Using R for Data Analysis and Graphics 1. Introduction
What is R? 1.1 What is R? R is a software environment for statistical computing. R is based on commands. Implements the S language. There is an inofficial menu based interface called R-Commander. Drawbacks of menus: difficult to store what you do. A script of commands documents the analysis and allows for easy repetition with changed data, options,... R is free software. http://www.r-project.org Supported operating systems: Linux, Mac OS X, Windows Language for exchanging statistical methods among researchers
Other Statistical Software 1.2 Other Statistical Software S-Plus: same programming language, commercial. Features a GUI. SPSS: good for standard procedures. SAS: all-rounder, good for large data sets, complicated analyses. Systat: Analysis of Variance, easy-to-use graphics system. Excel: Very limited collection of statistical methods. Good for getting the dataset ready. Matlab: Mathematical methods. Statistical methods limited. Similar paradigm, less flexible structure.
Introductory examples 1.3 Introductory examples A dataset that we have stored before in the system is called d.sport weit kugel hoch disc stab speer punkte OBRIEN 7.57 15.66 207 48.78 500 66.90 8824 BUSEMANN 8.07 13.60 204 45.04 480 66.86 8706 DVORAK 7.60 15.82 198 46.28 470 70.16 8664 : : : : : : : : : : : : : : : : : : : : : : : : CHMARA 7.75 14.51 210 42.60 490 54.84 8249 Draw a histogram of the results of variable kugel! We type hist(d.sport[,"kugel"]) The graphics window is opened automatically. We have called the S-function hist with argument d.sport[,"kugel"]. [,] is used to select the column.
Introductory examples 1.3 Introductory examples Scatter plot: type plot(d.sport[,"kugel"], d.sport[,"speer"]) First argument: x coordinates; second: y coordinates Many optional arguments! plot(d.sport[,"kugel"], d.sport[,"speer"], xlab="ball push", ylab="javelin", pch=7) Scatter plot matrix pairs(d.sport) Every column of d.sport is plotted against all other columns.
Introductory examples 1.3 Introductory examples Get a dataset from a text file and assign it to a name: d.sport <- read.table(...) "http://stat.ethz.ch/teaching/datasets /WBL/sport.dat", header=true) Start browser of operating system to get a file: d.sport <- read.table(file...())
Using R 1.4 Using R Within a window running R, you will see the prompt >. You type a command and get a result and a new prompt. > hist(d.sport[,"kugel"]) > An incomplete statement can be continued on the next line > plot(d.sport[,"kugel"], + d.sport[,"speer"]) R stores objects in your workspace > d.sport <- read.table(...) Objects have names like a, fun, d.sport R provides a huge number of functions and other objects
Using R 1.4 Using R An R statement consists of a name of an object object is displayed > d.sport a call to a function graphical or numerical result > hist(d.sport[,"kugel"]) an assignment > a <- 2*pi/360 > mn <- mean(d.sport[,"kugel"]) stores the mean of d.sport[,"kugel"] under the name mn
Using R 1.4 Using R Some special and useful functions (more details later): documentation on the arguments etc. of a function (or dataset provided by the system): > help(hist) or?hist list all objects (names) in the workspace: > objects() leave the R session: > q() You get the question: Save workspace image? [y/n/c]: If you answer y, your objects will be available for your next session.
