[R] chisq.test: decreasing p-value

[soeren.vogel at eawag.ch]

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?
(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?
(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, Sören


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