about Test mean - reference mean (Difference), enter an estimate for the standard deviation of the difference values.
• For a hypothesis about Test mean / reference mean (Ratio, by log transformation), enter an estimate for the standard deviation of the differences between log-transformed values.
If you already collected and analyzed data, you can use the standard deviation from the sample data. If you do not have data, base your estimate on related research, design specifications, pilot studies, subject-matter knowledge, or similar information.
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