# TOST (Equivalence test)

TOST (Equivalence test) is used to validate the equivalence of two means. Run equivalence tests in Excel using the XLSTAT add-on statistical software.

## What is an equivalence test TOST

Unlike classical hypothesis testing, **equivalence tests** are used to validate the fact that **a difference is in a given interval**.

This type of test is used primarily to validate bioequivalence. When we want to show the equivalence of two drugs, classical hypothesis testing does not apply. It is preferable to use equivalence testing which will validate the equivalence between the two drugs.

In a classical hypothesis test, we try to reject the null hypothesis of equality. As part of an equivalence test, we try to validate the equivalence between two samples. The TOST (two one-sided test) is a test of equivalence that is based on the classical t test used to test the hypothesis of equality between two means.

So we will have two samples, a theoretical difference between the means as well as a range within which we can say that the sample means are equivalent.

The test is known as parametric because the assumption is made that the samples are normally distributed. This hypothesis could be tested using normality tests.

The TOST test uses Student's test to check the equivalence between the means of two samples. A detailed description of such tests can be found in the chapter dedicated to t tests.

## The Equivalence TOST test in XLSTAT

XLSTAT offers two equivalent methods to test equivalence using the TOST test.

- Using the 100 * (1-2 * alpha)% confidence interval around the mean. By comparing this interval to the user-defined interval of equivalence, we can conclude the equivalence or non equivalence. Thus, if the confidence interval is within the interval defined by the user, we conclude the equivalence between the two samples. If one of the bounds of the confidence interval is outside the interval defined by the user, then the two samples are not equivalent.
- Using two one-sided tests, one on the right and one on the left. We apply a right one-sided t-test on the lower bound of the interval defined by the user and a left one-sided t-test on the upper bound of the interval defined by the user. We obtain p-values for both tests. We take the greatest of these p-values as p-value of the equivalence test.

These two tests are similar and should give similar results. They were introduced by Schuirman's (1987).

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