Equivalence tests are new in Minitab v17. We will use an equivalence test to determine if the mean of a sample can be found to be equivalent for a target value.
These tests are similar to t-tests, but where the t-test null hypothesis is no difference, an equivalence test uses a null hypothesis of there is a difference.
The example dataset here is fill volumes of syringes. The target fill volume is 15 ml; we would like to know if the fill volumes of this process are equivalent to the goal of 15 to within +/- .25 ml around the target.
The following steps compare the measured volumes to the target of 15:
- Navigate to Stat | Equivalence Tests | 1 Sample….
- Enter Volume for the Sample: column.
- Enter
15as Target:. - For Lower limit:, enter
-.25. - For Upper limit:, enter
.25. - Click on OK.
Equivalence tests are also known as two one-Sided t-tests. The 1-Sample equivalence test uses two 1-Sample t-tests. The first null hypothesis is that the mean - target is less than equal to lower limit, with an alternative of greater than.
The second null hypothesis is that the mean - target is greater than or equal to upper limit with an alternative of less than.
When both null hypotheses can be rejected, we can prove that the mean - target is greater than the lower limit, and lesser than the upper limit, proving that the mean-target is within the equivalence limits.
If one null hypothesis cannot be rejected, then the mean - target is outside the equivalence region.
This is the opposite of a t-test. With a t-test, we can only prove a difference between a target or between means. With the equivalence test, we swap the null hypothesis to be a difference so that we can then look for evidence of no difference.
This becomes useful when we would like to prove that a process is on target.
T-tests cannot be used to prove that we are on target. This is because we never prove the null hypothesis. A t-test can show us that we cannot prove a difference, but this may be because we didn't take enough data to be able to observe that difference.
Equivalence tests, unlike t-tests, look for evidence to prove that there is no difference. If we do not have enough data to prove no difference, then we would fail to reject the null hypothesis that there is a difference.
Like t-tests, Minitab has power and sample size tools for the equivalence tests, tests for 2 samples, and paired equivalence. See the Calculating the sample size for a 1-Sample equivalence test recipe.
It is also possible to set a limit based on a multiplication around the target instead of a difference. Setting a lower limit at -0.1 and the upper at +0.1 will put the equivalence limits at -1.5 or +1.5 around the target of 15. This can be useful if specifying equivalence to a stated percentage of the target.