[R] OT: Likelihood ratio for the randomization/permutation test?

Charles C. Berry cberry at tajo.ucsd.edu
Wed Mar 11 18:38:07 CET 2009

On Wed, 11 Mar 2009, Mike Lawrence wrote:

> Hi guRus,
>
> My discipline (experimental psychology) is gradually moving away from
> Null Hypothesis Testing and towards measures of evidence. One measure
> of evidence that has been popular of late is the likelihood ratio.
> Glover & Dixon (2005) demonstrate the calculation of the likelihood
> ratio from ANOVA tables, but I'm also interested in non-parametric
> statistics and wonder if anyone has any ideas on how to compute a
> likelihood ratio from a randomization test (aka. permutation test)?
>

You cannot get the likelihood ratio from just the null, you need an
alternative. The alternative would have to provide different probabilities
to the individual permutations than under the null I guess, so if you have
a framework where this makes sense you are in business.

I suspect you might be aiming in the direction of "empirical likelihood"
for which there is a literature - Google 'empirical likelihood'.

Also to turn this back to R, check out 'emplik' on CRAN.

HTH,

Chuck

> Say one had two groups and were interested in whether the mean scores
> of the two groups differ in a manner consistent with random chance or
> in a manner consistent with a non-null effect of some manipulation
> applied to the two groups. The randomization test addresses this by
> randomly re-assigning the participants to the groups, re-computing the
> difference between means, and repeating many times, yielding a
> distribution of simulated difference scores that represents the
> distribution expected by chance.
>
> Within a Null Hypothesis Testing framework you then estimate the
> probability of the null by observing the proportion of simulated
> difference scores that are greater in magnitude than the observed
> difference score. Any guesses on how to translate this into a
> quantification of evidence?
>
> Mike
>
> --
> Mike Lawrence
> Graduate Student
> Department of Psychology
> Dalhousie University
>
> Looking to arrange a meeting? Check my public calendar:
> http://tinyurl.com/mikes-public-calendar
>
> ~ Certainty is folly... I think. ~
>
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Charles C. Berry                            (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901

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