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sampling [2017/03/22 09:16] – [Probability sampling] hkimscil | sampling [2018/03/13 16:49] – [Sample statistics] hkimscil |
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{{IQRandomSample02.jpg}} | {{IQRandomSample02.jpg}} |
caption="n=2 4 16 25 100 400 900 1600 일때의 샘플평균들의 분포 (distribution of sampling means)" | 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> |
| {{SE.pdf}} |
| |
* Variation See, [[:Variance]]: 225.0584138 (15^2) | * Variation See, [[:Variance]]: 225.0584138 (15^2) |