Cuadra and to those who have responded to this thread. Thank you for some guidance. I think an explanation of what I am trying to do is in order to get some help.
Why do I want to do a TOST test?
It is a customer requirement for me. The TOST test should be performed if you are qualifying one part number from one machine to another machine with the same tonnage and process. In the past we would compare capability results from one machine to another. However, good capability results did not always yield equivalence.
Requirements:
(1) Measurement system meets requirements (2) Variances are equivalent (3) Data are normally distributed (4) Samples are
representative (5) Practical significance equates to the point of detection by customers, or performance degradation
This test is to be performed specifically for demonstrating practical equivalency between two data sets with 95% confidence.
A practical significance must defined before entering the data. Practical significance is defined as the positive half of the acceptable shift in mean. This value is how much they can differ with no practical on performance, or detectability.
For example: Nominal = 1.0 Tolerance = +/-0.05. The acceptable shift would usually be 20% of the tolerance. In this case the practical significance would be = 0.02(0.05) =0.01 (Not 1.0 + 0.01)
If the Confidence Interval is completely contained within the Acceptance Interval, then the means are practically equivalent.
There are 3 conclusions to be made after the test as per the customer requirement.
The means are practically equivalent significant at alpha = 0.05
The means are not practically equivalent significant at alpha = 0.05
Test is inconclusive due to non normal data or unequal variances.
If the last two conditions exist then I must go and perform a Mann Whitney Test for non normal data.
The customer provided a locked excel template but it is quite cumbersome to use as you can only use 2 dimension per template (We usually have 5 to 64 dimensions that have to be tested in such a way). If the test fails I constantly have to go back in to Minitab and do a Mann Whitney test. I would post the template here but its locked and I can't distribute it per confidentiality agreements. Ideally I would like to be able to run a macro so that if the test is inconclusive or not equivalent Minitab would automatically do Mann Whitney.
I hope this makes things clearer.