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```
# PValRule function is a secondary function which generates decision rules for the Bonferroni, Holm,
# Hommel, Hochberg, fixed-sequence and fallback procedures in hypothesis testing problems with
# equally weighted null hypotheses
pvalrule<-function(rawp,alpha,proc)
# RAWP, Vector of raw p-values
# ALPHA, Familywise error rate
# PROC, Procedure name
{
# Number of p-values
m<-length(rawp)
cat("Hypothesis testing problem\n\n")
cat("Familywise error rate: alpha=",alpha,"\n",sep="")
# List of original null hypotheses and raw p-values
cat("Original null hypotheses: ",sep="")
for (i in 1:m) cat("H",i," ",sep="")
cat("(equally weighted)\n")
cat("Original raw p-values: ")
for (i in 1:m) cat("p",i,"=",round(rawp[i],4)," ",sep="")
cat("\n")
# List of ordered null hypotheses and raw p-values
o<-order(rawp)
orderp<-rawp[o]
cat("Ordered null hypotheses: ",sep="")
for (i in 1:m) cat("H(",i,") ",sep="")
cat("\n")
cat("Ordered raw p-values: ")
for (i in 1:m) cat("p(",i,")=",round(orderp[i],4)," ",sep="")
cat("\n\n")
# Print decision rules for each specified procedure
proc.to.print <- proc
for(p in proc.to.print) {
# Bonferroni procedure (parameters needed: m, rawp, alpha)
if (p=="Bonferroni")
{
cat("\n\n")
cat("Decision rules for the Bonferroni procedure:\n\n",sep="")
for (i in 1:m)
{
cat("Original null hypothesis H",i,sep="")
level<-alpha/m
if (rawp[i]<=level) cat(" is rejected since p",i,"<=alpha/",m,"=",round(level,4),"\n\n",sep="")
else cat(" is accepted since p",i,">alpha/",m,"=",round(level,4),"\n\n",sep="")
}
}
# Fixed-sequence procedure
if (p=="Fixed-sequence")
{
cat("\n\n")
cat("Decision rules for the fixed-sequence procedure:\n\n",sep="")
for (i in 1:m)
{
cat("Step ",i,"\n",sep="")
cat("Original null hypothesis H",i,sep="")
if (i==1)
{
# Current null hypothesis is rejected
if (rawp[1]<=alpha)
{
current<-1
cat(" is rejected since p1<=alpha=",round(alpha,4),"\n\n",sep="")
}
# Current null hypothesis is accepted
if (rawp[1]>alpha)
{
current<-0
cat(" is accepted since p1>alpha=",round(alpha,4),"\n\n",sep="")
}
}
if (i>1)
{
# Preceding null hypothesis
prec<-current
# Current null hypothesis is rejected
if (rawp[i]<=alpha & prec==1) current<-1
# Current null hypothesis is accepted
if (rawp[i]>alpha | prec==0) current<-0
if (rawp[i]<=alpha & prec==1) cat(" is rejected since p",i,"<=alpha=",round(alpha,4)," and the preceding original null hypothesis is rejected\n\n",sep="")
if (rawp[i]>alpha & prec==1) cat(" is accepted since p",i,">alpha=",round(alpha,4),"\n\n",sep="")
if (prec==0) cat(" is accepted since the preceding original null hypothesis is accepted\n\n",sep="")
}
}
}
# Fallback procedure
if (p=="Fallback")
{
cat("\n\n")
cat("Decision rules for the fallback procedure:\n\n",sep="")
numer<-1
for (i in 1:m)
{
cat("Step ",i,"\n",sep="")
cat("Original null hypothesis H",i,sep="")
level<-numer*alpha/m
if (i<m)
{
# Current null hypothesis is rejected
if (rawp[i]<=level)
{
cat(" is rejected since p",i,"<=",numer,"*alpha/",m,"=",round(level,4)," and the significance level used in this test is carried over to the next original null hypothesis\n\n",sep="")
numer<-numer+1
}
# Current null hypothesis is accepted
if (rawp[i]>level)
{
current<-0
cat(" is accepted since p",i,">",numer,"*alpha/",m,"=",round(level,4),"\n\n",sep="")
numer<-1
}
}
if (i==m)
{
if (rawp[i]<=level) cat(" is rejected since p",i,"<=",numer,"*alpha/",m,"=",round(level,4),"\n\n",sep="")
else cat(" is accepted since p",i,">",numer,"*alpha/",m,"=",round(level,4),"\n\n",sep="")
}
}
}
# Holm procedure (parameters needed: m, rawp, orderp, alpha)
if (p=="Holm")
{
cat("Decision rules for the Holm procedure:\n\n",sep="")
for (i in 1:m)
{
cat("Step ",i,"\n",sep="")
cat("Ordered null hypothesis H(",i,") [Original null hypothesis H",o[i],"]",sep="")
level<-alpha/(m-i+1)
if (i==1)
{
# Current null hypothesis is rejected
if (orderp[1]<=level) current<-1
# Current null hypothesis is accepted
if (orderp[1]>level) current<-0
if (orderp[1]<=level) cat(" is rejected since p(1)<=alpha/",m,"=",round(level,4),"\n\n",sep="")
else cat(" is accepted since p(1)>alpha/",m,"=",round(level,4),"\n\n",sep="")
