#Optimal alpha ANOVA R code version 1.1, updated for compatibility with R version 3.x.
#Authored by Joe Mudge (questions or comments? contact: joe.mudge83@gmail.com).

optab.anova<-function (u=NULL,v=NULL,f2=NULL,T1T2cratio=1,HaHopratio=1){

beta.glm.test<-function (u = NULL, v = NULL, f2 = NULL, sig.level = 0.05, power = NULL){
if (!is.null(f2) && f2 < 0)
stop("f2 must be positive")
if (!is.null(u) && u < 1)
stop("degree of freedom u for numerator must be at least 1")
if (!is.null(v) && v < 1)
stop("degree of freedom v for denominator must be at least 1")
if (!is.null(sig.level) && !is.numeric(sig.level) || any(0 >
sig.level | sig.level > 1))
stop(sQuote("sig.level"), " must be numeric in [0, 1]")
p.body <- quote({
lambda <- f2 * (u + v + 1)
pf(qf(sig.level, u, v, lower = FALSE), u, v, lambda,lower = FALSE)
})
1-eval(p.body)
}

w.average.error.glm<-function (alpha=NULL,u=NULL,v=NULL,f2=NULL,T1T2cratio=1,HaHopratio=1)
((alpha*T1T2cratio+(HaHopratio*beta.glm.test(u=u,v=v,f2=f2,sig.level=alpha))))/(HaHopratio+T1T2cratio)

min.average.error.glm<-function (u=NULL,v=NULL,f2=NULL,T1T2cratio=1,HaHopratio=1)
unlist(optimize(w.average.error.glm,c(0,1),tol=0.00000000001,u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio))[2]

alpha.glm<-function (u=NULL,v=NULL,f2=NULL,T1T2cratio=1,HaHopratio=1)
unlist(optimize(w.average.error.glm,c(0,1),tol=0.000000000001,u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio))[1]

beta.glm<-function (u=NULL,v=NULL,f2=NULL,T1T2cratio=1,HaHopratio=1)
((T1T2cratio+HaHopratio)*min.average.error.glm(u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio)-T1T2cratio*alpha.glm(u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio))/HaHopratio

t(data.frame(
"numerator degrees of freedom"=u,
"denominator degrees of freedom"=v,
"among vs within group variance ratio effect size"=f2,
"Type I/II error cost ratio"=T1T2cratio,
"Ha/Ho prior probability ratio"=HaHopratio,
"overall probability of error"= (alpha.glm(u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio)+HaHopratio*beta.glm(u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio))/(1+HaHopratio),
"cost-weighted probability of error"= min.average.error.glm(u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio),
"optimal alpha"= alpha.glm(u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio),
"optimal beta"= beta.glm(u=u,v=v,f2=f2,T1T2cratio=T1T2cratio,HaHopratio=HaHopratio)
))
}

#The function used to calculate optimal alphas is: optab.anova(u=NULL,v=NULL,f2=NULL,T1T2cratio=1,HaHopratio=1)
#The arguments 'u' and 'v' are the numerator and denominator degrees of freedom, respectively.
#The argument 'f2' is the 'Cohen's f^2' standardized critical effect size. Cohen's f^2 = variance among group means/pooled within group variance
#The argument 'T1T2cratio' is the cost ratio of Type I errors relative to Type II errors. T1T2cratio is set at 1 as a default, making Type I and Type II errors equally serious.
#The argument 'HaHopratio' is the prior probability of the alternate hypothesis relative to the prior probability of the null hypothesis. HaHopratio is set at 1 as a default, to not weight alpha and beta by their prior probabilities (assuming they are unknown).
#This code is partially based on code modified from the R package 'pwr'(Champely 2009)