Sample Size Planning for the Coefficient of Variation Given the Goal of Accuracy in Parameter Estimation Approach to Sample Size Planning

Determines the necessary sample size so that the expected confidence interval width for the coefficient of variation will be sufficiently narrow, optionally with a desired degree of certainty that the interval will not be wider than desired. The population coefficient of variation may be given directly as C_of_V or through mu and sigma, in which case C_of_V is taken as sigma / mu. The value of C_of_V should be positive.

Usage

ss_aipe_cv(
  C_of_V = NULL,
  width = NULL,
  conf_level = 0.95,
  assurance = NULL,
  mu = NULL,
  sigma = NULL,
  alpha_lower = NULL,
  alpha_upper = NULL,
  ...
)

Arguments

C_of_V: Population coefficient of variation on which the sample size procedure is based
width: Desired (full) width of the confidence interval
conf_level: Confidence interval coverage; 1-Type I error rate
assurance: Value with which confidence can be placed that describes the likelihood of obtaining a confidence interval less than the value specified (e.g., .80, .90, .95)
mu: Population mean (specified with sigma when C_of_V is not specified)
sigma: Population standard deviation (specified with mu when C_of_V is not specified)
alpha_lower: Type I error for the lower confidence limit
alpha_upper: Type I error for the upper confidence limit
...: For modifying parameters of functions this function calls

Value

Returns the necessary sample size given the input specifications.

References

Chattopadhyay, B., & Kelley, K. (2016). Estimation of the coefficient of variation with minimum risk: A sequential method for minimizing sampling error and study cost. Multivariate Behavioral Research, 51(5), 627–648. doi:10.1080/00273171.2016.1203279

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

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 3.)

Author

Ken Kelley kkelley@nd.edu

Examples

# Suppose one wishes to have a confidence interval with an expected width of .10
# for a 99% confidence interval when the population coefficient of variation is .10.
ss_aipe_cv(C_of_V = .1, width = .1, conf_level = .99)
#> Warning: During the iterative sample size search, the noncentrality parameter exceeded 37.62 in magnitude (the limit of R's noncentral t accuracy) in 6 intermediate evaluations. The returned sample size accounts for this; see ?conf_limits_nct.
#>  term        value
#>  necessary_N 20   
#> 
#> Confidence level: 99%

# The same planning problem parameterized by the population mean and standard
# deviation: mu = 10 and sigma = 1 imply the same coefficient of variation, .10.
ss_aipe_cv(mu = 10, sigma = 1, width = .1, conf_level = .99)
#> Warning: During the iterative sample size search, the noncentrality parameter exceeded 37.62 in magnitude (the limit of R's noncentral t accuracy) in 6 intermediate evaluations. The returned sample size accounts for this; see ?conf_limits_nct.
#>  term        value
#>  necessary_N 20   
#> 
#> Confidence level: 99%

# Ensuring that the confidence interval will be sufficiently narrow with a 99\%
# certainty for the situation above.
ss_aipe_cv(C_of_V = .1, width = .1, conf_level = .99, assurance = .99)
#> Warning: During the iterative sample size search, the noncentrality parameter exceeded 37.62 in magnitude (the limit of R's noncentral t accuracy) in 6 intermediate evaluations. The returned sample size accounts for this; see ?conf_limits_nct.
#> Warning: During the iterative sample size search, the noncentrality parameter exceeded 37.62 in magnitude (the limit of R's noncentral t accuracy) in 6 intermediate evaluations. The returned sample size accounts for this; see ?conf_limits_nct.
#>  term        value
#>  necessary_N 33   
#> 
#> Confidence level: 99%