ci_var {confintr} R Documentation

## Confidence Interval for the Population Variance

### Description

This function calculates confidence intervals for the population variance. By default, classic confidence intervals are calculated based on the chi-squared distribution, assuming normal distribution (see Smithson). Bootstrap confidence intervals are also available and are recommended for the non-normal case as the chi-squared confidence intervals are sensitive to deviations from normality.

### Usage

ci_var(
x,
probs = c(0.025, 0.975),
type = c("chi-squared", "bootstrap"),
boot_type = c("bca", "perc", "stud", "norm", "basic"),
R = 9999,
seed = NULL,
...
)


### Arguments

 x A numeric vector. probs Error probabilites. The default c(0.025, 0.975) gives a symmetric 95% confidence interval. type Type of confidence interval. One of "chi-squared" (default) or "bootstrap". boot_type Type of bootstrap confidence interval ("bca", "perc", "stud", "norm", "basic"). 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

Bootstrap confidence intervals are calculated by the package "boot", see references. The default bootstrap type is "bca" (bias-corrected accelerated) as it enjoys the property of being second order accurate as well as transformation respecting (see Efron, p. 188). The "stud" (bootstrap t) bootstrap uses a general formula for the standard error of the sample variance given in Wilks.

### Value

A list with class cint containing these components:

• parameter: The parameter in question.

• interval: The confidence interval for the parameter.

• estimate: The estimate for the parameter.

• probs: A vector of error probabilities.

• type: The type of the interval.

• info: An additional description text for the interval.

### References

1. Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

2. S.S. Wilks (1962), Mathematical Statistics, Wiley & Sons.

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

4. Canty, A and Ripley B. (2019). boot: Bootstrap R (S-Plus) Functions.

ci_sd.
x <- 1:100