# CoefQuartVarCI: R6 Confidence Intervals for the Coefficient of Quartile... In MaaniBeigy/DescObs: Versatile Exploration of Data

## Description

The R6 class `CoefQuartVarCI` for the confidence intervals of coefficient of quartile variation (cqv)

## Arguments

 `x` An `R` object. Currently there are methods for numeric vectors `na.rm` a logical value indicating whether `NA` values should be stripped before the computation proceeds. `digits` integer indicating the number of decimal places to be used. `methods` the available computation methods of confidence intervals are: "bonett_ci", "norm_ci", "basic_ci", "perc_ci", "bca_ci" or "all_ci". `R` integer indicating the number of bootstrap replicates.

## Details

Coefficient of Quartile Variation

cqv = ((q3-q1)/(q3 + q1))*100 ,

where q3 and q1 are third quartile (i.e., 75th percentile) and first quartile (i.e., 25th percentile), respectively. The cqv is a measure of relative dispersion that is based on interquartile range (iqr). Since cqv is unitless, it is useful for comparison of variables with different units. It is also a measure of homogeneity [1, 2].

## Value

An object of type "list" which contains the estimate, the intervals, and the computation method. It has two components:

\$method

A description of statistical method used for the computations.

\$statistics

A data frame representing three vectors: est, lower and upper limits of 95% confidence interval `(CI)`:

est:

((q3-q1)/(q3 + q1))*100

Bonett 95% CI:

exp{ln(D/S)C +/- (z(1 - alpha/2) * sqrt(v))},

where C = n/(n - 1) is a centering adjustment which helps to equalize the tail error probabilities. For this confidence interval, D = q3 - q1 and S = q3 + q1; z(1 - alpha/2) is the 1 - alpha/2 quantile of the standard normal distribution [1, 2].

Normal approximation 95% CI: The intervals calculated by the normal approximation [3, 4], using boot.ci.

Basic bootstrap 95% CI: The intervals calculated by the basic bootstrap method [3, 4], using boot.ci.

Bootstrap percentile 95% CI: The intervals calculated by the bootstrap percentile method [3, 4], using boot.ci.

Adjusted bootstrap percentile (BCa) 95% CI: The intervals calculated by the adjusted bootstrap percentile (BCa) method [3, 4], using boot.ci.

## References

[1] Bonett, DG., 2006, Confidence interval for a coefficient of quartile variation, Computational Statistics & Data Analysis, 50(11), 2953-7, DOI: http://doi.org/10.1016/j.csda.2005.05.007

[2] Altunkaynak, B., Gamgam, H., 2018, Bootstrap confidence intervals for the coefficient of quartile variation, Simulation and Computation, 1-9, DOI: http://doi.org/10.1080/03610918.2018.1435800

[3] Canty, A., & Ripley, B, 2017, boot: Bootstrap R (S-Plus) Functions. R package version 1.3-20.

[4] Davison, AC., & Hinkley, DV., 1997, Bootstrap Methods and Their Applications. Cambridge University Press, Cambridge. ISBN 0-521-57391-2

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```y <- c( 0.2, 0.5, 1.1, 1.4, 1.8, 2.3, 2.5, 2.7, 3.5, 4.4, 4.6, 5.4, 5.4, 5.7, 5.8, 5.9, 6.0, 6.6, 7.1, 7.9 ) CoefQuartVarCI\$new(x = y)\$bonett_ci() cqv_y <- CoefQuartVarCI\$new( x = y, alpha = 0.05, R = 1000, digits = 2 ) cqv_y\$bonett_ci() cqv_y\$norm_ci() cqv_y\$basic_ci() cqv_y\$perc_ci() cqv_y\$bca_ci() cqv_y\$all_ci() R6::is.R6(cqv_y) ```

MaaniBeigy/DescObs documentation built on May 23, 2019, 9:37 a.m.