Enter your data for 2-Sample Equivalence Test

Stat > Equivalence Tests > 2-Sample

Enter your data

Select the option that best describes your data.

Samples in one column

If your data are in one column of the worksheet, complete the following steps.

  1. From the drop-down list, select Samples in one column.
  2. In Samples, enter the column of numeric data that you want to analyze.
    Tip

    Click in Samples to see the columns that are available for your analysis.

  3. In Sample IDs, enter the column that identifies the group (the test sample or the reference sample) for each data value.
  4. In Reference level, select the group that represents a proven product or process. For example, the reference level could be the original formulation of a popular cat food.
In this worksheet, Protein contains the amount of protein in a random sample of cat food. Formulation identifies whether the sample is from the original formulation or the modified formulation.
C1 C2
Protein Formulation
250.1 Original
253.0 Original
247.8 Modified
248.2 Modified

Samples in different columns

If your data are in separate columns of the worksheet, complete the following steps.

  1. From the drop-down list, select Samples in different columns.
  2. 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.

  3. 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, Generic Drug contains the strength of a new generic drug (the test sample). Current Drug contains the strength of a leading brand-name version of the same drug (the reference sample).
C1 C2
Generic Drug Current Drug
5.03 4.97
4.95 5.01
4.92 5.00
4.98 5.05

Summarized data

If you have summary statistics for each sample, rather than actual sample data in the worksheet, complete the following steps.

  1. From the drop-down list, select Summarized data.
  2. Enter the Sample size, Mean, and Standard deviation for the Test sample.
  3. Enter the Sample size, Mean, and Standard deviation for the Reference sample.

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.

Note

This option is not available for summarized data.

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 wants to determine whether the mean strength of a new generic drug is within ± 10 mg/ml of the mean strength of a brand-name drug.

Test mean > reference mean

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

For example, a food analyst wants to determine whether an improved formulation of a dog food has more mean protein per 100g than the current formulation.

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, an analyst wants to determine whether the mean waiting time in the emergency department of a hospital in one location does not exceed the mean waiting time of a hospital in another location by more than 5 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 wants to determine whether the amount of active ingredient in a new cold remedy formulation is between 0.8 and 1.2 times that found in a standard cold remedy.

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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