Michael Grant wrote:
I believe the binom.test procedure is producing one tailed p values
rather than the two tailed value implied by the alternative hypothesis
language. A textbook and SAS both show 2*9.94e-07 = 1.988e-06 as the
two tailed value. As does the R summation syntax from R below. It
looks to me like the alternative hypothesis language should be revised
to something like " ... greater than or equal to ..." Am I mistaken?
Yes. Or maybe, it is a matter of definition. The problem is that
> (0:25)[dbinom(0:25,25,.061) <= dbinom(10,25,.061)]
[1] 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
so with R's definition of "more extreme", all such values are in the
upper tail.
Actually, if you look at the actual distribution, I think you'll agree
that it is rather difficult to define a lower tail with positive
probability that corresponds to X >= 10.
> round(dbinom(0:25,25,.061),6)
[1] 0.207319 0.336701 0.262476 0.130726 0.046708 0.012744
[7] 0.002760 0.000487 0.000071 0.000009 0.000001 0.000000
[13] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
[19] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
[25] 0.000000 0.000000
In any case, you would be hard pressed to find a subset of 0:25 that has
the probability that SAS and your textbook claims as the p value.
M.C.Grant
2*sum(dbinom(c(10:25),25,0.061))
[1] 1.987976e-06
binom.test(10,25,0.061)
Exact binomial test
data: 10 and 25
number of successes = 10, number of trials = 25, p-value = 9.94e-07
alternative hypothesis: true probability of success is not equal to
0.061
95 percent confidence interval:
0.2112548 0.6133465
sample estimates:
probability of success
0.4
[[alternative HTML version deleted]]
______________________________________________
R-help@r-project.org 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.
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907
______________________________________________
R-help@r-project.org 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.
