# [R] chisq.test: decreasing p-value

David Winsemius dwinsemius at comcast.net
Wed Mar 11 12:32:07 CET 2009

```On Mar 11, 2009, at 6:36 AM, soeren.vogel at eawag.ch wrote:

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