[R] prop.test or chisq.test ..?

[Dylan Beaudette]

On Wednesday 28 February 2007 01:07, Christoph Buser wrote:
> Hi
>
> Some comments are inside.
>
> Dylan Beaudette writes:
>  > Hi everyone,
>  >
>  > Suppose I have a count the occurrences of positive results, and the
>  > total number of occurrences:
>  >
>  >
>  > pos <- 14
>  > total <- 15
>  >
>  > testing that the proportion of positive occurrences is greater than 0.5
>  > gives a p-value and confidence interval:
>  >
>  > prop.test( pos, total, p=0.5, alternative='greater')
>  >
>  >         1-sample proportions test with continuity correction
>  >
>  > data:  14 out of 15, null probability 0.5
>  > X-squared = 9.6, df = 1, p-value = 0.0009729
>  > alternative hypothesis: true p is greater than 0.5
>  > 95 percent confidence interval:
>  >  0.706632 1.000000
>  > sample estimates:
>  >         p
>  > 0.9333333
>
> First of all by default there is a continuity correction in
> prop.test(). If you use
>
> prop.test(pos, total, p=0.5, alternative="greater", correct = FALSE)
>
> 	1-sample proportions test without continuity correction
>
> data:  pos out of total, null probability 0.5
> X-squared = 11.2667, df = 1, p-value = 0.0003946
> alternative hypothesis: true p is greater than 0.5
> 95 percent confidence interval:
>  0.7492494 1.0000000
> sample estimates:
>         p
> 0.9333333
>
> Remark that know the X-squared is identical to  your result from
> chisq.test(), but the p-value is 0.0007891/2
>
> The reason is that you are testing here the against the
> alternative "greater"
>
> If you use a two sided test
>
> prop.test(pos, total, p=0.5, alternative="two.sided", correct = FALSE)
>
> then you reporduce the results form chisq.test().
>
>  > My question is how does the use of chisq.test() differ from the above
>  > operation. For example:
>  >
>  > chisq.test(table( c(rep('pos', 14), rep('neg', 1)) ))
>  >
>  >         Chi-squared test for given probabilities
>  >
>  > data:  table(c(rep("pos", 14), rep("neg", 1)))
>  > X-squared = 11.2667, df = 1, p-value = 0.0007891
>  >
>  > ... gives slightly different results. I am corrent in interpreting that
>  > the chisq.test() function in this case is giving me a p-value associated
>  > with the test that the probabilities of pos are *different* than the
>  > probabilities of neg -- and thus a larger p-value than the prop.test(...
>  > , p=0.5, alternative='greater') ?
>
> Yes. In your example chisq.test() tests the null hypothesis if
> all population probabilities are equal
>
> ?chisq.test says:
> "In this case, the hypothesis tested is whether the population
> probabilities equal those in 'p', or are all equal if 'p' is not
> given."
>
> which means p1 = p2 = 0.5 in your two population case against
> the alternative p1 != p2.
>
> This is similar to the test in prop.test() p=0.5 against p!=0.5
> and therefore you get identical results if you choose
> alternative="two.sided" in prop.test().
>
>  > I realize that this is a rather elementary question, and references to a
>  > text would be just as helpful. Ideally, I would like a measure of how
>  > much I can 'trust' that a larger proportion is also statistically
>  > meaningful. Thus far the results from prop.test() match my intuition,
>  > but
>  > affirmation would be
>
> Your intuition was correct. Nevertheless in your original
> results (with the continuity correction), the p-value of
> prop.test()  (0.0009729) was larger than the p-value of
> chisq.test() (0.0007891) and therefore against your intuition.
>
>  > great.
>  >
>  > Cheers,
>  >
>  >
>  > --
>  > Dylan Beaudette
>  > Soils and Biogeochemistry Graduate Group
>  > University of California at Davis
>  > 530.754.7341
>  >
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>
> Hope this helps
>
> Christoph Buser
>

Thanks for the tips Christoph, this was the help that I was looking for.

cheers,

-- 
Dylan Beaudette
Soils and Biogeochemistry Graduate Group
University of California at Davis
530.754.7341