Equivalence Test with Paired Dataoverview how to example data see also
Equivalence Test with Paired DataStat > Equivalence Tests > Paired
Use to evaluate the equivalence between a test mean and a reference mean using paired observations. For example, suppose that you want to determine whether 2 blades are equally good at cutting through leather. Because pieces of leather vary in grain and toughness, you decide to take a pair of measurements from each piece, one using the test blade and one using the reference blade. Because both measurements are affected by the toughness of the particular piece, they are dependent.
If the observations are not paired, but instead are independently selected from two populations, use Stat > Equivalence Tests > 2-Sample.
You can also evaluate whether the test mean is greater than or less than the reference mean.
Test sample: Enter the column that contains the data from the test sample.
Reference sample: Enter the column that contains the data from the reference sample.
Test mean - reference mean: Choose to specify your equivalence criteria in terms of the difference between the test mean and the reference mean.
What do you want to determine? (Alternative hypothesis)
Lower limit < test mean - reference mean < upper limit: Test whether the difference between the means is within the limits that you specify.
Lower limit: Specify the lowest value for the difference that you consider functionally equivalent (for example, -0.2).
Upper limit: Specify the highest value for the difference that you consider functionally equivalent (for example, 0.2).
Multiply by reference mean: Check to specify that the limit represents a proportion of the reference mean. For example, check to specify the limit as 0.2 multiplied by the mean weight of the reference sample, rather than as the fixed value of 0.2 grams.
Test mean > reference mean: Test whether the test mean is greater than the reference mean.
Test mean < reference mean: Test whether the test mean is less than the reference mean.
Test mean - reference mean > lower limit: Test whether the test mean is greater than the reference mean by a specific amount. For example, you can test whether the mean weight of the test population is at least 0.2 grams greater than the weight of the reference population.
Lower limit: Specify the difference to test (for example, 0.2).
Multiply by reference mean: Check to specify that the limit represents a proportion of the reference mean. For example, check to specify the limit as 0.2 multiplied by the mean weight of the reference sample, rather than as the fixed value of 0.2 grams.
Test mean - reference mean < upper limit: Test whether the test mean is less than the reference mean by a specific amount. For example, you can test whether the mean weight of the test population is at least 0.2 grams less than the weight of the reference population.
Upper limit: Specify the difference to test (for example, -0.2).
Multiply by reference mean: Check to specify that the limit represents a proportion of the reference mean. For example, check to specify the limit as 0.2 multiplied by the mean weight of the reference sample, rather than as the fixed value of 0.2 grams.
Test mean / reference mean: Choose to specify your equivalence criteria in terms of the ratio of the test mean to the reference mean.
What do you want to determine? (Alternative hypothesis)
Lower limit < test mean / reference mean < upper limit: Test whether the ratio of the test mean to the reference mean 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.
Lower limit: Specify the smallest ratio that you consider equivalent (for example, 0.9). The limit must be greater than zero.
Upper limit: Specify the largest ratio that you consider equivalent (for example, 1.1). The limit must be greater than zero.
Test mean / reference mean > lower limit: Test whether the ratio of the test mean to the reference mean is larger than the limit that you specify. For example, you can test whether the mean of the test population is at least twice as large as the mean of the reference population.
Lower limit: Specify the ratio to test (for example, 2). The limit must be greater than zero.
Test mean / reference mean < upper limit: Test whether the ratio of the test mean to the reference mean is smaller than the limit that you specify. For example, you can test whether the mean of the test population is, at most, half as large as the mean of the reference population.
Upper limit: Specify the ratio to test (for example, 0.5). The limit must be greater than zero.
Test mean / reference mean (by log transformation): Choose to specify your equivalence criteria in terms of the ratio of the test mean to the reference mean, as modeled with a log transformation of the original data. For this option, all observations must be greater than zero.
What do you want to determine? (Alternative hypothesis)
Lower limit < test mean / reference mean < upper limit: Test whether the ratio of the test mean to the reference mean 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.
Lower limit: Specify the smallest ratio that you consider equivalent (for example, 0.9). The limit must be greater than zero.
Upper limit: Specify the largest ratio that you consider equivalent (for example, 1.1). The limit must be greater than zero.
Test mean / reference mean > lower limit: Test whether the ratio of the test mean to the reference mean is larger than the limit that you specify. For example, you can test whether the mean of the test population is at least twice as large as the mean of the reference population.
Lower limit: Specify the ratio to test (for example, 2). The limit must be greater than zero.
Test mean / reference mean < upper limit: Test whether the ratio of the test mean to the reference mean is smaller than the limit that you specify. For example, you can test whether the mean of the test population is, at most, half as large as the mean of the reference population.
Upper limit: Specify the ratio to test (for example, 0.5). The limit must be greater than zero.