[R] Proportion test in three-chices experiment

[Spencer Graves]

	  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)
[1] 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 
them.  Perhaps someone else will reply to my reply.

	  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,
> 

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