Confidence interval for sample variance or standard deviation
Computes the standard normal (i.e., chi-square) confidence intervals for a sample variance or standard deviation.
## S3 method for class 'var' confint(object, parm, level=0.95, ...) ## S3 method for class 'sd' confint(object, parm, level=0.95, ...)
object |
a numeric vector possibly with a |
parm |
degrees of freedom in the estimated variance or standard deviation. |
level |
the confidence level required |
... |
optional arguments not used. |
1. If object is not numeric, throw
an error.
2. If parm is missing, look for an
attribute of object starting with
df. If present, use that for
parm. If parm is absent or
not numeric, throw an error.
3. replicate object, parm, and
level to the same length. Issue a warning
if the longest is not a multiple of the others.
4. alph2 <- (1-level)/2
5. Qntls <- cbind(lower=qchisq(alph2, parm,
lower=FALSE), upper=qchisq(alph2, parm))
6. CI <- (object*parm/Qntls)
7. attr(CI, 'level') <- Level
7. return(CI)
a matrix with columns "lower" and "upper",
nrow = the longest of the lengths
of object, parm, and level,
and an attribute "level".
Spencer Graves
Wikipedia, "Standard deviation", accessed 2016-07-06.
##
## 1. simple examples
##
(CI.v <- confint.var(c(1,1,4), c(1, 9, 9)))
(CI.s <- confint.sd(c(1,1,2), c(1, 9, 9)))
# Compare with the examples on Wikipedia
all.equal(CI.s, sqrt(CI.v))
WikipEx <- t(matrix(c(0.45, 31.9, 0.69, 1.83, 1.38, 3.66),
nrow=2))
colnames(WikipEx) <- c('lower', 'upper')
(dCI <- (CI.s-WikipEx))
#Confirm within 2-digit roundoff
max(abs(dCI))<0.0102
##
## 2. test df attributes
##
v <- c(1,1,4)
attr(v, 'df.') <- c(1, 9, 9)
class(v) <- 'var'
vCI <- confint(v)
# check
all.equal(vCI, CI.v)
s <- sqrt(v)
class(s) <- 'sd'
sCI <- confint(s)
# check
all.equal(sCI, CI.s)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.