# MeanCI: Confidence Interval for the Mean In DescTools: Tools for Descriptive Statistics

## 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

 ```1 2 3``` ```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

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```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) ```

### Example output

```    mean   lwr.ci   upr.ci
48.03037 37.16348 58.89726
mean   lwr.ci   upr.ci
48.03037 33.14181 62.91892
mean lwr.ci upr.ci
NA     NA    Inf

One Sample t-test

data:  x
t = 9.2858, df = 18, p-value = 1.379e-08
alternative hypothesis: true mean is greater than 0
95 percent confidence interval:
39.06103      Inf
sample estimates:
mean of x
48.03037

mean   lwr.ci   upr.ci
48.03037 36.78920 59.27153
mean   lwr.ci   upr.ci
48.03037 38.39504 58.20331
mean   lwr.ci   upr.ci
47.71441 36.87307 58.31414
mean   lwr.ci   upr.ci
47.71441 36.44935 57.91800
mean   lwr.ci   upr.ci
47.71441 36.83194 58.99912
mean   lwr.ci   upr.ci
47.71441 37.53741 58.37588
mean   lwr.ci   upr.ci
47.71441 36.77244 59.03681
mean   lwr.ci   upr.ci
47.71441 37.45178 58.30295
mean    lwr.ci    upr.ci
index     605.000   585.299   624.701
date    16145.260 16144.746 16145.774
week       11.403    11.327    11.479
weekday     4.441     4.325     4.556
```

DescTools documentation built on June 17, 2021, 5:12 p.m.