<font size="3"><span style="font-family: times new roman,times,serif;"> ---+++!! R Notes for Classes Some of R codes for classes are listed where [EMS] refers to [[http://www.blackwellpublishing.com/essentialmedstats][Essential Medical Statistics]]. %TOC% ---++++ [EMS] Chapter 3 Displaying the data *Shapes of frequency distributions* [[%ATTACHURL%/distributionShape.R][R code]]: ---++++ [EMS] Chapter 4 Means, standard deviations and standard errors * Underlying distribution is normal <verbatim> ## population mean and s.d. set.seed(20) mu <- 80 # the mean of population dbp sigma <- 10 # the s.d. of population dbp N <- 20000 Y <- rnorm(N, mean=mu, sd=sigma) ## distribution of population hist(Y, xlim=c(40, 120)) ## sampling from the population n <- 30 # the number of observation in each sample y.sam <- sample(Y, size=n, replace=FALSE) ## sample mean and s.d mean(Y) mean(y.sam) sd(Y) sd(y.sam) bin <- 10 ## comparison of distributions between population and one sample par(mfrow=c(1,2)) hist(Y, xlim=c(40, 120)) hist(y.sam, bin, xlim=c(40, 120)) ## sampling variation n <- 30 n.trial <- 100 # the number of trials sampling.var <- function(n, n.trial, sigma, mu, N){ Y <- rnorm(N, mean=mu, sd=sigma) sam.mean <- NULL for(i in 1:n.trial){ y.sam <- sample(Y, size=n, replace=FALSE) sam.mean <- c(sam.mean, mean(y.sam) ) } return(sam.mean) } sam.mean <- sampling.var(n = n, n.trial=n.trial, sigma=sigma, mu=mu, N=N) ## standard error y.sam <- sample(Y, size=n, replace=FALSE) s <- sd(y.sam) s/sqrt(n) sigma/sqrt(n) par(mfrow=c(1,1)) plot(50.5, mean(Y), xlab="", col=2, pch=15, cex=1.3, xlim=c(1,100), ylim=c(65, 95)) abline(h=mu, col=3, lty=2) points(1:n.trial, sam.mean) ## sampling distribution as function of n and sigma hist(sam.mean, bin, xlim=c(40, 120)) sam.mean.10.s10 <- sampling.var(n = 10, n.trial=n.trial, sigma=10, mu=mu, N=N) # n=10, sigma=10 sam.mean.30.s10 <- sampling.var(n = 30, n.trial=n.trial, sigma=10, mu=mu, N=N) # n=30, sigma=10 sam.mean.10.s20 <- sampling.var(n = 10, n.trial=n.trial, sigma=20, mu=mu, N=N) # n=10, sigma=20 sam.mean.30.s20<- sampling.var(n = 30, n.trial=n.trial, sigma=20, mu=mu, N=N) # n=30, sigma=20 par(mfrow=c(2,2)) hist(sam.mean.10.s10, bin, xlim=c(40, 120)) hist(sam.mean.30.s10, bin, xlim=c(40, 120)) hist(sam.mean.10.s20, bin, xlim=c(40, 120)) hist(sam.mean.30.s20, bin, xlim=c(40, 120)) </verbatim> * Underlying distribution is non-normal: [[%ATTACHURL%/samplingVariation.R][R code]]: ---++++ [EMS] Chapter 5 The normal distribution [[%ATTACHURL%/normalDistribution.R][R code for learning normal distributions and standard normal distributions]] ---++++ [EMS] Chapter 6 Confidence interval for a mean * Interpretation of confidence interval: * Confidence interval using _t_ distributions: * normal vs. _t_ distribution: ---++++ [EMS] Chapter 7 Comparison of two means: confidence intervals, hypothesis tests and p-values <verbatim> </verbatim>
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