## Equivalence Test when Variances are Unequal

New Contributor

Joined:

Aug 20, 2017

Is there a built in way (or straightforward way to script) to test for equivalence of means with a procedure similar to TOST when the variances of groups are unequal (significant result from the appropriate test under JMP's "Unequal Variances" report).

I am assuming that since the TOST procedure that is part of JMP's "Equivalence Test" option in the Fit Y by X platform relies on two t-tests, the variance is pooled by default.

Thank you.

1 ACCEPTED SOLUTION

Accepted Solutions

Staff

Joined:

Apr 26, 2012

Solution

Its not clear from your post exactly how you're going to use the test for equivalence.  In TOST I set an upper and lower limit, and then I put the 95% CI on the limits and make sure that my mean is between the confidence intervals. In the distribution platform you get a result like this (below) and there is no pooling of variance. Its just the variance of the univariate statistic.

This graph has the upper and lower equivalence limits (defined by me as the difference to consider negligible) with the variable's mean bordered by a one side 95% CI on each side (or 90% CI of the mean, same thing). If the CI crosses the equivalence boundary, then it is not equivalent.  The more precise a measurement system is the closer I can get to the boundary with out crossing it.

I can use the Fit Y by X platform to calculate 90% CIs for a whole group of variables (by JSL) the grab the results table as a data table (by JSL) and use the Graph Builder to make a similar plot (save the graph script and use that too.)   Since equivalence testing compares each group mean and its variance with the equivalence limits, there is no pooling of variance. Variance is pooled (or not pooled) when I'm comparing the group means to each other like in a t-test.

JMP Systems Engineer, Pharm and BioPharm Sciences

Staff

Joined:

Apr 26, 2012

Solution

Its not clear from your post exactly how you're going to use the test for equivalence.  In TOST I set an upper and lower limit, and then I put the 95% CI on the limits and make sure that my mean is between the confidence intervals. In the distribution platform you get a result like this (below) and there is no pooling of variance. Its just the variance of the univariate statistic.

This graph has the upper and lower equivalence limits (defined by me as the difference to consider negligible) with the variable's mean bordered by a one side 95% CI on each side (or 90% CI of the mean, same thing). If the CI crosses the equivalence boundary, then it is not equivalent.  The more precise a measurement system is the closer I can get to the boundary with out crossing it.

I can use the Fit Y by X platform to calculate 90% CIs for a whole group of variables (by JSL) the grab the results table as a data table (by JSL) and use the Graph Builder to make a similar plot (save the graph script and use that too.)   Since equivalence testing compares each group mean and its variance with the equivalence limits, there is no pooling of variance. Variance is pooled (or not pooled) when I'm comparing the group means to each other like in a t-test.

JMP Systems Engineer, Pharm and BioPharm Sciences