# Using power.anova.test to calculate power or sample size in the one-way ANOVA 

# Suppose r=4, alpha = 0.05, and the required power for the F-test is 0.80. 

# Suppose we wish to detect when the four treatment means differ by at least 10 (max - min = 10). 
# And we believe the standard deviation is 5. 

groupmeans <- c(10, 15, 15, 20)
power.anova.test(groups = length(groupmeans),
                 between.var=var(groupmeans),
                 within.var=5^2, sig.level= 0.05, power=.80)

# How does the power/sample size change if the treatment population means are more evenly spead out? 

groupmeans <- c(10, 13.3, 16.7, 20)
power.anova.test(groups = length(groupmeans),
                 between.var=var(groupmeans),
                 within.var=5^2, sig.level= 0.05, power=.80)

# We can also specify the sample size we have and determine the power of the F-test we will get. 

groupmeans <- c(10, 15, 15, 20)
power.anova.test(groups = length(groupmeans),
                 between.var=var(groupmeans),
                 within.var=5^2, sig.level= 0.05, n=10)


groupmeans <- c(10, 13.3, 16.7, 20)
power.anova.test(groups = length(groupmeans),
                 between.var=var(groupmeans),
                 within.var=5^2, sig.level= 0.05, n=10)

# We can see the relationship between power and sample size by plotting the power for a variety of sample sizes: 

n.vec <- seq(2,20,by=1)
my.power <- rep(0, times = length(n.vec))
groupmeans <- c(10, 15, 15, 20)
for (i in 1:length(n.vec)){
my.power[i]<-power.anova.test(groups = length(groupmeans),
                 between.var=var(groupmeans),
                 within.var=5^2, sig.level= 0.05, n=n.vec[i])$power
}

plot(n.vec, my.power, type='b',xlab='sample size per group', ylab='Power of F-test')