[R] Test for equivalence

[Albyn Jones]

Reading the original post it was clear to me that the poster was looking for
a test of equivalence, but obviously there was room for interpretation!

albyn

On Mon, Feb 14, 2011 at 09:46:13AM -0700, Greg Snow wrote:
> Reading the original post it is fairly clear that the original poster's question does not match with the traditional test of equivalence, but rather is trying to determine "distinguishable or indistinguishable".  If the test in my suggestion is statistically significant (and note I did not suggest only testing the interaction) then that meets one possible interpretation of "distinguishable", a non-significant result could mean either equivalence or low power, the combination of which could be an interpretation of "indistinguishable".
> 
> I phrased my response as a question in hopes that the original poster would think through what they really wanted to test and get back to us with further details.  It could very well be that my response is very different from what they were thinking, but explaining how it does not fit will better help us understand the real problem.
> 
> -- 
> Gregory (Greg) L. Snow Ph.D.
> Statistical Data Center
> Intermountain Healthcare
> greg.snow at imail.org
> 801.408.8111
> 
> 
> > -----Original Message-----
> > From: Albyn Jones [mailto:jones at reed.edu]
> > Sent: Sunday, February 13, 2011 9:53 PM
> > To: Greg Snow
> > Cc: syrvn; r-help at r-project.org
> > Subject: Re: [R] Test for equivalence
> > 
> > testing the null hypothesis of no interaction is not the same as a
> > test of equivalence for the two differences.  There is a literature on
> > tests of equivalence.  First you must develop a definition of
> > equivalence, for example the difference is in the interval (-a,a).
> > Then, for example,  you test the null hypothesis that the difference
> > is in [a,inf) or (-inf,-a] (a TOST, or two one sided tests).  One
> > simple procedure: check to see if the 90% CI for the difference
> > (difference of the differences or the interaction effect) is contained
> > in the interval (-a,a).
> > 
> > albyn
> > 
> > Quoting Greg Snow <Greg.Snow at imail.org>:
> > 
> > > Does it make sense for you to combine the 2 data sets and do a 2-way
> > > anova with treatment vs. control as one factor and experiment number
> > > as the other factor?  Then you could test the interaction and
> > > treatment number factor to see if they make a difference.
> > >
> > > --
> > > Gregory (Greg) L. Snow Ph.D.
> > > Statistical Data Center
> > > Intermountain Healthcare
> > > greg.snow at imail.org
> > > 801.408.8111
> > >
> > >
> > >> -----Original Message-----
> > >> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> > >> project.org] On Behalf Of syrvn
> > >> Sent: Saturday, February 12, 2011 7:30 AM
> > >> To: r-help at r-project.org
> > >> Subject: [R] Test for equivalence
> > >>
> > >>
> > >> Hi!
> > >>
> > >> is there a way in R to check whether the outcome of two different
> > >> experiments is statistically distinguishable or indistinguishable?
> > More
> > >> preciously, I used the wilcoxon test to determine the differences
> > >> between
> > >> controls and treated subjects for two different experiments. Now I
> > >> would
> > >> like to check whether the two lists of analytes obtained are
> > >> statistically
> > >> distinguishable or indistinguishable
> > >>
> > >> I tried to use a equivalence test from the 'equivalence' package in
> > R
> > >> but it
> > >> seems that this test is not applicable to my problem. The test in
> > the
> > >> 'equivalence' package just determines similarity between two
> > conditions
> > >> but
> > >> I need to compare the outcome of two different experiments.
> > >>
> > >> My experiments are constructed as follows:
> > >>
> > >> Exp1:
> > >> 8 control samples
> > >> 8 treated samples
> > >> -> determine significantly changes (List A)
> > >>
> > >> Exp2:
> > >> 8 control samples
> > >> 8 treated samples
> > >> -> determine significantly changes (List B)
> > >>
> > >>
> > >> Now i would like to check whether List A and List B are
> > distinguishable
> > >> or
> > >> indistinguishable.
> > >>
> > >> Any advice is very much appreciated!
> > >>
> > >> Best,
> > >> beginner
> > >> --
> > >> View this message in context: http://r.789695.n4.nabble.com/Test-
> > for-
> > >> equivalence-tp3302739p3302739.html
> > >> Sent from the R help mailing list archive at Nabble.com.
> > >>
> > >> ______________________________________________
> > >> R-help at r-project.org mailing list
> > >> https://stat.ethz.ch/mailman/listinfo/r-help
> > >> PLEASE do read the posting guide http://www.R-project.org/posting-
> > >> guide.html
> > >> and provide commented, minimal, self-contained, reproducible code.
> > >
> > > ______________________________________________
> > > R-help at r-project.org mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide http://www.R-project.org/posting-
> > guide.html
> > > and provide commented, minimal, self-contained, reproducible code.
> > >
> > >
> 
> 

-- 
Albyn Jones
Reed College
jones at reed.edu