Scripts and Editors 1.5 Scripts and Editors Instead of typing commands into the R window, you can generate commands by an editor and then send them to the R window.... and later modify (correct) them and send again. Text Editors supporting R WinEdt: Emacs: ESS: Tinn-R: http://www.winedt.com/ http://www.gnu.org/software/emacs/ http://stat.ethz.ch/ess/ http://www.sciviews.org/tinn-r/
Scripts and Editors 1.5 Scripts and Editors The Tinn-R Window
Scripts and Editors 1.5 Scripts and Editors Define Tinn-R Keyboard Shortcuts: Use dialog R / Hotkeys of R
Using R for Data Analysis and Graphics 2. Basics
Vectors 2.1 Vectors Functions and operations are usually applied to whole collections instead of single numbers, including vectors, matrices, data.frames ( d.sport ) Numbers can be combined into vectors using the function c() ( combine ) > t.v <- c(4,2,7,8,2) > t.a <- c(3.1, 5, -0.7, 0.9, 1.7) > t.u <- c(t.v,t.a) > t.u
Vectors 2.1 Vectors Generate a sequence of consecutive integers: > seq(1, 9) [1] 1 2 3 4 5 6 7 8 9 Since sequences of integers are needed very often, this can be abbreviated to 1:9. Equally spaced numbers: Use argument by (default: 1) > seq(0, 3, by=0.5) [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Repetition: > rep(0.7, 5) [1] 0.7 0.7 0.7 0.7 0.7 > rep(c(1, 3, 5), length=8) [1] 1 3 5 1 3 5 1 3
Vectors 2.1 Vectors Basic functions for vectors: Call, Example length(t.v) sum(t.v) mean(t.v) var(t.v) range(t.v) Description Length of a vector, number of elements Sum of all elements arithmetic mean empirical variance range
Arithmetic 2.2 Arithmetic Simple arithmetic is as expected: > 2+5 [1] 7 Operations: + - * / ˆ (Exponentiation) These operations are applied to vectors elementwise. > (2:5) ˆ c(2,3,1,0) [1] 4 27 4 1 Priorities as usual. Use parentheses! > (2:5) ˆ 2 [1] 4 9 16 25
Arithmetic 2.2 Arithmetic Elements are recycled: > (1:6)*(1:2) [1] 1 4 3 8 5 12 > (1:5)-(0:1) [1] 1 1 3 3 5 Warning message: longer object length is not a multiple of shorter object length in: (1:5) - (0:1) > (1:6)-(0:1) [1] 1 1 3 3 5 5 Be careful, there is no warning in this case!
Character Vectors 2.3 Character Vectors Character strings: "abc", nut 999 Combine strings into vector of mode character: > t.names <- c("urs", "Anna", "Max", "Pia") Length of strings: > nchar(t.names) [1] 3 4 3 5 String manipulations: > substring(t.names,3,4) [1] "s" "na" "x" "ud" > paste(t.names,"z.") [1] "Urs Z." "Anna Z." "Max Z." "Pia Z." > paste("x",1:3, sep="") [1] "X1" "X2" "X3"
Logical Vectors 2.4 Logical Vectors Logical vectors contain elements TRUE or FALSE > rep(c(true, FALSE), length=6) [1] TRUE FALSE TRUE FALSE TRUE FALSE often result from comparisons: < <= > >= ==!= > (1:5)>=3 [1] FALSE FALSE TRUE TRUE TRUE Logical operations: & (and), (or),! (not). > t.i <- (t.a>2)&(t.a<5) > t.i [1] TRUE FALSE FALSE FALSE FALSE
Selecting elements 2.5 Selecting elements Select elements from vectors or data.frames: [ ], [,] > t.v[c(1,3,5)] [1] 15.66 15.82 16.32 > d.sport[c(1,3,5),1:3] weit kugel hoch OBRIEN 7.57 15.66 207 DVORAK 7.60 15.82 198 HAMALAINEN 7.48 16.32 198 For data.frames, use names of columns or rows: > d.sport[c("obrien","dvorak"), c("kugel","speer","punkte")] kugel speer punkte OBRIEN 15.66 66.90 8824 DVORAK 15.82 70.16 8664
Selecting elements 2.5 Selecting elements Using logical vectors: > t.a[c(true,false,true,true,false,false)] [1] 3.1-0.7 0.9 > d.sport[d.sport[,"kugel"] > 16, c(2,7)] kugel punkte HAMALAINEN 16.32 8613 PENALVER 16.91 8307 SMITH 16.97 8271
Matrices 2.6 Matrices Matrices are data tables like data.frames, but they can only contain data of a single type (numeric or character) Generate a matrix: > t.m1 <- matrix(1:10, nrow=2, ncol=5) > t.m1 [,1] [,2] [,3] [,4] [,5] [1,] 1 3 5 7 9 [2,] 2 4 6 8 10 > t.m2 <- matrix(1:10, ncol=2, + byrow=true) Transpose: t(t.m1) equals t.m2.
