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LeenaRNotes
(14 Jan 2007,
LeenaChoi
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<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 * [EMS] Example 4.4 on page 39 <verbatim> ## population mean and s.d. set.seed(20) mu <- 78.2 # the mean of population dbp sigma <- 9.4 # the s.d. of population dbp N <- 250 Y <- round(rnorm(N, mean=mu, sd=sigma), 2) Y[1:10] # 10 values of the population ## distribution of population hist(Y, xlim=c(40, 120)) ## sampling from the population n <- 10 # the number of observation in each sample y.sam <- sample(Y, size=n, replace=FALSE) y.sam # this is what you got ## sample mean and s.d mean(Y) mean(y.sam) sd(Y) sd(y.sam) ## comparison of distributions between population and one sample par(mfrow=c(1,2)) hist(Y, xlim=c(40, 120)) hist(y.sam, xlim=c(40, 120)) ## sampling variation 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) } n <- 10 n.trial <- 100 # the number of trials y.sam <- sample(Y, size=n, replace=FALSE) y.sam # observe what you got; try another sample set.seed(20) sam.mean <- sampling.var(n = n, n.trial=n.trial, sigma=sigma, mu=mu, N=N) ## standard error (s.e.) se <- sigma/sqrt(n) #theoretical s.e. se sd(sam.mean) y.sam <- sample(Y, size=n, replace=FALSE) # you only have one sample s <- sd(y.sam) s/sqrt(n) par(mfrow=c(1,1)) plot(50.5, mean(Y), xlab="Identification number of trial", ylab="Sample mean", 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) abline(h=mu+1.96*se, col=4, lty=3) abline(h=mu-1.96*se, col=4, lty=3) ## sampling distribution as function of n and sigma bin <- 10 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: [[%ATTACHURL%/CI.R][R code for Fig. 6.2]] * Confidence interval using _t_ distributions: * normal vs. _t_ distribution: <verbatim> mu.mean <- 0 mu <- seq(mu.mean-5, mu.mean+5, 0.001) sigma <- 1 t.plot <- function(df){ plot(mu, dnorm(mu, mu.mean, sigma), col=1, lty=2, ylim=c(0.002, 0.6), type="l", xlab="", ylab=" ", xaxs="i", yaxs="i", yaxt="n", bty="n") lines(mu, dt(mu, df=df), col=2, lty=1) text(2.2, .4, "normal distribution") text(3, .3, paste("t distribution with",df, "d.f."), col=2 ) } t.plot(df=5) # try another df </verbatim>
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Topic revision: r7 - 14 Jan 2007,
LeenaChoi
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