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

[Christoph Buser]

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
 > 
 > ______________________________________________
 > R-help at stat.math.ethz.ch mailing list
 > https://stat.ethz.ch/mailman/listinfo/r-help
 > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
 > and provide commented, minimal, self-contained, reproducible code.


Hope this helps

Christoph Buser

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