Enter your data for Equivalence Test with Paired Data

Stat > Equivalence Tests > Paired

Enter your data

  1. Enter a column of numeric data for the Test sample.

    The test sample is often from a new or unproven product or process. For example, the test sample in a pharmaceutical study might be a new generic drug that you hope to prove is as effective as the leading brand name (reference) drug.

  2. Enter a column of numeric data for the Reference sample.

    The reference sample is often from a proven product or process. For example, the reference sample in a pharmaceutical study might be a drug that has already been shown to have the desired effect.

In this worksheet, each row contains paired observations from the same patient. For example, row 1 of the New Device column contains the blood glucose level of a patient when measured with a new glucose measuring device. Row 1 of the Current Device contains the blood glucose level of the same patient when measured with a currently approved glucose measuring device.
C1 C2
New Device Current Device
103 100
68 71
95 93
137 133

Hypothesis about

From the drop-down list, indicate how you want to express your equivalence criteria.

Test mean - reference mean

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

Define equivalence in terms of the ratio of the mean of the test population to the mean of the reference population.

Test mean / reference mean (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.

Alternative hypothesis

From the drop-down list, select the hypothesis that you want to prove or demonstrate.

Hypothesis about: Test mean - reference mean

To test the difference between the test mean and the reference mean, 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.

Hypothesis about: Test mean / reference mean

To test the ratio of the test mean to the reference mean, 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 0. A ratio of 1 indicates that the two means are equal.

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 between 95% and 105% of the mean glucose reading of the currently approved device.

Test mean / reference mean > lower limit

Test whether the ratio of 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 1.5 times greater than the mean reduction induced by the current medication.

Test mean / reference mean < upper limit

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

For example, an analyst wants to prove that the mean response time for a new therapy does not exceed the response time for an established therapy by 5% or more. The analyst tests whether the ratio of the mean response times is less than 1.05.

Hypothesis about: Test mean / reference mean (by log transformation)

To test the ratio of the test mean to the reference mean using a log transformation of the original data, 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 0. 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.

Equivalence limits

Enter a value for each equivalence limit that is 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.

Multiply by reference mean

Select this option to specify that the limit represents a proportion of the reference mean. Use to test whether the mean of the test population is within a certain percentage of the mean of the reference population. For example, select this option to change the limit from a fixed value of 0.1 to a value that equals 10% of the reference mean.

Note

This option is displayed only when you express equivalence in terms of a difference between the test mean and the reference mean.

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