Matrices 2.6 Matrices Selection of elements as with data.frames: > t.m1[2,1:3] [1] 2 4 6 Matrix multiplication: > t.m1 %*% t.m2 [,1] [,2] [1,] 95 220 [2,] 110 260 Vectors are treated as 1-row or 1-column matrices (mostly) Functions for linear algebra are available.
Using R for Data Analysis and Graphics 3. Simple Statistics
Simple Statistical Functions 3.1 Simple Statistical Functions Count number of cases with same value: > table(d.blast[,"loc"]) L1 L2 L3 L4 L5 L6 14 10 14 10 24 24 Cross-table > table(d.blast[,"loc"], + d.blast[,"loading"]) 2.08 2.18 2.5 2.6 3.12 3.33 3.64 L1 2 2 1 5 1 2 1 L2 2 0 0 4 3 1 0...
Simple Statistical Functions 3.1 Simple Statistical Functions Estimation of a location parameter : mean(x) median(x) Variance: var(x) ; correlation: > cor(d.sport[,"kugel"], d.sport[,"speer"]) Correlation matrix: > t.cor <- cor(d.sport[,1:3]) > round(100*t.cor) weit kugel hoch weit 100-63 34 kugel -63 100-9 hoch 34-9 100
Hypothesis Tests 3.2 Hypothesis Tests Do two groups differ in their location? Wilcoxon s Rank Sum Test > t.y1 <- sleep[sleep[, group ]==1, extra ] > t.y2 <- sleep[sleep[, group ]==2, extra ] > wilcox.test(t.y1, t.y2, paired=false) Wilcoxon rank sum test with continuity correction data: t.y1 and t.y2 W = 25.5, p-value = 0.06933 alternative hyp.: true location shift not equal to 0
Hypothesis Tests 3.2 Hypothesis Tests More well-known: t-test. Assumes normal distributions. > t.test(t.y2,t.y1,alternative="two.sided", + paired=f) Welch Two Sample t-test data: t.y1 and t.y2 t = -1.8608, df = 17.776, p-value = 0.0794 alternative hyp.: true diff. in means not equal to 0 95 percent confidence interval: -3.365 0.205 sample estimates: mean of x mean of y 0.75 2.33 Confidence interval!
Two Groups 3.3 Two Groups Plots for two samples of data. > boxplot(t.y1,t.y2,ylab="extra") > plot(sleep[,"group"],sleep[,"extra"], + xlab="group", ylab="extra")
Statistical Models, Formula Objects 3.4 Statistical Models, Formula Objects Statistics is concerned with relations between variables. Prototype: Relationship between target variable Y and explanatory variables X1, X2,... Regression. Symbolic notation of such a relation: Y X1 + X2 This symbolic notation is an S object (of class formula ) (The notation is also used in other statistical packages.) Use of formula : > plot(punkte kugel + speer, + data = d.sport) gives 2 scatterplots, punkte (vertical) against kugel and speer, respectively (horizontal axis).
Statistical Models, Formula Objects 3.4 Statistical Models, Formula Objects Grouping or nominal or categorical variables, e.g., location, type, group, species, plot,... Role in models different from continuous variables S must know! stores them as factor s Character variables enter data.frame as factor s Grouping var. with numerical labels can be declared as factor > sleep[, group ] <- + factor(sleep[, group ]) > plot(extra group, data = sleep) produces two box plots.