# Equivalence testing with ANOVA

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This topic contains 5 replies, has 4 voices, and was last updated by lin 10 years, 4 months ago.

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- March 5, 2009 at 9:44 pm #51960
I’m pretty well versed in doing 2 one-sided testing for equivalence, but I’m having trouble translating this to multiple samples using ANOVA. I have Wellek’s text “Testing Statistical Hypothesis of Equivalence”, but I can’t decipher his explanation for multiple samples in ch.7. Any of you dark-siders out there able to help with this?

0March 6, 2009 at 1:43 pm #182082

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.I don’t know the text and the tech library I use doesn’t have a copy so I’m guessing that what you are referring to is the issue of multiple pairwise comparisons. If this guess is correct then my next guess would be that you are trying to understand the need for corrections such as Tukey-Kramer or Bonferroni.

Since we are now possibly two guesses removed from reality and the question you really want to answer could you provide some more details concerning what you are trying to do and perhaps a thumbnail summary of what you think the book is trying to say?

0March 6, 2009 at 3:05 pm #182086Robert,

Thanks for the reply. WHat I’m specifically trying to do is use a simple one-way ANOVA to show equivalence. It’s relatively easy to choose the “zone of indeifference” in a 2 sample equivalence test, since this is a pretty intuitive thing. For example, if I want to prove equivalence between the strength of two different materials, I would say “if the sample averages are within 10% of each other, this is equivalent for my purposes”. Then I would do two one-sided tests to confirm that the lower and upper confidence limits are contained within the +/- 10% zone.

THe problem with doing this with ANOVA is that the “zone of indifference” is no longer expressed in the original units of measurement, but in the ratio of the variances (F-score). I just can’t seem to make the logical leap that makes this intuitve. For example, I could say “the zone of indifference (equivalence of multiple samples) is when the F-score is less than 2”. This would be a hard limit that you could then select appropriate sample sizes to achieve, then test against. But expressing equivalence in terms of an F-score is just not intuitive – to me at least.

Clear as mud?0March 6, 2009 at 3:16 pm #182088

Gary ConeParticipant@garyacone**Include @garyacone in your post and this person will**

be notified via email.I also do not have the book you reference, but this is simply a sample

size question. Your simple example implies a sample to give your +/-

10% with some degree of confidence. Multiple samples will do the

same thing – figure out your zone of indifference (how big does the

difference need to be before I care), figure out the level of confidence

you require and get a sample size. Once you know that, you will know

the degrees of freedom associated with the levels and the error. That

will dictate your maximum F.0March 9, 2009 at 10:20 am #182156Sounds as though you are trying to answer a textbook question. Is that the case? Or, is this a real-world problem?

0March 9, 2009 at 5:26 pm #182178No, not a book question. I’m trying to apply this as a way to compare destructive testing methods at different manufacturing sites. I have multiple moisture analyzers that I need to compare.

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