cqv_versatile: Coefficient of Quartile Variation (cqv)
In MaaniBeigy/DescObs: Versatile Exploration of Data

Description Arguments Details Value References Examples

Versatile function for the coefficient of quartile variation (cqv)

`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.
`method`	a scalar representing the type of confidence intervals required. The value should be any of the values "bonett", "norm", "basic", "perc", "bca" or "all".
`R`	integer indicating the number of bootstrap replicates.

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].

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.

[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

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
)
cqv_versatile(x)
cqv_versatile(x, na.rm = TRUE, digits = 2)
cqv_versatile(x, na.rm = TRUE, digits = 2, method = "bonett")
cqv_versatile(x, na.rm = TRUE, digits = 2, method = "norm")
cqv_versatile(x, na.rm = TRUE, digits = 2, method = "basic")
cqv_versatile(x, na.rm = TRUE, digits = 2, method = "perc")
cqv_versatile(x, na.rm = TRUE, digits = 2, method = "bca")
cqv_versatile(x, na.rm = TRUE, digits = 2, method = "all")