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Confidence Interval for a Variance

Source: R/varCI.R
varCI.Rd

Computes confidence intervals for a population variance using classical chi-square, Bonett, or bootstrap methods.

Usage

varCI(
  x,
  conf.level = 0.95,
  sides = c("two.sided", "left", "right"),
  method = c("classic", "bonett", "boot"),
  na.rm = FALSE,
  ...
)

Arguments

x

a (non-empty) numeric vector of data values.

conf.level

confidence level of the interval.

sides

a character string specifying the side of the confidence interval, must be one of "two.sided" (default), "left" or "right". You can specify just the initial letter. "left" would be analogue to a hypothesis of "greater" in a t.test.

method

vector of character strings representing the type of intervals required. The value should be any subset of the values "classic", "bonett", "norm", "boot". Bootstrap type can be set by the ... arguments. See boot::boot.ci().

na.rm

logical. Should missing values be removed? Defaults to FALSE.

...

further arguments, can be used to provide further arguments to the boot function.

Value

A named numeric vector with elements:

est

point estimate.

lci

lower confidence interval bound.

uci

upper confidence interval bound.

Details

The confidence interval for the variance is very sensitive to non-normality in the data. Bonett (2006) has proposed an interval that is nearly exact when the data is normally distributed and provides good performance for moderately non-normal data. See the references for the details.

References

Bonett (2006) Approximate Confidence Interval for Standard Deviation of Nonnormal Distributions, Computational Statistics and Data Analysis, Vol. 50, pp. 775 - 782.
https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/sdconfli.htm (might be outdated)

See also

meanCI(), medianCI(), varTest(), DescToolsX::varX

Other test.variance: leveneTest(), mosesTest(), siegelTukeyTest(), varTest()

Examples

x <- mtcars$mpg

varCI(x, na.rm=TRUE)
#>      est      lci      uci 
#> 36.32410 23.34653 64.20343 
varCI(x, conf.level=0.99, na.rm=TRUE)
#>      est      lci      uci 
#> 36.32410 20.47258 77.88527 

x <- c(14.816, 14.863, 14.814, 14.998, 14.965, 14.824, 14.884, 14.838, 14.916,
       15.021, 14.874, 14.856, 14.860, 14.772, 14.980, 14.919)
varCI(x, conf.level=0.9)
#>         est         lci         uci 
#> 0.005285333 0.003171734 0.010918691 

# and for the standard deviation
sqrt(varCI(x, conf.level=0.9))
#>        est        lci        uci 
#> 0.07270030 0.05631815 0.10449254 


# from Bonett's paper
# expected results:
# ------------------------------------
#  conf.lvl       sd      lci      uci
# ------------------------------------
#      90.0   0.5168   0.3592   0.9359
#      95.0   0.5168   0.3263   1.0841
#      99.0   0.5168   0.2607   1.5109

p <- c(15.83, 16.01, 16.24, 16.42, 15.33, 15.44, 16.88, 16.31)
sqrt(varCI(p, method="bonett", conf.level=0.9))
#>       est       lci       uci 
#> 0.5167965 0.3592151 0.9359420 
sqrt(varCI(p, method="bonett"))
#>       est       lci       uci 
#> 0.5167965 0.3263123 1.0840670 
sqrt(varCI(p, method="bonett", conf.level=0.99))
#>       est       lci       uci 
#> 0.5167965 0.2607127 1.5108922 

# some bootstrap intervals
varCI(x, method="boot", type="norm")
#>         est         lci         uci 
#> 0.005285333 0.002935139 0.008293970 
varCI(x, method="boot", type="perc")
#>         est         lci         uci 
#> 0.005285333 0.002081296 0.007595129 
varCI(x, method="boot", type="bca")
#>         est         lci         uci 
#> 0.005285333 0.003153558 0.009063481