sample_sizing_anova: ANOVA Sample Sizing
In Bolshom/anovasize: A package to calculate sample sizes for ANOVA experiments

Description Usage Arguments Value Author(s) References Examples

This function calculates ANOVA sample sizes for three different situations, based on the book "Design and Analysis of Experiments".

1	sample_sizing_anova(method, means = 0, var = 0, diff = 0, a = 0, perc = 0, alpha, power)

`method`	method="With means" when you have the vector of means from each group, and want to find the sample size to reject the null hypotesis from ANOVA F test. method = "Max difference" when you intend to reject the null hypotesis when the difference between any two treatment means exceeds a certain value. method = "Percentage variance" to find the ANOVA sample sizes when you want to find a certain percentage variation on standard deviation or variance.
`means`	The vector of means from your groups.
`var`	The population variance or estimated from your analyzed factor.
`diff`	The max difference between two treatment means, to reject the null hypotesis.
`a`	Number of groups on your experiment.
`perc`	The percentage (p.e. 20 for 20 percent) of variation on your S.D. or Variance.
`alpha`	The level of significance of your analysis.
`power`	The probability that you want to detect the phenomenon.

`n`	The function returns the sample size for each group to guarantee at least the power percentage.

Natan Freitas Leite

"Design and Analysis of Experiments" - Douglas C. Montgomery

## The function is currently defined as
function (method, means = 0, var = 0, diff = 0, a = 0, perc = 0,
    alpha, power)
{
    if (method == "With means") {
        ss_mean_vec = function(means, var, alpha, power) {
            n = 2:10000
            overall_mean = mean(means)
            tau = means - overall_mean
            a = length(means)
            fi2_n = n * sum(tau^2)/(a * var)
            power_vector = 1 - pf(qf(1 - alpha, a - 1, a * (n -
                1)), a - 1, a * (n - 1), a * fi2_n)
            n = n[min(which(power_vector > power))]
            return(n)
        }
        return(ss_mean_vec(means, var, alpha, power))
    }
    if (method == "Max difference") {
        ss_diff = function(diff, a, var, alpha, power) {
            n = 2:10000
            fi2_n = n * diff^2/(2 * a * var)
            power_vector = 1 - pf(qf(1 - alpha, a - 1, a * (n -
                1)), a - 1, a * (n - 1), a * fi2_n)
            n = n[min(which(power_vector > power))]
            return(n)
        }
        return(ss_diff(diff, a, var, alpha, power))
    }
    if (method == "Percentage variance") {
        ss_sd_diff = function(perc, a, alpha, power) {
            n = 2:10000
            fi2_n = (sqrt((1 + 0.01 * perc)^2 - 1) * sqrt(n))^2
            power_vector = 1 - pf(qf(1 - alpha, a - 1, a * (n -
                1)), a - 1, a * (n - 1), a * fi2_n)
            n = n[min(which(power_vector > power))]
            return(n)
        }
        return(ss_sd_diff(perc, a, alpha, power))
    }
  }

##On the example 3-14 on the book, there are 5 observations
##from three different batteries brands. The phenomenon studied are the
##weeks of life from those batteries.

data=data.frame("weeks"=c(100,96,92,96,92,76,80,75,84,82,108,100,96,98,100)
,"brand"=c(rep("1",5),rep("2",5),rep("3",5)))

##Sample sizing from group means:
means_vector=mean(plyr::ddply(data,"brand",summarise,mean=mean(weeks))[,2])

est_var=mean(plyr::ddply(data,"brand",summarise,var=var(weeks))[,2])

ss=sample_sizing_anova("With means",means=means_vector,var=est_var,alpha=.05,power=.9)

ss

##Sample sizing from max difference between means:
est_var=mean(plyr::ddply(data,"brand",summarise,var=var(weeks))[,2])

##The max difference is 10, so diff=10:
ss=sample_sizing_anova("Max difference",diff=10,a=3,var=est_var,alpha=.05,power=.9)


ss

##Sample sizing from percentage increase in variance or standard deviation:
##If we want to find the sample size for a 25 percentage variation, we input "perc=25":
ss=sample_sizing_anova("Percentage variance",perc=25,a=3,alpha=.05,power=.9)

ss