Differences

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--- sampling [2017/03/22 09:16] – [Probability sampling] hkimscil
+++ sampling [2018/03/13 16:48] – [Sample statistics] hkimscil
@@ Line 62: / Line 62: @@
 {{IQRandomSample02.jpg}}
 caption="n=2 4 16 25 100 400 900 1600 일때의 샘플평균들의 분포 (distribution of sampling means)"
+<code>rm(list=ls())
+var_ <- new.env()
+n<-20            ## Sample n individuals at a time
+p_mean<-0        ## Population mean
+p_sd<-1            ## Population standard deviation
+N<-500            ## Number of times the experiment (sampling) is replicated
+pdf('SE.pdf')
+for(i in 1:N)                                ## do the experiment N times
+{
+smp<-rnorm(n,p_mean,p_sd)                 ## sample n data points from the population
+var_$x_bar<-c(var_$x_bar,mean(smp))         ## keep track of the mean (x_bar) from each sample
+hist(var_$x_bar,probability=TRUE,col="red",xlim=c(-4,4),xlab="x / x_bar",main="",ylim=c(0,2.2))  # Plot a histogram of x_bar values
+points(mean(smp),0,pch=19,cex=1.5,col='black')
+curve(dnorm(x,p_mean,p_sd/sqrt(n)),lwd=3,add=TRUE)
+text(2.5,1.75,labels=paste('sd/sqrt(n) = ',round(p_sd/sqrt(n),2),sep=''))
+text(2.5,1.5,labels=paste('standard deviation of\nsample means = ',round(sd(var_$x_bar),2),sep='') )
+curve(dnorm(x,p_mean,p_sd),main="",ylab="",xlim=c(-4,4),xlab="X",col="blue",lwd=3,add=TRUE) ## Plot the sample
+text(2.5,0.5,labels=paste('# of means drawn = ',i,sep=''))
+text(2.5,0.35,labels=paste('Sample size (n) = ',n,sep=''))
+points(smp,rep(0,n),pch=19,cex=1.5,col='purple')
+abline(v= mean(smp),col='purple',lwd=4)
+legend("topleft",legend=c('Sample points','Population Distribution','Sample mean','Theoretical SE','Empirical SE'),
+lty=c(0,1,1,1,1,1,1),lwd=c(0,3,3,3,3,3,3),pch=c(16,NA,NA,NA,NA,NA,NA),col=c('purple','blue','purple','black','red'))
+print(paste(i," of ",N))
+}
+dev.off()
+</code>