# VarCI: Confidence Intervals for the Variance In DescTools: Tools for Descriptive Statistics

## Description

Calculates confidence intervals for the variance. Available approachs are the classical one using the ChiSquare distribution, a more robust version proposed by Bonett and the bootstrap options available in the package `boot`.

## Usage

 ```1 2 3``` ```VarCI(x, method = c("classic", "bonett", "norm", "basic", "stud", "perc", "bca"), conf.level = 0.95, sides = c("two.sided", "left", "right"), na.rm = FALSE, R = 999) ```

## Arguments

 `x` a (non-empty) numeric vector of data values. `method` vector of character strings representing the type of intervals required. The value should be any subset of the values `"classic"`, `"bonett"`, `"norm"`, `"basic"`, `"stud"`, `"perc"`, `"bca"`. 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` logical. Should missing values be removed? Defaults to FALSE. `R` number of bootstrap replicates. Usually this will be a single positive integer. For importance resampling, some resamples may use one set of weights and others use a different set of weights. In this case R would be a vector of integers where each component gives the number of resamples from each of the rows of weights. See `boot`.

## Details

The confidence interval for the variance is very sensitive to non-normality in the data. Bonett (2006) has proposed an interval that is nearly exact when the data is normally distributed and provides good performance for moderately non-normal data. See the references for the details.

## Value

a numeric vector with 3 elements:

 `var` variance `lwr.ci` lower bound of the confidence interval `upr.ci` upper bound of the confidence interval

## Author(s)

Andri Signorell <andri@signorell.net>

## References

Bonett (2006) Approximate Confidence Interval for Standard Deviation of Nonnormal Distributions, Computational Statistics and Data Analysis, Vol. 50, pp. 775 - 782.
https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/sdconfli.htm (might be outdated)

`MeanCI`, `MedianCI`, `VarTest`, `Var`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```VarCI(d.pizza\$price, na.rm=TRUE) VarCI(d.pizza\$price, conf.level=0.99, na.rm=TRUE) x <- c(14.816, 14.863, 14.814, 14.998, 14.965, 14.824, 14.884, 14.838, 14.916, 15.021, 14.874, 14.856, 14.860, 14.772, 14.980, 14.919) VarCI(x, conf.level=0.9) # and for the standard deviation sqrt(VarCI(x, conf.level=0.9)) # from Bonett's paper # expected results: # ------------------------------------ # conf.lvl sd lci uci # ------------------------------------ # 90.0 0.5168 0.3592 0.9359 # 95.0 0.5168 0.3263 1.0841 # 99.0 0.5168 0.2607 1.5109 p <- c(15.83, 16.01, 16.24, 16.42, 15.33, 15.44, 16.88, 16.31) sqrt(VarCI(p, method="bonett", conf.level=0.9)) sqrt(VarCI(p, method="bonett")) sqrt(VarCI(p, method="bonett", conf.level=0.99)) # some bootstrap intervals VarCI(x, method="norm") VarCI(x, method="perc") VarCI(x, method="bca") ```

### Example output

```     var   lwr.ci   upr.ci
467.9136 432.5641 507.8033
var   lwr.ci   upr.ci
467.9136 422.1248 521.1730
var      lwr.ci      upr.ci
0.005285333 0.003171734 0.010918691
var     lwr.ci     upr.ci
0.07270030 0.05631815 0.10449254
var    lwr.ci    upr.ci
0.5167965 0.3592151 0.9359420
var    lwr.ci    upr.ci
0.5167965 0.3263123 1.0840670
var    lwr.ci    upr.ci
0.5167965 0.2607127 1.5108922
var      lwr.ci      upr.ci
0.005285333 0.002869147 0.008322241
var      lwr.ci      upr.ci
0.005285333 0.002348917 0.007658533
var      lwr.ci      upr.ci
0.005285333 0.003136747 0.008976974
```

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