Functional Size with Bootstrapped Confidence Intervals

This function is a master function, calling other functions it needs, and reporting results in some detail

Usage

func_size_report(lineup_vec, target_pos, k, R = 1000)

Arguments

lineup_vec: A numeric vector of lineup choices
target_pos: A scalar, representing target position in lineup. Must be declared by user
k: Number of members in lineup. Must be specified by user (scalar).
R: Number of bootstrap samples. Defaults to 1000

Value

Invisibly returns the functional-size estimate; the normal, percentile and BCa bootstrap intervals; the exact interval; the number of replications; the number of replications in which nobody chose the target (n_infinite); and the bootstrap object, whose statistic is the proportion choosing the target.

Details

Functional size is the reciprocal of the proportion of mock witnesses choosing the target, p. The bootstrap resamples p, which stays finite when a resample contains no target choices, and the interval limits for p are inverted. Percentile and BCa intervals respect monotone transformations, so they are the intervals for functional size itself, computed from the whole bootstrap distribution; a lower limit of 0 for p gives an unbounded (Inf) upper limit. The normal interval is the normal-theory interval for p, inverted. The exact interval inverts the Clopper-Pearson interval for p (binom.test). Near zero or one, empirical bootstrap intervals can have severe undercoverage, including a degenerate interval when the suspect was never chosen. Prefer the exact interval in these cases; retaining infinite limits alone does not guarantee nominal bootstrap coverage.

Function depends on functions from package 'boot'

References

Davison, A.C. & Hinkley, D.V. (1997). Bootstrap methods and their application. Cambridge University Press.

Tredoux, C. G. (1998). Statistical inference on measures of lineup fairness. Law and Human Behavior, 22(2), 217-237.

Tredoux, C. (1999). Statistical considerations when determining measures of lineup size and lineup bias. Applied Cognitive Psychology, 13, S9-S26.

Wells, G. L.,Leippe, M. R., & Ostrom, T. M. (1979). Guidelines for empirically assessing the fairness of a lineup. Law and Human Behavior, 3(4), 285-293.

Examples

#Data:
lineup_vec <- round(runif(100, 1, 6))
target_pos <- 3

#Call:
x <- func_size_report(lineup_vec, target_pos, 6)
#> Functional size of lineup is 5.556
#> Confidence intervals [95%]
#> Normal Theory 3.936 9.623 
#> Bootstrap: percentile (R = 1000) 3.846 9.091 
#> Bootstrap: bias-corrected (R = 1000) 4.021 10 
#> Exact (Clopper-Pearson) 3.711 9.065 
x <- func_size_report(lineup_vec, 3, 6)
#> Functional size of lineup is 5.556
#> Confidence intervals [95%]
#> Normal Theory 3.894 9.684 
#> Bootstrap: percentile (R = 1000) 3.846 9.091 
#> Bootstrap: bias-corrected (R = 1000) 4 10 
#> Exact (Clopper-Pearson) 3.711 9.065