# Re: st: equivalence tests

 From "Cathy L. Antonakos" To Statalist Subject Re: st: equivalence tests Date Tue, 10 Jul 2007 18:54:20 -0400 (EDT)

```On Wed, 11 Jul 2007, Joseph Coveney wrote:

```
```Also, I'm curious as to what problems Celine had in resolving the results in
the Stata Technical Bulletin article for -equim- and -equip with formulas in
the Hwang and Morikawa review article (full text at
http://www.diahome.org/content/abstract/1999/d3341205.pdf ).

Joseph Coveney

```
```Joseph, I had the problem with resolving results in two different sources, not Celine.

The difficulty was in taking output from the STB article for -equim- and plugging those numbers (mean, sd, n) into the Hwang & Morikawa formulas for

Z1 = (d + delta) / s_d

lower limit of the one-sided CI = ( 2 - Z_0.95 * s_d)

Z3 = d / s_d

where d = the difference between means, s_d = sqrt(2 * s^2 / n1), and s is the pooled SD.

I was not clear on what to pay attention to in the unfamiliar -equim- output. It would have been convenient to figure out a way to use parts of the output as input for determining non-inferiority and superiority of a non-standard method.

Z1 and the lower limit of CI are used in Hwang & Morikawa, to establish non-inferiority for a given delta. Z3 and the lower limit of CI are used to establish superiority.

To try to get clarity on any pieces of the -equim- output I could use, I tried matching up the STB results with results I calculated by hand using the Hwang & Morikawa formulas. I couldn't get them to match.

Another problem was that d (difference between means) in Hwang & Morikawa was not identified as the absolute value of the difference, but I think it should have been. I could be wrong about that.

This method is not what I would have chosen. My hunch is that introducing delta, which is not generated from the data, into equations with parameters that are generated by the data, creates problems. I could be wrong about that, too.

That's all I have.
HTH.
Cathy Antonakos
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