}
if (i>1)
{
# Preceding null hypothesis
prec<-current
# Current null hypothesis is rejected
if (orderp[i]<=level & prec==1) current<-1
# Current null hypothesis is accepted
if (orderp[i]>level | prec==0) current<-0
if (orderp[i]<=level & prec==1) cat(" is rejected since p(",i,")<=alpha/",m-i+1,"=",round(level,4)," and the preceding ordered null hypothesis is rejected\n\n",sep="")
if (orderp[i]>level & prec==1) cat(" is accepted since p(",i,")>alpha/",m-i+1,"=",round(level,4),"\n\n",sep="")
if (prec==0) cat(" is accepted since the preceding ordered null hypothesis is accepted\n\n",sep="")
}
}
}
# Hochberg procedure (parameters needed: m, rawp, orderp, alpha)
if (p=="Hochberg")
{
cat("Decision rules for the Hochberg procedure:\n\n",sep="")
for (i in 1:m)
{
cat("Step ",i,"\n",sep="")
level<-alpha/i
if (i==1)
{
if (orderp[m]<=level)
{
cat("Ordered null hypothesis H(",m,") [Original null hypothesis H",o[m],"]",sep="")
cat(" is rejected since p(",m,")<=alpha/1=",round(level,4),"\n\n",sep="")
if (m>1)
{
for (j in (m-1):1)
{
cat("Ordered null hypothesis H(",j,") [Original null hypothesis H",o[j],"]",sep="")
cat(" is rejected since the preceding ordered null hypothesis is rejected\n\n",sep="")
}
}
break
}
if (orderp[m]>level)
{
cat("Ordered null hypothesis H(",m,") [Original null hypothesis H",o[m],"]",sep="")
cat(" is accepted since p(",m,")>alpha/1=",round(level,4),"\n\n",sep="")
}
}
if (i>1)
{
if (orderp[m-i+1]<=level)
{
cat("Ordered null hypothesis H(",m-i+1,") [Original null hypothesis H",o[m-i+1],"]",sep="")
cat(" is rejected since p(",m-i+1,")<=alpha/",i,"=",round(level,4),"\n\n",sep="")
if (m-i+1>1)
{
for (j in (m-i):1)
{
cat("Ordered null hypothesis H(",j,") [Original null hypothesis H",o[j],"]",sep="")
cat(" is rejected since the preceding ordered null hypothesis is rejected\n\n",sep="")
}
}
break
}
if (orderp[m-i+1]>level)
{
cat("Ordered null hypothesis H(",m-i+1,") [Original null hypothesis H",o[m-i+1],"] ",sep="")
cat("is accepted since p(",m-i+1,")>alpha/",i,"=",round(level,4),"\n\n",sep="")
}
}
}
}
# Hommel procedure (parameters needed: m, rawp, orderp, alpha)
if (p=="Hommel")
{
cat("Decision rules for the Hommel procedure:\n\n",sep="")
for (i in 1:m)
{
cat("Step ",i,"\n",sep="")
if (i==1)
{
if (orderp[m]<=alpha)
{
cat("Ordered null hypothesis H(",m,") [Original null hypothesis H",o[m],"]",sep="")
cat(" is rejected since p(",m,")<=alpha/1=",round(alpha,4),"\n\n",sep="")
if (m>1)
{
for (j in (m-1):1)
{
cat("Ordered null hypothesis H(",j,") [Original null hypothesis H",o[j],"]",sep="")
cat(" is rejected since the preceding ordered null hypothesis is rejected\n\n",sep="") }
}
break
}
if (orderp[m]>alpha)
{
cat("Ordered null hypothesis H(",m,") [Original null hypothesis H",o[m],"]",sep="")
cat(" is accepted since p(",m,")>alpha/1=",round(alpha,4),"\n\n",sep="")
}
}
if (i>1)
{
# All p-values are greater than corresponding significance levels
all<-1
hyprej<-0
jrej<-0
irej<-0
for (j in 1:i)
{
if (orderp[m-i+j]<=j*alpha/i)
{
if (hyprej==0)
{
all<-0
hyprej<-m-i+j
jrej<-j
irej<-i
}
}
}
if (all==1)
{
cat("Ordered null hypothesis H(",m-i+1,") [Original null hypothesis H",o[m-i+1],"] ",sep="")
cat("is accepted since",sep="")
for (j in 1:(i-1)) cat(" p(",m-i+j,")>",j,"*alpha/",i,"=",round(j*alpha/i,4)," and",sep="")
cat(" p(",m,")>alpha/1=",round(alpha,4),"\n\n",sep="")
}
if (all==0)
{
cat("p(",hyprej,")<=",jrej,"*alpha/",irej,"=",round(jrej*alpha/irej,4),sep="")
cat(" and thus all remaining hypotheses are tested with alpha/",i-1,"=",round(alpha/(i-1),4),": \n\n",sep="")
allsub<-1
for (j in (m-i+1):1)
{
cat("Ordered null hypothesis H(",j,") [Original null hypothesis H",o[j],"]",sep="")
if (orderp[j]<=alpha/(i-1))
{
if (allsub==1)
{
allsub<-0
cat(" is rejected since p(",j,")<=alpha/",i-1,"=",round(alpha/(i-1),4),"\n\n",sep="")
}
else cat(" is rejected since the preceding ordered null hypothesis is rejected\n\n",sep="")
}
if (orderp[j]>alpha/(i-1)) cat(" is accepted since p(",j,")>alpha/",i-1,"=",round(alpha/(i-1),4),"\n\n",sep="")
}
break
}
}
}
}
cat("\n\n")
}
}
# End of pvalrule
```

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