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# Function: BonferroniAdj.CI
# Argument: p, Vector of p-values (1 x m)
# par, List of procedure parameters: vector of hypothesis weights (1 x m)
# Description: Bonferroni multiple testing procedure.
BonferroniAdj.CI = function(est, par) {
# Number of point estimate
m = length(est)
# Extract the vector of hypothesis weights (1 x m)
if (is.null(par[[2]]$weight)) w = rep(1/m, m)
else w = par[[2]]$weight
# Extract the sample size
if (is.null(par[[2]]$n)) stop("Bonferroni procedure: Sample size must be specified (n).")
n = par[[2]]$n
# Extract the standard deviation
if (is.null(par[[2]]$sd)) stop("Bonferroni procedure: Standard deviation must be specified (sd).")
sd = par[[2]]$sd
# Extract the simultaneous coverage probability
if (is.null(par[[2]]$covprob)) stop("Bonferroni procedure: Coverage probability must be specified (covprob).")
covprob = par[[2]]$covprob
# Error checks
if (length(w) != m) stop("Bonferroni procedure: Length of the weight vector must be equal to the number of hypotheses.")
if (m != length(est)) stop("Bonferroni procedure: Length of the point estimate vector must be equal to the number of hypotheses.")
if (m != length(sd)) stop("Bonferroni procedure: Length of the standard deviation vector must be equal to the number of hypotheses.")
if (sum(w)!=1) stop("Bonferroni procedure: Hypothesis weights must add up to 1.")
if (any(w < 0)) stop("Bonferroni procedure: Hypothesis weights must be greater than 0.")
if (covprob>=1 | covprob<=0) stop("Bonferroni procedure: simultaneous coverage probability must be >0 and <1")
# Standard errors
stderror = sd*sqrt(2/n)
# T-statistics associated with each test
stat = est/stderror
# Compute degrees of freedom
nu = 2*(n-1)
# Compute raw one-sided p-values
rawp = 1-stats::pt(stat,nu)
# Compute the adjusted p-values
adjustpval = BonferroniAdj(rawp, list("Analysis", list(weight = w)))
# Alpha
alpha = 1-covprob
# Lower simultaneous confidence limit
ci = est - stderror*stats::qnorm(1-(alpha*w))
return(ci)
}
# End of BonferroniAdj.CI
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