CoefVarCI: R6 Confidence Intervals for the Coefficient of Variation (cv)

Description Arguments Details Value References Examples

Description

The R6 class CoefVarCI for the confidence intervals of coefficient of variation (cv)

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.

method

a scalar representing the type of confidence intervals required. The value should be any of the values "kelley_ci", "mckay_ci", "miller_ci", "vangel_ci", "mahmoudvand_hassani_ci", "equal_tailed_ci", "shortest_length_ci", "normal_approximation_ci", "norm_ci","basic_ci", or "all_ci".

alpha

The allowed type I error probability

R

integer indicating the number of bootstrap replicates.

correction

returns the unbiased estimate of the coefficient of variation if TRUE is determined.

Details

Coefficient of Variation

CV = σ/μ

where σ and μ are standard deviation and mean, respectively. The cv is a measure of relative dispersion representing the degree of variability relative to the mean [1]. Since cv is unitless, it is useful for comparison of variables with different units. It is also a measure of homogeneity [1].

Value

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

$method

A description of statistical method used for the computations.

$statistics

A data frame representing three vectors: est, lower and upper limits of (1-α)% confidence interval (CI); additional description vector is provided when "all" is selected:

est:

(sd/mean)*100

Kelley Confidence Interval: Thanks to package MBESS [2] for the computation of confidence limits for the noncentrality parameter from a t distribution conf.limits.nct [3].

McKay Confidence Interval: The intervals calculated by the method introduced by McKay [4], using χ^2 distribution.

Miller Confidence Interval: The intervals calculated by the method introduced by Miller [5], using the standard normal distribution.

Vangel Confidence Interval: Vangel [6] proposed a method for the calculation of CI for cv; which is a modification on McKay’s CI.

Mahmoudvand-Hassani Confidence Interval: Mahmoudvand and Hassani [7] proposed a new CI for cv; which is obtained using ranked set sampling (RSS)

Normal Approximation Confidence Interval: Wararit Panichkitkosolkul [8] proposed another CI for cv; which is a normal approximation.

Shortest-Length Confidence Interval: Wararit Panichkitkosolkul [8] proposed another CI for cv; which is obtained through minimizing the length of CI.

Equal-Tailed Confidence Interval: Wararit Panichkitkosolkul [8] proposed another CI for cv; which is obtained using χ^2 distribution.

Bootstrap Confidence Intervals: Thanks to package boot by Canty & Ripley [9] we can obtain bootstrap CI around cv using boot.ci.

References

[1] 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

[2] Kelley, K., 2018, MBESS: The MBESS R Package. R package version 4.4. 3., Retrieved from http://cran.r-project.org/package=MBESS

[3] Kelley, K., 2007, Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach, Behavior Research Methods, 39(4), 755–766, DOI: http://doi.org/10.3758/BF03192966

[4] McKay, AT., 1932, Distribution of the Coefficient of Variation and the Extended“ t” Distribution, Journal of the Royal Statistical Society, 95(4), 695–698

[5] Miller, E., 1991, Asymptotic test statistics for coefficients of variation, Communications in Statistics-Theory and Methods, 20(10), 3351–3363

[6] Vangel, MG., 1996, Confidence intervals for a normal coefficient of variation, The American Statistician, 50(1), 21–26

[7] Mahmoudvand, R., & Hassani, H., 2009, Two new confidence intervals for the coefficient of variation in a normal distribution, Journal of Applied Statistics, 36(4), 429–442

[8] Panichkitkosolkul, W., 2013, Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean, Journal of Probability and Statistics, 2013, 1–11, http://doi.org/10.1155/2013/324940

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

Examples

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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
)
CoefVarCI$new(x = y)$kelley_ci()
cv_y <- CoefVarCI$new(
   x = y,
   alpha = 0.05,
   R = 1000,
   digits = 2,
   correction = TRUE
)
cv_y$kelley_ci()
cv_y$mckay_ci()
cv_y$miller_ci()
cv_y$vangel_ci()
cv_y$mh_ci()
cv_y$equal_ci()
cv_y$shortest_ci()
cv_y$normaapprox_ci()
cv_y$norm_ci()
cv_y$basic_ci()
cv_y$perc_ci()
cv_y$bca_ci()
cv_y$all_ci()
R6::is.R6(cv_y)

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