Enter your data for Equivalence Test for a 2x2 Crossover Design

Stat > Equivalence Tests > 2x2 Crossover Design

Enter your data

Select the option that best describes your data.

Data for two sequences are unstacked

If your data are in four columns of the worksheet, and each column contains data for only one period of a sequence, complete the following steps.

  1. From the drop-down list, select Data for two sequences are unstacked.
  2. In Treatment order for sequence 1, indicate whether treatment with the test drug came before or after treatment with the reference drug in the first sequence of your study.
  3. In each Response box, enter the column that contains the data for each period of each sequence.
    Tip

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

In this worksheet, the treatment order for sequence 1 is Test, Reference. Group 1 Generic Drug contains the response for the test drug in period 1 of sequence 1. Group 1 Brand Drug contains the response for the reference drug in period 2 of sequence 1. Group 2 Brand Drug contains the response for the reference drug in sequence 2, period 1. Group 2 Generic Drug contains the response for the test drug in sequence 2, period 2.
C1 C2 C3 C4
Group 1 Generic Drug Group 1 Brand Drug Group 2 Brand Drug Group 2 Generic Drug
3.92 4.01 3.76 3.51
4.22 4.66 4.69 3.73
5.55 3.76 4.53 3.91
3.66 3.51 3.32 3.21

Data for two sequences are stacked

If your data for the two sequences are stacked, with one column for the period 1 responses, one column for the period 2 responses, and another column to identify the sequence, complete the following steps.

  1. From the drop-down list, select Data for two sequences are stacked.
  2. In Sequence ID, enter the column that identifies which sequence each row belongs to.
  3. Enter a column that contains the response data for period 1.
  4. Enter a column that contains the response data for period 2.
  5. Enter the ID value for the sequence that applied the reference treatment in period 1 and the test treatment in period 2.
In this worksheet, Period 1 contains the response data for the test and reference treatments in period 1. Period 2 contains the response data for the test and reference treatments in period 2. Sequence identifies the sequence for each response value. The reference, test treatment order was used in sequence 1. Therefore, the values in Period 1 represent the reference drug for sequence 1 and the test drug for sequence 2.
C1 C2 C3
Period 1 Period 2 Sequence
5.03 4.97 1
4.95 5.01 1
4.92 5.00 2
4.98 5.05 2

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 wants to determine whether the mean gastric pH induced by a new antacid is within 10% of the mean gastric pH induced by a brand-name antacid.

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 an improved formulation of a nutritional supplement results in higher blood levels of an essential mineral 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 results in a mean diastolic blood pressure that is lower than that of 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 wants to determine whether the mean bioavailability of a test drug is between 0.8 and 1.2 times that of a reference drug.

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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