chisq.test: decreasing p-value

A Likert scale may have produced counts of answers per category.  
According to theory I may expect equality over the categories. A  
statistical test shall reveal the actual equality in my sample.

When applying a chi square test with increasing number of  
repetitions (simulate.p.value) over a fixed sample, the p-value  
decreases dramatically (looks as if converge to zero).

(1) Why?
With low numbers of repetitions the test has low power, i.e, it may  
give you the wrong answer to the question: are those two vectors from  
the same distribution? As you increase in number, the simulated value  
approaches the "truth".
(2) (If this test is wrong), then which test can check what I want  
to check, that is: are the two distributions of frequencies  
(observed and expected) in principle the same?
"In principle" they are not the same. Do you want a test that tells  
you they are?
(3) By the way, how to deal with low frequency cells?

r <- c(10, 100, 500, 1000, 2000, 5000)
v <- c(35, 40, 45, 45, 40, 35)
sapply(list(r), function (x) { chisq.test(v, p=c(rep.int(40, 6)),  
rescale.p=T, simulate.p.value=T, B=x)$p.value })

Thank you, S?ren

-- 
S?ren Vogel, PhD-Student, Eawag, Dept. SIAM
http://www.eawag.ch, http://sozmod.eawag.ch

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chisq.test: decreasing p-value

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