[Rd] prop.test confidence intervals (PR#2794)
rbaer at kcom.edu
rbaer at kcom.edu
Fri Apr 18 20:01:05 MEST 2003
Full_Name: Robert W. Baer, Ph.D.
Version: 1.6.2
OS: Windows 2000
Submission from: (NULL) (198.209.172.106)
Problem: prop.test() does not seem to produce appropriate confidence intervals
for the case where the vector length of x and n is one. (I am not certain about
higher vector lengths.)
As an example, I include x=6 and n=42 which has a mean proportion of 0.115.
When I calculate the 95% CI using the normal approximation by hand (and no
continuity correction) I get (0.028, 0.202). The exact binomial CI from
binom.test() is (0.044, 0.234). With correct=FALSE prop.test produces CI95 =
(0.05396969, 0.22971664) which is neither of these. With correct=TRUE it
produces (0.04778925, 0.2412937) This seems reasonably like a normal
approximation 95% CI (which I presume is what is used by prop.test()) of the
true binomial but I did not actually check it by hand.
BUG summary. The prop.test() calculation of 95% CI of sample proportions is
improperly calculated when continuity correction is turned off.
-----------------------------
Sample R code and output shown below:
> x= 6;n=52
> prop.test(x,n,correct=TRUE)
1-sample proportions test with continuity correction
data: x out of n, null probability 0.5
X-squared = 29.25, df = 1, p-value = 6.362e-08
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.04778925 0.24129372
sample estimates:
p
0.1153846
> prop.test(x,n,correct=FALSE)
1-sample proportions test without continuity correction
data: x out of n, null probability 0.5
X-squared = 30.7692, df = 1, p-value = 2.906e-08
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.05396969 0.22971664
sample estimates:
p
0.1153846
> binom.test(x,n)
Exact binomial test
data: x and n
number of successes = 6, number of trials = 52, p-value = 1.033e-08
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
0.0435412 0.2344083
sample estimates:
probability of success
0.1153846
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