Confidence Intervals for the Mean

Collection of several approaches to determine confidence intervals for the mean. Both, the classical way and bootstrap intervals are implemented for both, normal and trimmed means.

Usage

meanCI(
  x,
  conf.level = 0.95,
  sides = c("two.sided", "left", "right"),
  method = c("classic", "boot"),
  sd = NULL,
  trim = 0,
  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". "left" would be analogue to a hypothesis of "greater" in a t.test. You can specify just the initial letter.
method: A vector of character strings representing the type of intervals required. The value should be any subset of the values "classic", "boot". See boot::boot.ci().
sd: the standard deviation of x. If provided it's interpreted as sd of the population and the normal quantiles will be used for constructing the confidence intervals. If left to NULL (default) the sample sd(x) will be calculated and used in combination with the t-distribution.
trim: the fraction (0 to 0.5) of observations to be trimmed from each end of x before the mean is computed. Values of trim outside that range are taken as the nearest endpoint.
na.rm: a logical value indicating whether NA values should be stripped before the computation proceeds. Defaults to FALSE.
...: further arguments are passed to the boot::boot() function. Supported arguments are type ("norm", "basic", "stud", "perc", "bca"), parallel and the number of bootstrap replicates R. If not defined those will be set to their defaults, being "basic" for type, option "boot.parallel" (and if that is not set, "no") for parallel and 999 for R.

Value

A named numeric vector with elements:

est: point estimate
lci: lower confidence interval bound
uci: upper confidence interval bound

Details

The confidence intervals for the trimmed means use winsorized variances as described in the references.

The bootstrap type "stud" (studentized) requires a variance estimate to be returned alongside the point estimate on every bootstrap replicate; this is supported for both the trimmed and untrimmed mean.

References

Wilcox, R. R., Keselman H. J. (2003) Modern robust data analysis methods: measures of central tendency Psychol Methods, 8(3):254-74

Wilcox, R. R. (2005) Introduction to robust estimation and hypothesis testing Elsevier Academic Press

Examples


x <- mtcars$mpg

meanCI(x, na.rm=TRUE)
#>      est      lci      uci 
#> 20.09062 17.91768 22.26357 
meanCI(x, conf.level=0.99, na.rm=TRUE)
#>      est      lci      uci 
#> 20.09062 17.16706 23.01419 

meanCI(x, sides="left", na.rm=TRUE)
#>      est      lci      uci 
#> 20.09062 18.28418      Inf 
# same as:
t.test(x, alternative="greater")
#> 
#> 	One Sample t-test
#> 
#> data:  x
#> t = 18.857, df = 31, p-value < 2.2e-16
#> alternative hypothesis: true mean is greater than 0
#> 95 percent confidence interval:
#>  18.28418      Inf
#> sample estimates:
#> mean of x 
#>  20.09062 
#> 

meanCI(x, sd=25, na.rm=TRUE)
#>      est      lci      uci 
#> 20.09062 11.42873 28.75252 

# the different types of bootstrap confints
meanCI(x, method="boot", type="norm", na.rm=TRUE)
#>      est      lci      uci 
#> 20.09062 18.00729 22.19484 
meanCI(x, trim=0.1, method="boot", type="norm", na.rm=TRUE)
#>      est      lci      uci 
#> 19.69615 17.55049 21.84337 
meanCI(x, trim=0.1, method="boot", type="basic", na.rm=TRUE)
#>      est      lci      uci 
#> 19.69615 17.24615 21.81154 
meanCI(x, trim=0.1, method="boot", type="stud", na.rm=TRUE)
#>      est      lci      uci 
#> 19.69615 17.56002 22.71807 
meanCI(x, trim=0.1, method="boot", type="perc", na.rm=TRUE)
#>      est      lci      uci 
#> 19.69615 17.70385 21.83462 
meanCI(x, trim=0.1, method="boot", type="bca", na.rm=TRUE)
#>      est      lci      uci 
#> 19.69615 17.87268 22.25566 

meanCI(x, trim=0.1, method="boot", type="bca", R=1999, na.rm=TRUE)
#>      est      lci      uci 
#> 19.69615 17.82699 22.22681 

# Getting the meanCI for more than 1 column
round(t(sapply(mtcars[, c("mpg", "hp")], meanCI, na.rm=TRUE)), 3)
#>         est     lci     uci
#> mpg  20.091  17.918  22.264
#> hp  146.688 121.968 171.407