# [R] Proportion test in three-chices experiment

Spencer Graves spencer.graves at pdf.com
Sat Jul 16 15:33:18 CEST 2005

```	  Have you considered "BTm" in library(BradleyTerry)?  Consider the
following example:

> cond1 <- data.frame(winner=rep(LETTERS[1:3], e=2),
+           loser=c("B","C","A","C","A","B"),
+           Freq=1:6)
> cond2 <- data.frame(winner=rep(LETTERS[1:3], e=2),
+           loser=c("B","C","A","C","A","B"),
+           Freq=6:1)
> fit1 <- BTm(cond1~..)
> fit2 <- BTm(cond2~..)
> fit12 <- BTm(rbind(cond1, cond2)~..)
> Dev12 <- (fit1\$deviance+fit2\$deviance
+           -fit12\$deviance)
> pchisq(Dev12, 2, lower=FALSE)
 0.8660497

This says the difference between the two data sets, cond1 and cond2,
are not statistically significant.

Do you present each subject with onely one pair?  If yes, then this
model is appropriate.  If no, then the multiple judgments by the same
subject are not statistically independent, as assumed by this model.
However, if you don't get statistical significance via this kind of
computation, it's unlikely that a better model would give you
statistical significance.  If you get a p value of, say, 0.04, then the
difference is probably NOT statistically significant.

The p value you get here would be an upper bound.  You could get a
lower bound by using only one of the three pairs presented to each
subject selected at random.  If that p value were statistically
significant, then I think it is safe to say that your two sets of
conditions are significantly different.  For any value in between, it
would depend on how independent the three choices by the same subject.
You might, for example, delete one of the three pairs at random and use
the result of that comparison.

There are doubtless better techniques, but I'm not familiar with

spencer graves

Rafael Laboissiere wrote:

> Hi,
>
> I wish to analyze with R the results of a perception experiment in which
> subjects had to recognize each stimulus among three choices (this was a
> forced-choice design).  The experiment runs under two different
> conditions and the data is like the following:
>
>    N1 : count of trials in condition 1
>    p11, p12, p13: proportions of choices 1, 2, and 3 in condition 1
>
>    N2 : count of trials in condition 2
>    p21, p22, p23: proportions of choices 1, 2, and 3 in condition 2
>
> How can I test whether the triple (p11,p12,p13) is different from the
> triple (p21,p22,p23)?  Clearly, prop.test does not help me here, because
> it relates to two-choices tests.
>
> I apologize if the answer is trivial, but I am relatively new to R and
> could not find any pointers in the FAQ or in the mailing list archives.
>
> Thanks in advance for any help,
>

--
Spencer Graves, PhD
Senior Development Engineer
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333 West San Carlos Street Suite 700
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