Bradley's (1978) empirical robustness interval

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

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?

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

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples

# interval criteria used for empirical detection rates
Bradley1978()
#> liberal.lower liberal.upper 
#>         0.025         0.075 
Bradley1978(type = 'stringent')
#> stringent.lower stringent.upper 
#>           0.045           0.055 
Bradley1978(alpha = .01, type = 'stringent')
#> stringent.lower stringent.upper 
#>           0.009           0.011 

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

Bradley1978(edr)
#>          test1          test2          test3          test4          test5 
#>       "robust"       "robust"       "robust"      "liberal" "conservative" 
Bradley1978(edr, out.logical=TRUE) # is robust?
#> test1 test2 test3 test4 test5 
#>  TRUE  TRUE  TRUE FALSE FALSE 

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

Bradley1978(CI = TRUE)
#> liberal.lower liberal.upper 
#>         0.925         0.975 
Bradley1978(CI = TRUE, type = 'stringent')
#> stringent.lower stringent.upper 
#>           0.945           0.955 
Bradley1978(CI = TRUE, alpha = .01, type = 'stringent')
#> stringent.lower stringent.upper 
#>           0.989           0.991 

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

Bradley1978(ecr, CI=TRUE)
#>          test1          test2          test3          test4          test5 
#>       "robust"       "robust"       "robust"      "liberal" "conservative" 
Bradley1978(ecr, CI=TRUE, out.logical=TRUE) # is robust?
#> test1 test2 test3 test4 test5 
#>  TRUE  TRUE  TRUE FALSE FALSE