cvcqv

cvcqv provides some easy-to-use functions and classes to calculate Coefficient of Variation (cv) and Coefficient of Quartile Variation (cqv) with confidence intervals provided with all available methods.

Overview

Background

There are abundant methods available for the calculation of confidence intervals of a dispersion measure like coefficient of variation (cv) or coefficient of quartile variation (cqv), which have not yet been implemented in R. Also, cqv is quite useful in conditions where the distribution of variables does not follow normal distribution.

Coefficient of Variation

cv is a measure of relative dispersion representing the degree of variability relative to the mean (Albatineh et al, 2014). Since cv is unitless, it is useful for comparison of variables with different units. It is also a measure of homogeneity (Albatineh et al, 2014).

Coefficient of Quartile Variation

cqv is a measure of relative dispersion that is based on interquartile range (IQR). Since cqv is unitless, it is also useful for comparison of variables with different units. It is also a measure of homogeneity (Bonett, 2006; Altunkaynak, 2018).

Confidence Interval

Since the measurements of cv and cqv are obtained from samples, we cannot easily generalize them and decide based upon them. Confidence Intervals (CI) help us to make a probabilistic interval around the estimation of calculated cv and cqv. For example, 95% CI indicates that it is 95% probable that the measurement for a population lies between the lower and upper bounds of that CI.

Aims

The authors' intention is to create a small R package adhering to K-I-S-S principle to facilitate the use of the most available rigorous methods for calculation of confidence intervals around the variability measures of cv and cqv.

Convention

We are bound by the high standards of functional programming (FP) and object-oriented programming (OOP). The majority of tools provided by cvcqv are developed as both FP tools and R6 classes, for sake of versatility, portability and efficiency.

Getting started

If you are an ubuntu user, you are going to need these non-R packages:

sudo apt install libcurl4-openssl-dev libssl-dev libxml2-dev libgsl-dev   

The cvcqv package is available on CRAN. To install:

install.packages("cvcqv")

The cvcqv package is also available on github. To install it in R, use:

devtools::install_github('MaaniBeigy/cvcqv')  

* Currently, these tools are available:

name	is.R6..	Description
CoefVar	TRUE	Coefficient of Variation (cv)
CoefQuartVar	TRUE	Coefficient of Quartile Variation (cqv)
CoefVarCI	TRUE	Confidence Intervals for cv
CoefQuartVarCI	TRUE	Confidence Intervals for cqv
SampleQuantiles	TRUE	Sample Quantiles
cv_versatile	FALSE	Coefficient of Variation
cqv_versatile	FALSE	Coefficient of Quartile Variation
BootCoefVar	TRUE	Bootstrap Resampling for cv
BootCoefQuartVar	TRUE	Bootstrap Resampling for cqv

* This package is inspired by dplyr, R6, SciView, boot, and MBESS.

Examples

Here, we want to observe all available confidence intervals for the cv of variable x:

x <- 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
)
results <- CoefVarCI$new(x, digits = 3)$all_ci()  # R6 class
# or alternatively: 
results <- cv_versatile(x, digits = 3, method = "all")  # functional programming

The results will be:

	est	lower	upper	description
kelley	57.774	41.287	97.894	cv with Kelley 95% CI
mckay	57.774	41.441	108.483	cv with McKay 95% CI
miller	57.774	34.053	81.495	cv with Miller 95% CI
vangel	57.774	41.264	105.426	cv with Vangel 95% CI
mahmoudvand_hassani	57.774	43.476	82.857	cv with Mahmoudvand-Hassani 95% CI
equal_tailed	57.774	43.937	84.383	cv with Equal-Tailed 95% CI
shortest_length	57.774	42.015	81.013	cv with Shortest-Length 95% CI
normal_approximation	57.774	44.533	85.272	cv with Normal Approximation 95% CI
norm	57.774	38.799	78.937	cv with Normal Approximation Bootstrap 95% CI
basic	57.774	35.055	78.167	cv with Basic Bootstrap 95% CI
perc	57.774	38.879	79.174	cv with Bootstrap Percentile 95% CI
bca	57.774	40.807	82.297	cv with Adjusted Bootstrap Percentile (BCa) 95% CI

Next, we want to find all of the available confidence intervals for the cqv of variable x:

results <- CoefQuartVarCI$new(x, digits = 3)$all_ci()  # R6 class
# or alternatively:
results <- cqv_versatile(x, , digits = 3, method = "all")  # functional programming

The results will be:

	est	lower	upper	description
bonett	45.625	24.785	77.329	cqv with Bonett CI
norm	45.625	19.957	70.840	cqv with normal approximation CI
basic	45.625	18.992	73.917	cqv with basic bootstrap CI
percent	45.625	17.122	68.683	cqv with bootstrap percentile CI
bca	45.625	24.273	83.264	cqv with adjusted bootstrap percentile (BCa) CI

Documentation

Download the cvcqv_1.0.0.tar.gz. Install the source package cvcqv from the Packages >> Install >> Package Archive File (.tar.gz) >> Browse >> cvcqv_1.0.0.tar.gz. Or run an installation code like:

install.packages("~/cvcqv_1.0.0.tar.gz", repos = NULL, type = "source")

Then, browse for vignettes:

browseVignettes("cvcqv")

Then, select html to show the vignette.

References

Albatineh, AN., Kibria, BM., Wilcox, ML., & Zogheib, B, 2014, Confidence interval estimation for the population coefficient of variation using ranked set sampling: A simulation study, Journal of Applied Statistics, 41(4), 733–751, DOI: http://doi.org/10.1080/02664763.2013.847405

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

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