How many samples do you need

Post-hoc power analysis

#### POST-HOC POWER ANALYSIS ####
## To obtain a power analysis, I need to look at the probability of obtaining a significant p-value (a<=0.05)
## What I could do is use bootstrapping to estimate the population mean and standard deviation (sd)
## Once I have the population mean and sd, I can then simulate 1000 trials, and look at the achieved 'power'
k=(length(unique(ARCdata$Tank)))
n=10000
popmean<-matrix(data=NA, nrow=n, ncol=k)
popsd<-matrix(data=NA, nrow=n, ncol=k)
for (i in 1:n){
ARCdatanew<-lapply(split(ARCdata, ARCdata$Tank),
                   function(subdf) 
                     subdf[sample(1:nrow(subdf), 35, replace=TRUE),]) # with replacement to follow bootstrapping rules
new<-do.call(rbind, lapply(ARCdatanew, data.frame, stringsAsFactors=FALSE))
popmean[i,]<-tapply(new$gain, new$Tank, mean, na.rm=TRUE)
popsd[i,]<-tapply(new$gain, new$Tank, sd, na.rm=TRUE)
}
# Obtain population mean and SD by tank
popmean<-as.data.frame(popmean)
popmean<-colMeans(popmean, na.rm=TRUE)
popsd<-as.data.frame(popsd)
popsd<-colMeans(popsd,na.rm=TRUE)
samplemean<-tapply(ARCdata$gain, ARCdata$Tank, mean, na.rm=TRUE)
samplesd<-tapply(ARCdata$gain, ARCdata$Tank, sd, na.rm=TRUE)
popmean<-as.array(popmean)
popsd<-as.array(popsd)
for (i in 1:12){
  rownames(popmean)[i]<-rownames(samplemean)[i]
  rownames(popsd)[i]<-rownames(samplesd)[i]
}
# Compare population mean and sd to sample mean and sd
popmean-(tapply(ARCdata$gain, ARCdata$Tank, mean, na.rm=TRUE)) # this is the bias for the mean by looking at the sample we had
popsd-(tapply(ARCdata$gain, ARCdata$Tank, sd, na.rm=TRUE)) # this is the bias for the sd by looking at the sample we had