Using R. Liang Peng Georgia Institute of Technology January 2005

Transcription

1 Using R Liang Peng Georgia Institute of Technology January 2005

2 1. Introduction Quote from R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R. R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering,...) and graphical techniques, and is highly extensible. The S language is often the vehicle of choice for research in statistical methodology, and R provides an Open Source route to participation in that activity. One of R s strengths is the ease with which well-designed publicationquality plots can be produced, including mathematical symbols and formulae where needed. Great care has been taken over the defaults for the minor design choices in graphics, but the user retains full control.

3 R is available as Free Software under the terms of the Free Software Foundation s GNU General Public License in source code form. It compiles and runs on a wide variety of UNIX platforms and similar systems (including FreeBSD and Linux), Windows and MacOS. 2. Installing R under Windows Go to click Windows (95 and later), click base, click rw2100.exe, and then save it to disk. Just double-click the file rw2100.exe at the directory where you just saved, and follow the instructions. 3. Starting R Creat a shortcut icon, R, on the desktop. Right click this icon and select Properties. In Start in, type D : \ 3770Spring05 as a working directory for this course. Now simply double-click the R icon to start R. After starting R, click Packages at the top and install or update packages. 4. Objects Generating random vectors: rnorm(10,mean=1, sd=2); runif(10); rchisq(10, df=2); rt(10, df=2); rcauchy(10)

4 Some elementary graphics functions: 1) plot(x,y,type= l,lty=1,xlim,ylim,,xlab,ylab,main); 2) Adding things to a plot. points(x,y) #add points lines(x,y) #add lines text(x,y,labels) #point labels 3) Lines of various kinds. abline(a,b) # int. a, slope b abline(h=c) #horizontal at c abline(v=c) # vertical at c 4) Diagnostic plot. qqnorm(y) #normal scores 5) Miscellaneous. hist(x) #histograms barchart(f) #histogram-like dotchart(x,labels) pie(f) Standard & Poor stock index: x=read.table( spidata.txt,sep=, ) # input data from file spidata.txt x # look data

5 dim(x) # dimension x[,1] # first column (daily return of stock price) x[,2] # second column (daily volume) length(x[,1]) plot(x[,1]) plot(x[,2]) plot(x[,1],x[,2],type= l, lty=1, xlab= daily return, ylab= daily volume, main= Comparison ) hist(x[,1]) hist(x[,1],probability=true) qqnorm(x[,1]) qqline(x[,1]) sort(x[,1]) sort(x[,1],decreasing=true) order(x[,1]) abs(x[,1]) x[,1]*x[,2] x[,1]+x[,2] x[,1][5:10] min(x[,1])

6 max(x[,1]) summary(x[,1]) 5. Control, Loops and Functions 1) general forms: for(var in vector) statement while (condition) statement repeat statement 2) Define a function: fname=function(arg1, arg2,...) statement 6. Basic statistics Standard statistical procedures are in the package stats. For instance, the one sample t-test and corresponding confidence interval may be performed with the command t.test. Type in help( t.test ) to obtain the following information. Student s t-test Description: Performs one sample t-tests on vectors of data.

7 Usage: t.test(x,...) Arguments: x: a numeric vector of data values. alternative: a character string specifying the alternative hypothesis, must be one of two.sided (default), greater or less. You can specify just the initial letter. mu: a number indicating the true value of the mean. conf.level: confidence level of the interval. To complete the classical approach, we first need to determine a rejection region for the t-statistic. Recall that a critical value is in fact a quantile, and hence we may compute a critical value for the t-statistic by means of the command qt. help( TDist ) The Student t Distribution Description: Density, distribution function, quantile function and random generation for the t distribution with df degrees of freedom. Usage: dt(x, df) pt(q, df) qt(p, df) rt(n, df)

8 In Exercise 8.32 we are asked to do a two-sided test of the null hypothesis H 0 : µ = 100, using α = 0.05 [which corresponds to confidence level 95%]. First, we compute the critical value t 0.025, which corresponds to the quantile of the t-distribution with 12 1 = 11 degrees of freedom. qt(0975,df=11) [1] Hence, we now know that the rejection region is equal to {t : t }. Next, we compute the value taken by the test statistic. t.test(c1,mu=100,conf.level=0.95) Arguments: x, q: vector of quantiles. p: vector of probabilities. n: number of observations. If length(n) > 1, the length is taken to be the number required. df: degrees of freedom (> 0, maybe non-integer). Value: dt gives the density, pt gives the distribution function, qt gives the quantile function, and rt generates random deviates. 7. An example

9 This produces the following output One Sample t-test data: C1 t = , df = 11, p-value = alternative hypothesis: true mean is not equal to percent confidence interval: sample estimates: mean of x The test statistic takes the value , outside the rejection region. Hence, we do not reject: there is no evidence that the population mean reading µ is not equal to 100. Note that the output also contains the P -value, which is larger than the significance level Hence, it immediately follows that the null hypothesis is not rejected. In this way we could have avoided the computation of the critical value. Moreover, the output shows that the 95% confidence interval for µ contains 100. That is, H 0 : µ = 100 is not rejected.

10 8. Generating data Many of the exercises in Devore s book only involve summarized data, and accordingly the data sets only contain summarized data. For instance, if you open the SPSS-file with the data for Exercise 9.7, you may obtain the following output. library(foreign) ex09.07 = read.spss( d:/manual Install/Datasets/SPSS/Ch09/ex9-07.sav ) summary(ex09.07) Length Class Mode GENDER 2 -none- character SAMP LE S 2 -none- numeric SAMP LE M 2 -none- numeric SAMP LE 1 2 -none- numeric attach(ex09.07) data.frame(gender,samp LE S,SAMP LE M,SAMP LE 1 ) GENDER SAMP LE S SAMP LE M SAMP LE 1 1 Males Females The use of statistical software typically requires the original data. Thus, we

11 need original data with the sample sample means and sample standard deviation as reported in the summary. We may simulate the male data as follows: (i) generate 97 independent standard normal random variables; (ii) scale them, so as to obtain a random sample with mean 0 and standard deviation 1; (iii) multiply each value in the sample by 4.83 and add The output below shows that this approach works. males = 4.83*scale(rnorm(97)) mean(males) [1] 10.4 sd(males) [1] 4.83 In the same way, we may simulate the female data, and compare both samples by means of a two-sample t-test. females = 4.68*scale(rnorm(148))+9.26 t.test(males,females) Welch Two Sample t-test data: males and females t = 1.829, df = , p-value = alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:

12 sample estimates: mean of x mean of y