Bradley1978 {SimDesign}

Bradley's (1978) empirical robustness interval

Description

Robustness interval criteria for empirical detection rate estimates and empirical coverage estimates defined by Bradley (1978). See EDR and ECR to obtain such estimates.

Usage

Bradley1978(
  rate,
  alpha = 0.05,
  type = "liberal",
  CI = FALSE,
  out.logical = FALSE,
  out.labels = c("conservative", "robust", "liberal"),
  unname = FALSE
)

Arguments

rate

(optional) numeric vector containing the empirical detection rate(s) or empirical confidence interval estimates. If supplied a character vector with elements defined in out.labels or a logical vector will be returned indicating whether the detection rate estimate is considered 'robust'.

When the input is an empirical coverage rate the argument CI must be set to TRUE.

If this input is missing, the interval criteria will be printed to the console

alpha

Type I error rate to evaluated (default is .05)

type

character vector indicating the type of interval classification to use. Default is 'liberal', however can be 'stringent' to use Bradley's more stringent robustness criteria

CI

logical; should this robust interval be constructed on empirical detection rates (FALSE) or empirical coverage rates (TRUE)?

out.logical

logical; should the output vector be TRUE/FALSE indicating whether the supplied empirical detection rate/CI should be considered "robust"? Default is FALSE, in which case the out.labels elements are used instead

out.labels

character vector of length three indicating the classification labels according to the desired robustness interval

unname

logical; apply unname to the results to remove any variable names?

Author(s)

Phil Chalmers [e-mail]

References

Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.

Chalmers, R. P., & Adkins, M. C. (2020). Writing Effective and Reliable Monte Carlo Simulations with the SimDesign Package. The Quantitative Methods for Psychology, 16(4), 248-280. doi:10.20982/tqmp.16.4.p248

Sigal, M. J., & Chalmers, R. P. (2016). Play it again: Teaching statistics with Monte Carlo simulation. Journal of Statistics Education, 24(3), 136-156. doi:10.1080/10691898.2016.1246953

See Also

EDR, ECR, Serlin2000

Examples

# interval criteria used for empirical detection rates
Bradley1978()
Bradley1978(type = 'stringent')
Bradley1978(alpha = .01, type = 'stringent')

# intervals applied to empirical detection rate estimates
edr <- c(test1 = .05, test2 = .027, test3 = .051, test4 = .076, test5 = .024)

Bradley1978(edr)
Bradley1978(edr, out.logical=TRUE) # is robust?

#####
# interval criteria used for coverage estimates

Bradley1978(CI = TRUE)
Bradley1978(CI = TRUE, type = 'stringent')
Bradley1978(CI = TRUE, alpha = .01, type = 'stringent')

# intervals applied to empirical coverage rate estimates
ecr <- c(test1 = .950, test2 = .973, test3 = .949, test4 = .924, test5 = .976)

Bradley1978(ecr, CI=TRUE)
Bradley1978(ecr, CI=TRUE, out.logical=TRUE) # is robust?