# Minitab equivalence test

#### mgubellini

##### New Member
Hi all,
I've come across some strange results in Minitab.
The CI at the same % confidence of a difference between two datasets have different values if I use a 2 sample t test or the equivalence test in Minitab 17.
In particular it looks like what for the 2 sample t test is the 90% CI is reported as the 95% CI for the equivalence test.
The results of the 2 sample t test are definitely correct.

Am I missing something?

Thanks

#### Miner

##### TS Contributor
The two tests are not interchangeable. That is, they are not comparable like a 2-sample t-Test and a Mood's Median test.

They have completely different null hypotheses. The 2-sample t-Test's null hypothesis is that mean_1 = mean_2.
The equivalence test's null hypothesis is different. It's null is the mean_1 $$\neq$$ mean_2.

In the 2-sample test you can only "prove" the samples are different. You cannot "prove" they are equivalent.
In the equivalence test, you "prove" they are equivalent, but cannot "prove" they are different.

#### rogojel

##### TS Contributor
Hi Miner,
deep down the equivalence test is using two two-sample t-tests, only set up differently, if I understand this correctly. Is there a correction for multiple testing inside the procedure (like Bonferroni)?

regards

#### Miner

##### TS Contributor
Hello rogojel,
I don't see that. Here are a copy of blogs from Minitab on the subject: Equivalence Testing for Quality Analysis (Part I): What are You Trying to Prove? and Equivalence Testing for Quality Analysis (Part II): What Difference Does the Difference Make?. The following is an R - related article on the topic: Absence of evidence is not evidence of absence: Testing for equivalence

I also reviewed the methods and formulae in Minitab HELP and the formulae were nothing similar to the t-test formulae.

#### rogojel

##### TS Contributor
Hi Miner,
thanks for the links. Looking at the R code article, it explicitely says :
"A very simple EHT approach is the ‘two-one-sided t-tests’ (TOST) procedure (Schuirmann, 1987). Its simplicity makes it wonderfully easy to use."
and then it discusses only this approach. I think Minitab is also using TOST - so I guess this is a kindof a frontend to the t-test SW. One could set up the TOST just using the t-test menu but it is much better to have all the drudgery be done automatically.

regards

#### hlsmith

##### Less is more. Stay pure. Stay poor.
TOST is pretty common. I know their are lots of ways to calculate the CIs in non-inferiority tests. I wonder if it is more of the same here.