# ci.cv: Confidence interval for the coefficient of variation In MBESS: The MBESS R Package

 ci.cv R Documentation

## Confidence interval for the coefficient of variation

### Description

Function to calculate the confidence interval for the population coefficient of variation using the noncentral `t`-distribution.

### Usage

``````ci.cv(cv=NULL, mean = NULL, sd = NULL, n = NULL, data = NULL,
conf.level = 0.95, alpha.lower = NULL, alpha.upper = NULL, ...)
``````

### Arguments

 `cv` coefficient of variation `mean` sample mean `sd` sample standard deviation (square root of the unbiased estimate of the variance) `n` sample size `data` vector of data for which the confidence interval for the coefficient of variation is to be calculated `conf.level` desired confidence level (1-Type I error rate) `alpha.lower` the proportion of values beyond the lower limit of the confidence interval (cannot be used with `conf.level`). `alpha.upper` the proportion of values beyond the upper limit of the confidence interval (cannot be used with `conf.level`). `...` allows one to potentially include parameter values for inner functions

### Details

Uses the noncentral t-distribution to calculate the confidence interval for the population coefficient of variation.

### Value

 `Lower.Limit.CofV` Lower confidence interval limit `Prob.Less.Lower` Proportion of the distribution beyond `Lower.Limit.CofV` `Upper.Limit.CofV` Upper confidence interval limit `Prob.Greater.Upper` Proportion of the distribution beyond `Upper.Limit.CofV` `C.of.V` Observed coefficient of variation

### Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

### References

Johnson, B. L., & Welch, B. L. (1940). Applications of the non-central t-distribution. Biometrika, 31, 362–389.

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.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1–24.

McKay, A. T. (1932). Distribution of the coefficient of variation and the extended t distribution, Journal of the Royal Statistical Society, 95, 695–698.

`cv`

### Examples

``````set.seed(113)
N <- 15
X <- rnorm(N, 5, 1)
mean.X <- mean(X)
sd.X <- var(X)^.5

ci.cv(mean=mean.X, sd=sd.X, n=N, alpha.lower=.025, alpha.upper=.025,
conf.level=NULL)
ci.cv(data=X, conf.level=.95)
ci.cv(cv=sd.X/mean.X, n=N, conf.level=.95)

``````

MBESS documentation built on Oct. 26, 2023, 9:07 a.m.