# R in Action (2nd ed): Chapter 10
# Power analysis
# requires packages pwr to be installed
# install.packages("pwr")
#---------------------------------------

par(ask=TRUE)

library(pwr)

# t tests
pwr.t.test(d=.8, sig.level=.05,power=.9, type="two.sample",  
           alternative="two.sided")
pwr.t.test(n=20, d=.5, sig.level=.01, type="two.sample", 
           alternative="two.sided")


# ANOVA
pwr.anova.test(k=5,f=.25,sig.level=.05,power=.8)

# Correlations
pwr.r.test(r=.25, sig.level=.05, power=.90, alternative="greater")

# Linear Models
pwr.f2.test(u=3, f2=0.0769, sig.level=0.05, power=0.90)

# Tests of proportions
pwr.2p.test(h=ES.h(.65, .6), sig.level=.05, power=.9, 
            alternative="greater")

# Chi-square tests
prob <- matrix(c(.42, .28, .03, .07, .10, .10), byrow=TRUE, nrow=3)
ES.w2(prob)
pwr.chisq.test(w=.1853, df=3 , sig.level=.05, power=.9)

# Sample sizes for detecting significant effects in a One-Way ANOVA
es <- seq(.1, .5, .01)
nes <- length(es)
samsize <- NULL
for (i in 1:nes){
     result <- pwr.anova.test(k=5, f=es[i], sig.level=.05, power=.9)
     samsize[i] <- ceiling(result$n)
}
plot(samsize,es,type="l", lwd=2, col="red", ylab="Effect Size", 
     xlab="Sample Size (per cell)", 
     main="One Way ANOVA with Power=.90 and Alpha=.05")

# Sample size curves for dtecting corelations of various sizes
library(pwr)        
r <- seq(.1,.5,.01)
nr <- length(r)
p <- seq(.4,.9,.1)
np <- length(p)
samsize <- array(numeric(nr*np), dim=c(nr,np))
for (i in 1:np){
     for (j in 1:nr){
          result <- pwr.r.test(n = NULL, r = r[j],
          sig.level = .05, power = p[i],
          alternative = "two.sided")
          samsize[j,i] <- ceiling(result$n)
  }
}
xrange <- range(r)
yrange <- round(range(samsize))
colors <- rainbow(length(p))
plot(xrange, yrange, type="n",
     xlab="Correlation Coefficient (r)",
     ylab="Sample Size (n)" )
for (i in 1:np){
     lines(r, samsize[,i], type="l", lwd=2, col=colors[i])
}
abline(v=0, h=seq(0, yrange[2], 50), lty=2, col="grey89")
abline(h=0, v=seq(xrange[1], xrange[2], .02), lty=2,
       col="grey89")
title("Sample Size Estimation for Correlation Studies\nSig=0.05 (Two-tailed)")
legend("topright", title="Power", as.character(p),
        fill=colors)