1. Example of multivariate data What is R? R is available as Free Software under the terms of the Free Software Foundation'sFree Software Foundation GNU General Public LicenseGNU 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. R can be extended (easily) via packages. There are about eight packages supplied with the R distribution and many more are available through the CRAN family of Internet sites covering a very wide range of modern statistics. R is a language and environment for statistical computing and graphics.

2. Example of multivariate data The R environment A fully planned and coherent system that includes: an effective data handling and storage facility, a suite of operators for calculations on arrays (matrices), a large, coherent, integrated collection of intermediate tools for data analysis, graphical facilities for data analysis and display (on-screen or on hardcopy), a well-developed, simple and effective programming languages which includes conditionals, loops, user-defined recursive functions and input and output facilities. http://www.r-project.org/Download R for free at:

3. Exam of multivariate data R Download

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11. Exam of multivariate data Install packages

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21. Essential commands in R

22. Example Vectors in R # Character vector: > c("Huey","Dewey","Louie") [1] "Huey" "Dewey" "Louie" # Logical vector: > c(T,T,F,T) [1] TRUE TRUE FALSE TRUE # Numeric vector: > c(2,3,5,7,9) [1] 2 3 5 7 9 #Functions that create vectors: c-“concatenate” seq-”sequence” rep-”replicate” > c(42,57,12,39) [1] 42 57 12 39 > seq(4,9) [1] 4 5 6 7 8 9 > rep(1:2,5) [1] 1 2 1 2 1 2 1 2 1 2 > rep(1:2,c(3,4)) [1] 1 1 1 2 2 2 2

23. Example Factors in R Factors – a data structure that makes it possible to assign meaningful names to the categories. > pain=c(0,3,2,2,1) > fpain=factor(pain,levels=0:3) > levels(fpain)=c("none","mild","medium","severe") > fpain [1] none severe medium medium mild Levels: none mild medium severe > levels(fpain) [1] "none" "mild" "medium" "severe"

24. Example Matrices and arrays > x=1:2 > x=1:12 > dim(x)=c(3,4) > x [,1] [,2] [,3] [,4] [1,] 1 4 7 10 [2,] 2 5 8 11 [3,] 3 6 9 12 > x=matrix(1:12,nrow=3,byrow=T) > rownames(x)=LETTERS[1:3] > x [,1] [,2] [,3] [,4] A 1 2 3 4 B 5 6 7 8 C 9 10 11 12 > t(x) A B C [1,] 1 5 9 [2,] 2 6 10 [3,] 3 7 11 [4,] 4 8 12 LETTERS- build in variable that contains the capital letters A-Z. t(x) – the transpose matrix of x.

25. Example Matrices and arrays > cbind(A=1:4,B=5:8,C=9:12) A B C [1,] 1 5 9 [2,] 2 6 10 [3,] 3 7 11 [4,] 4 8 12 > rbind(A=1:4,B=5:8,C=9:12) [,1] [,2] [,3] [,4] A 1 2 3 4 B 5 6 7 8 C 9 10 11 12 # Use the functions cbind and rbind to “bind” vectors together columnwise or rowwise.

26. Example Data frames Data frame – it is a list of vectors and/or factors of the same length, which are related “across”, such that data in the same position come from the same experimental unit (subject, animal, etc.). > conc=c(5,12,20,24,35,40) > vol=c(20,25,33,40,50,55) > d=data.frame(conc,vol) > d conc vol 1 5 20 2 12 25 3 20 33 4 24 40 5 35 50 6 40 55

27. Example of multivariate data Data manipulation in R Data: “Soil” Soil properties of two adjacent locations on Wimbledon common, a sandy lowland heath (site1), and adjoining spoil mounds of calcareous clay (site 2). Parameters: Site - site number rep - quadrat replicate number pH cond - electrical conductivity of soil solution OM - percentage organic matter composition of soil H2O – percentage water content of soil after drying to 105°F

28. Example of multivariate data Read data in R >Soil=read.csv("E:/Multivariate_analysis/Data/Soil.csv",header=T) > Soil Site rep pH cond OM H2O 1 1 1 4.5 55 26 17 2 1 1 5.4 60 16 21 3 1 3 5.1 49 NA 18 4 1 4 4.8 55 27 18 5 2 1 7.6 155 5 25 6 2 2 7.8 124 NA 35 7 2 3 7.2 141 6 32 8 2 4 7.3 166 8 29 A comment in R is marked with # #import a.text file: > Soil=read.table("E:/Multivariate_analysis/Data/Soil.txt",header=T) #import a.csv file:

29. Example of multivariate data Data manipulation in R > names(Soil) [1] "Site" "rep" "pH" "cond" "OM" "H2O" #Display the column names of “Soil” data: #Display the row names: > rownames(Soil) [1] "1" "2" "3" "4" "5" "6" "7" "8" #Display the dimensions of the Soil data: > dim(Soil) [1] 8 6 rows (observations) columns (variables)

30. Example of multivariate data Data manipulation in R #Select the second column of the data: #or: #Select the third row of the data: > Soil[,2] [1] 1 1 3 4 1 2 3 4 > Soil$rep [1] 1 1 3 4 1 2 3 4 >Soil[3,] Site rep pH cond OM H2O 3 1 3 5.1 49 34 18 #Select rows 2,4, and 5: > Soil[c(2,4,5),] Site rep pH cond OM H2O 2 1 1 5.4 60 16 21 4 1 4 4.8 55 27 18 5 2 1 7.6 155 5 25

