R: Confidence Interval for the Mean

MeanCI {DescTools} | R Documentation

## Confidence Interval for the Mean

### Description

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, sd = NULL, trim = 0, method = c("classic", "boot"),
           conf.level = 0.95, sides = c("two.sided", "left", "right"),
           na.rm = FALSE, ...)

### Arguments

`x` | a (non-empty) numeric vector of data values.
`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.
`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.ci`.
`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`.
`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` 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`.

### Details

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

Use `do.call`, `rbind` and `lapply` for getting a matrix with estimates and confidence intervals for more than 1 column. (See examples!)

### Value

a numeric vector with 3 elements:

`mean` | mean
`lwr.ci` | lower bound of the confidence interval
`upr.ci` | upper bound of the confidence interval

### Author(s)

Andri Signorell <andri@signorell.net>

### 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

### See Also

`t.test`, `MeanDiffCI`, `MedianCI`, `VarCI`

### Examples

    x <- d.pizza$price[1:20]

    MeanCI(x, na.rm=TRUE)
    MeanCI(x, conf.level=0.99, na.rm=TRUE)

    MeanCI(x, sides="left")
    # same as:
    t.test(x, alternative="greater")

    MeanCI(x, sd=25, na.rm=TRUE)

    # the different types of bootstrap confints
    MeanCI(x, method="boot", type="norm", na.rm=TRUE)
    MeanCI(x, trim=0.1, method="boot", type="norm", na.rm=TRUE)
    MeanCI(x, trim=0.1, method="boot", type="basic", na.rm=TRUE)
    MeanCI(x, trim=0.1, method="boot", type="stud", na.rm=TRUE)
    MeanCI(x, trim=0.1, method="boot", type="perc", na.rm=TRUE)
    MeanCI(x, trim=0.1, method="boot", type="bca", na.rm=TRUE)

    MeanCI(x, trim=0.1, method="boot", type="bca", R=1999, na.rm=TRUE)

    # Getting the MeanCI for more than 1 column
    round( do.call("rbind", lapply(d.pizza[, 1:4],  MeanCI, na.rm=TRUE)), 3)

[Package DescTools version 0.99.26 Index]