# ci_mean_diff: CI for the Population Mean Difference In confintr: Confidence Intervals

 ci_mean_diff R Documentation

## CI for the Population Mean Difference

### Description

This function calculates CIs for the population value of mean(x) - mean(y). The default is Student's method with Welch's correction for unequal variances, but also bootstrap CIs are available.

### Usage

``````ci_mean_diff(
x,
y,
probs = c(0.025, 0.975),
var.equal = FALSE,
type = c("t", "bootstrap"),
boot_type = c("stud", "bca", "perc", "norm", "basic"),
R = 9999L,
seed = NULL,
...
)
``````

### Arguments

 `x` A numeric vector. `y` A numeric vector. `probs` Lower and upper probabilities, by default `c(0.025, 0.975)`. `var.equal` Should the two variances be treated as being equal? The default is `FALSE`. If `TRUE`, the pooled variance is used to estimate the variance of the mean difference. Otherweise, Welch's approach is used. This also applies to the "stud" bootstrap. `type` Type of CI. One of "t" (default), or "bootstrap". `boot_type` Type of bootstrap CI. Only used for `type = "bootstrap"`. `R` The number of bootstrap resamples. Only used for `type = "bootstrap"`. `seed` An integer random seed. Only used for `type = "bootstrap"`. `...` Further arguments passed to `boot::boot()`.

### Details

The default bootstrap type is "stud" (bootstrap t) as it has a stable variance estimator (see Efron, p. 188). Resampling is done within sample. When `boot_type = "stud"`, the standard error is estimated by Welch's method if `var.equal = FALSE` (the default), and by pooling otherwise. Thus, `var.equal` not only has an effect for the classic Student approach (`type = "t"`) but also for `boot_type = "stud"`.

### Value

An object of class "cint", see `ci_mean()` for details.

### References

Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.

### Examples

``````x <- 10:30
y <- 1:30
ci_mean_diff(x, y)
t.test(x, y)\$conf.int
ci_mean_diff(x, y, type = "bootstrap", R = 999)  # Use larger R
``````

confintr documentation built on June 7, 2023, 6:24 p.m.