Dear R people,
I notice that the confidence intervals of a very small sample (e.g. n=6)
derived from the one-sample wilcox.test are just the maximum and minimum
values of the sample. This only occurs when the required confidence level is
higher than 0.93. Example:
> sample <- c(1.22, 0.89, 1.14, 0.98, 1.37, 1.06)
> summary(sample)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.89 1.00 1.10 1.11 1.20 1.37
> wilcox.test(sample,conf.int=TRUE,conf.lev=0.95)
Wilcoxon signed rank test
data: sample
V = 21, p-value = 0.03125
alternative hypothesis: true location is not equal to 0
95 percent confidence interval:
0.89 1.37
sample estimates:
(pseudo)median
1.1
According to "help", since my sample contains less than 50 values, an exact
p-value is calculated that should enable the confidence interval to be
obtained from Bauer (1972) (I have not read it):
<< By default (if âexactâ is not specified), an exact p-value is
computed if the samples contain less than 50 finite values and
there are no ties. Otherwise, a normal approximation is used.
...........
If exact p-values are available, an exact
confidence interval is obtained by the algorithm described in
Bauer (1972), and the Hodges-Lehmann estimator is employed.
Otherwise, the returned confidence interval and point estimate are
based on normal approximations. These are continuity-corrected
for the interval but _not_ the estimate (as the correction depends
on the âalternativeâ). With small samples it may not be possible to
achieve very high
confidence interval coverages. If this happens a warning will be
given and an interval with lower coverage will be substituted. >>
The latter indeed happens if I ask for confidence level of 0.99:
> wilcox.test(sample,mu=0,conf.int=TRUE,conf.lev=0.99)
Wilcoxon signed rank test
data: sample
V = 21, p-value = 0.03125
alternative hypothesis: true location is not equal to 0
96.9 percent confidence interval:
0.89 1.37
sample estimates:
(pseudo)median
1.1
Warning message:
In wilcox.test.default(sample, mu = 0, conf.int = TRUE, conf.lev = 0.99) :
Requested conf.level not achievable
My questions (finally!) are:
1. Why the above warning for conf.lev = 0.99 does not appear for 0.93 <
conf.lev < 0.98 although it produces the same summary?
2. For conf.lev = 0.95, is there anything else I can do in order to obtain
confidence intervals other than the max. and min. values of my sample or I am
limited from my sample's size ?
Thanks for your patience in reading this,
Panos
-------------------------------------------------------
Dr Panos Hadjinicolaou
Energy Environment& Water Research Center (EEWRC)
The Cyprus Institute
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