What is an equivalence test?

You can use an equivalence test to determine whether the means for product measurements or process measurements are close enough to be considered equivalent.

Small differences between products are not always functionally or practically important. For example, a difference of 1 mg in a 200 mg dose of a drug is unlikely to have any practical effect. When you use an equivalence test, you specify how large the difference must be to be considered important. Smaller differences are considered unimportant. Minitab then tests two separate null hypotheses:
  • The difference is less than or equal to your lower limit for equivalence.
  • The difference is greater than or equal to your upper limit for equivalence.

If both null hypotheses are rejected, then the difference falls within your equivalence interval and you can claim that the product means are equivalent.

This information is also conveyed graphically in an equivalence plot.

Example of an equivalence plot

If the confidence interval for the difference is completely within your equivalence limits, then you can claim equivalence.

An animal feed company creates a new, less expensive formulation of their popular cat food for discount retailers. Analysts want to ensure that the protein content of the discount food is the same as that of their original food. The analysts measure the amount of protein per 100 grams of food in both formulations and test whether they are equivalent within +/- 0.5 grams.

Which equivalence test should I use?

1-sample equivalence test

To perform this test, select Stat > Equivalence Tests > 1-Sample.

You can use a 1-sample equivalence test to compare the mean of a product or a process to a standard.

For example, an engineer experiments with a new way to seal potato chip bags. The engineer wants to ensure that the force required to open the bags is within 10% of the target value of 4.2 N (Newtons). The engineer collects 28 bags that are sealed using the new method and tests the force required to open them.

2-sample equivalence test

To perform this test, select Stat > Equivalence Tests > 2-Sample.

You can use a 2-sample equivalence test to evaluate the equivalence between a test mean and a reference mean when your samples are independent. If the observations are dependent or paired, use Stat > Equivalence Tests > Paired.

For example, a pet food company creates a new, less expensive formulation of their popular cat food for discount retailers. Analysts want to ensure that the protein content of the discount food is the same as that of their original food. The analysts measure the amount of protein per 100 grams of food in both formulations and test whether they are equivalent within +/- 0.5 grams.

Equivalence test for paired data

To perform this test, select Stat > Equivalence Tests > Paired.

You can use an equivalence test for paired data to evaluate the equivalence between a test mean and a reference mean when your samples are dependent (also called paired observations). If the observations are not paired, but instead are independently selected from two populations, use Stat > Equivalence Tests > 2-Sample.

For example, an eyewear company develops a new cleaning solution for contact lenses. Analysts want to verify that the new solution cleans lenses as well as the leading brand. Analysts have 14 participants wear contact lenses for a day, and then clean the lenses. Each participant cleans one lens in the new solution and the other lens in the leading brand. By pairing the observations, they reduce the amount of variability that is caused by differences between participants. Finally, they assess the cleanliness of each lens by measuring the angle of contact for a drop of fluid on the lens. The angle of contact is affected by film or deposits on the lens.

Equivalence test for 2x2 crossover design

To perform this test, select Stat > Equivalence Tests > 2x2 Crossover Design.

You can use an equivalence test for 2x2 crossover designs to determine whether the effects of a test drug are equivalent to the effects of a reference drug. Use this test when your data are collected in a 2x2 crossover design experiment.

For example, analysts at a pharmaceutical company want to determine whether their generic antacid is equivalent to a name-brand antacid. Two groups of participants receive 5-days of one antacid, followed by a 2-week washout period, and then 5-days of the other antacid. The analysts measure gastric pH on the last day of each treatment. Because lower pH values are more acidic, higher values mean the drug is more effective. They will consider the antacids equivalent if the test pH is within 10% of the reference pH.

What is a 2x2 crossover design?

In a typical 2x2 crossover study, participants in two groups each receive a test drug and a reference drug. Studying the effects of both drugs in the same participants allows you to reduce the amount of variability that is caused by differences between participants.

Each group receives the drugs in a different sequence. For example, in the illustration below, participants for Sequence 1 receive the reference drug during Period 1, followed by the test drug during Period 2. Participants in Sequence 2 receive the test drug during Period 1 and the reference drug during Period 2.

A washout period between Period 1 and Period 2 allows the effects of one drug to dissipate before the next drug is administered.

Sequence (group) Period
Period 1 Washout period Period 2
Sequence 1 Reference drug No drug Test drug
Sequence 2 Test drug No drug Reference drug

What are the test sample and the reference sample?

Choose the reference sample from a proven product or process. For example, the reference sample in pharmaceutical studies is often from a drug that was evaluated extensively and was proven to have the desired effect.

The test sample is often from a newer product or process. For example, the test sample in pharmaceutical studies is often from a new generic drug. You might use an equivalence test to determine whether the generic drug is as effective as the reference drug.

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