# ci_var: Confidence Interval for the Population Variance In confintr: Confidence Intervals

 ci_var 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