Versatile function for the coefficient of variation (cv)
An R object. Currently there are methods for numeric vectors
a logical value indicating whether NA values should be
stripped before the computation proceeds.
integer indicating the number of decimal places to be used.
a scalar representing the type of confidence intervals required. The value should be any of the values "kelley", "mckay", "miller", "vangel", "mahmoudvand_hassani", "equal_tailed", "shortest_length", "normal_approximation", "norm","basic", or "all".
returns the unbiased estimate of the coefficient of variation
The allowed type I error probability
integer indicating the number of bootstrap replicates.
An object of type "list" which contains the estimate, the intervals, and the computation method. It has two main components:
A description of statistical method used for the computations.
A data frame representing three
vectors: est, lower and upper limits of confidence interval (CI);
additional description vector is provided when "all" is selected:
est: cv*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 chi-square 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<U+2019>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
chi-square distribution. Bootstrap Confidence
Intervals: Thanks to package boot by Canty & Ripley [9] we
can obtain bootstrap CI around cv using boot.ci.
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].
[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<U+2013>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.
[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<U+2013>766, DOI:
http://doi.org/10.3758/BF03192966
[4] McKay, AT., 1932, Distribution of the Coefficient of
Variation and the Extended<U+201C> t<U+201D> Distribution, Journal of the Royal
Statistical Society, 95(4), 695<U+2013>698
[5] Miller, E., 1991, Asymptotic test statistics for
coefficients of variation, Communications in Statistics-Theory and Methods,
20(10), 3351<U+2013>3363
[6] Vangel, MG., 1996, Confidence intervals for a normal
coefficient of variation, The American Statistician, 50(1), 21<U+2013>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<U+2013>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<U+2013>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
# NOT RUN {
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
)
cv_versatile(x)
cv_versatile(x, correction = TRUE)
cv_versatile(x, na.rm = TRUE, digits = 3, method = "kelley", correction = TRUE)
cv_versatile(x, na.rm = TRUE, method = "mahmoudvand_hassani", correction = TRUE)
# }
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