Computes the noncentral t-based confidence interval for the population coefficient of variation, the standard deviation relative to the mean, so variability can be reported on a scale that is free of the measurement units.
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
Value
A 4-row data.frame with columns term, value,
prob_less, and prob_greater. The rows are ordered so the two
point estimates sit between the confidence limits:
"lower_limit" (lower confidence limit on the coefficient of
variation), "c_of_v" (the sample coefficient of variation),
"c_of_v_unbiased" (the unbiased estimator), and
"upper_limit" (upper confidence limit). The prob_less
and prob_greater columns report the achieved tail probabilities
of the noncentral t search at the limit values; they are NA for
the point-estimate rows.
Details
Uses the noncentral t-distribution to calculate the confidence interval for the population coefficient of variation.
References
Johnson, N. L., & Welch, B. L. (1940). Applications of the non-central t-distribution. Biometrika, 31(3–4), 362–389. doi:10.1093/biomet/31.3-4.362
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:10.3758/BF03192966
Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24. doi:10.18637/jss.v020.i08
Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 3.)
McKay, A. T. (1932). Distribution of the coefficient of variation and the extended t distribution. Journal of the Royal Statistical Society, 95(4), 695–698.
See also
Other confidence intervals for effect sizes:
ci_R2(),
ci_c(),
ci_c_ancova(),
ci_c_ancova_bp(),
ci_correlation,
ci_eta_squared(),
ci_eta_squared_generalized(),
ci_eta_squared_partial(),
ci_mahalanobis(),
ci_omega_squared(),
ci_pvaf(),
ci_rc(),
ci_reg_coef(),
ci_rmsea(),
ci_sc(),
ci_sc_ancova(),
ci_sm(),
ci_smd(),
ci_smd_c(),
ci_snr(),
ci_src(),
ci_srsnr(),
contrast_adjusted(),
plot_smd()
Author
Ken Kelley kkelley@nd.edu
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)
#> term value prob_less prob_greater
#> lower_limit 0.15 0.025 0.975
#> c_of_v 0.207 <NA> <NA>
#> c_of_v_unbiased 0.21 <NA> <NA>
#> upper_limit 0.335 0.975 0.025
ci_cv(data = X, conf_level = .95)
#> term value prob_less prob_greater
#> lower_limit 0.15 0.025 0.975
#> c_of_v 0.207 <NA> <NA>
#> c_of_v_unbiased 0.21 <NA> <NA>
#> upper_limit 0.335 0.975 0.025
#>
#> Confidence level: 95%
ci_cv(cv = sd.X / mean.X, n = N, conf_level = .95)
#> term value prob_less prob_greater
#> lower_limit 0.15 0.025 0.975
#> c_of_v 0.207 <NA> <NA>
#> c_of_v_unbiased 0.21 <NA> <NA>
#> upper_limit 0.335 0.975 0.025
#>
#> Confidence level: 95%