CI for the Population Mean — ci

This function calculates CIs for the population mean. By default, Student's t method is used. Alternatively, Wald and bootstrap CIs are available.

ci_mean(
  x,
  probs = c(0.025, 0.975),
  type = c("t", "Wald", "bootstrap"),
  boot_type = c("stud", "bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

x: A numeric vector.
probs: Lower and upper probabilities, by default c(0.025, 0.975).
type: Type of CI. One of "t" (default), "Wald", 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().

Value

An object of class "cint" containing these components:

parameter: Parameter specification.
interval: CI for the parameter.
estimate: Parameter estimate.
probs: Lower and upper probabilities.
type: Type of interval.
info: Additional description.

Details

The default bootstrap type for the mean is "stud" (bootstrap t) as it enjoys the property of being second order accurate and has a stable variance estimator (see Efron, p. 188).

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.
Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.

Examples

x <- 1:100
ci_mean(x)
#> 
#> 	Two-sided 95% t confidence interval for the population mean
#> 
#> Sample estimate: 50.5 
#> Confidence interval:
#>     2.5%    97.5% 
#> 44.74349 56.25651 
#> 
ci_mean(x, type = "bootstrap", R = 999, seed = 1)  # Use larger R
#> 
#> 	Two-sided 95% bootstrap confidence interval for the population mean
#> 	based on 999 bootstrap replications and the student method
#> 
#> Sample estimate: 50.5 
#> Confidence interval:
#>     2.5%    97.5% 
#> 44.92988 56.27187 
#>