31. Example of multivariate data Data manipulation in R #Display the length of the second column: #Add a new column log.pH containing the logarithmic transform of pH: > length(Soil[,2]) [1] 8 >Soil2=transform(Soil,log.pH=log(Soil$pH)) > Soil2 Site rep pH cond OM H2O log.pH 1 1 1 4.5 55 26 17 1.504077 2 1 1 5.4 60 16 21 1.686399 3 1 3 5.1 49 NA 18 1.629241 4 1 4 4.8 55 27 18 1.568616 5 2 1 7.6 155 5 25 2.028148 6 2 2 7.8 124 NA 35 2.054124 7 2 3 7.2 141 6 32 1.974081 8 2 4 7.3 166 8 29 1.987874

32. Example of multivariate data Data manipulation in R #Delete the third column (pH) of the “Soil2” data: > Soil3=Soil2[,-3] > Soil3 Site rep cond OM H2O log.pH 1 1 1 55 26 17 1.504077 2 1 1 60 16 21 1.686399 3 1 3 49 NA 18 1.629241 4 1 4 55 27 18 1.568616 5 2 1 155 5 25 2.028148 6 2 2 124 NA 35 2.054124 7 2 3 141 6 32 1.974081 8 2 4 166 8 29 1.987874

33. Example of multivariate data Data manipulation in R #Select the first four columns of the “Soil” data: > Soil4=Soil[,1:4] > Soil4 Site rep pH cond 1 1 1 4.5 55 2 1 1 5.4 60 3 1 3 5.1 49 4 1 4 4.8 55 5 2 1 7.6 155 6 2 2 7.8 124 7 2 3 7.2 141 8 2 4 7.3 166

34. Example of multivariate data Data manipulation in R #Obtain a subset of the “Soil” data with cond >100: > Soil5=subset(Soil,Soil$cond>100) > Soil5 Site rep pH cond OM H2O 5 2 1 7.6 155 5 25 6 2 2 7.8 124 NA 35 7 2 3 7.2 141 6 32 8 2 4 7.3 166 8 29 #Obtain a subset of the “Soil” data with cond >100 and H2O<32 >Soil6=subset(Soil,Soil$cond>100&Soil$H2O<32) > Soil6 Site rep pH cond OM H2O 5 2 1 7.6 155 5 25 8 2 4 7.3 166 8 29

35. Example of multivariate data Data manipulation in R #Obtain a subset of the “Soil” data with no missing values (NA): > Soil7=subset(Soil, !is.na(Soil$OM)) > Soil7 Site rep pH cond OM H2O 1 1 1 4.5 55 26 17 2 1 1 5.4 60 16 21 4 1 4 4.8 55 27 18 5 2 1 7.6 155 5 25 7 2 3 7.2 141 6 32 8 2 4 7.3 166 8 29 #Obtain a subset of the “Soil” data with missing values (NA): > Soil8=subset(Soil,is.na(Soil$OM)) > Soil8 Site rep pH cond OM H2O 3 1 3 5.1 49 NA 18 6 2 2 7.8 124 NA 35

36. Example of multivariate data Data manipulation in R #Identify which observations have pH<7: > which(Soil$pH<7) [1] 1 2 3 4 # observations (rows) 1,2,3,and 4 have pH<7. #Identify which observations have missing values for OM: > which(is.na(Soil$OM)) [1] 3 6 #observations 3 and 6 have missing values for OM. #Identify which observation has pH=5.4: > which(Soil$pH==5.4) [1] 2 > which(Soil$Site!=1) [1] 5 6 7 8 #Identify which observations are not from the Site 1:

37. Example of multivariate data Data manipulation in R #Order “Soil” data by pH: > Soil9=Soil[order(Soil$pH),] > Soil9 Site rep pH cond OM H2O 1 1 1 4.5 55 26 17 4 1 4 4.8 55 27 18 3 1 3 5.1 49 NA 18 2 1 1 5.4 60 16 21 7 2 3 7.2 141 6 32 8 2 4 7.3 166 8 29 5 2 1 7.6 155 5 25 6 2 2 7.8 124 NA 35 > Soil10=Soil[order(-Soil$pH),] > Soil10 Site rep pH cond OM H2O 6 2 2 7.8 124 NA 35 5 2 1 7.6 155 5 25 8 2 4 7.3 166 8 29 7 2 3 7.2 141 6 32 2 1 1 5.4 60 16 21 3 1 3 5.1 49 NA 18 4 1 4 4.8 55 27 18 1 1 1 4.5 55 26 17 Increasing Decreasing

38. Example of multivariate data Data manipulation in R #Save “Soil10” data from the R console to your computer: >write.table(Soil10,file="E:/Multivariate_analysis/pH_Order_Soil.csv“, row.names=F,col.names=names(Soil10),quote=F,sep=",") #Load a package in R (after installing it): > library(MASS)# load the package called MASS # Get help with R functions: >help(read.table) >?read.table or

39. Example of multivariate data Get help in R

40. Example of multivariate data Simple summary statistics #Calculate mean, standard deviation, variance, median, sum, and maximum and minimum values for “cond” in “Soil” data: > mean(Soil$cond) [1] 100.625 > sd(Soil$cond) [1] 50.54824 > var(Soil$cond) [1] 2555.125 > median(Soil$cond) [1] 92 > sum(Soil$cond) [1] 805 > max(Soil$cond) [1] 166 > min(Soil$cond) [1] 49

41. Example of multivariate data Graphics in R

42. Example of multivariate data Graphics in R