Part I { Getting Started & Manipulating Data with R

Transcription

1 Part I { Getting Started & Manipulating Data with R Gilles Lamothe February 21, 2017 Contents 1 URL for these notes and data 2 2 Origins of R 2 3 Downloading and Installing R 2 4 R Console and Editor 3 5 RStudio 3 6 Working Directory 3 7 Importing & Exporting data with R / Data structures (Vectors and Dataframes) 4 8 Types, Test and Coercion / sapply / Factors 8 9 Functions of a numerical vector (Descriptive Statistics) / Group statistics 9 10 Missing values / User build functions To source an R script Applying our new skills Logical vectors / Table of frequencies / Convert a numerical vector into a factor Operations on numerical vectors Cut Functions Revisited Plot a one numerical variable (Boxplot & Histogram) / Installing an R package Applying our new skills { Part II Saving the workspace 23 1

2 Intro to R Workshop - Psychology Statistics Club 2 Intro to R Workshop - Psychology Statistics Club 1 URL for these notes and data To download these notes, follow the link: aix1.uottawa.ca/~glamothe/psystatclub The name of the le is Rworkshop.pdf. To nd the corresponding data, follow the link: aix1.uottawa.ca/~glamothe/psystatclub The data is in the folder called data. 2 Origins of R R was designed by Ross Ihaka (computer scientist) and Robert Gentleman (statistician) in the early 1990's at the University of Auckland (New Zealand). R was developed at the Bell Laboratories in Murray Hill, New Jersey. R is much more than a statistical package. It is its own computer language and environment within wich statistical techniques are implemented. To know more ABOUT R, follow the link: R's strength is that is allows the user to retain full control. It is highly exible. 3 Downloading and Installing R To nd R, to google.ca and search for R. Follow the link for: Here is the URL: R: The R Project for Statistical Computing. Here is a youtube video for instructions concerning the installation of R.

3 Intro to R Workshop - Psychology Statistics Club 3 4 R Console and Editor R is a command based programming language. prompt > in the R console. We enter commands at the Here is an example, where we compute p We enter the command and the prompt and press ENTER. > sqrt(2)+4 [1] Alternatively, we can enter commands in an R editor window. Select File! New script in Windows or select File! New document on a Mac. In an Editor, we select the commands that we want to send to the prompt and we press CTRL-R in Windows or CMD-Enter on a Mac. 5 RStudio RStudio is a free and open-source integrated development environment (IDE) for R. RStudio is a more user-friendly interface to facilitate the use of R. To install RStudio, download the installer for your operating system from the following Webpage: You will see many windows, within the RStudio environment. There is, on the left-hand-side : { the console with the R prompt, which is waiting patiently for you commands. { an R editor window, within which was can work and eventually submit our commands to the console. 6 Working Directory We use the command getwd() to display the working directory. We use the function setwd() to display the working directory. Below, we set the directory to C:/Rstuff and we verify that the working directory has been properly set by displaying the current working directory. > setwd("c:/rstuff") > getwd() [1] "c:/rstuff"

4 Intro to R Workshop - Psychology Statistics Club 4 Comments: Windows users are used to seeing the blackslash (\) as the path separator. However, even for Windows, R uses the frontslash (/) as the path separator. Using a working directory will save you time. However, we will see later that we can ignore the working directory by using the function file.choose(). It forces R to open a window and ask you for the location of your le. 7 Importing & Exporting data with R / Data structures (Vectors and Dataframes) R does not have a good worksheet. So you will need to use some other editing software, e.g. excel or Open Office Calc, with a worksheet to save your data. We recommend that you save your data as a text le, preferably as tab delimited, or CSV (i.e. comma separated). We will be using tab delimited. This allows me to have commas in my le that are not interpreted as the start of a new column. R has four data structures: dataframe, vector, list, and matrix. For now, we will discuss the dataframe and the vector. Dataframe: { A dataframe is a data table. { The rows are the statistical units. { The columns are the variables that are used to describe the statistical units. { Here is an example of a dataframe: subject ID gender age (in years) measured response complient 1 Male Female Female Female Female Male { We saved the above table in the le example.txt. It is a tab-delimited text le. { Assuming that the le is in our working directory (for me it is: C:/Rstuff), then we can use the following command to assign the data in the le to a dataframe that we called data. > data<-read.table("example.txt",header=true,sep="\t") > names(data) [1] "subject.id" "gender" "age..in.years." [4] "measured.response" "complient"

5 Intro to R Workshop - Psychology Statistics Club 5 Vector: Comments: 1. <- is used for assignments. Using the read.table function, we assigned a dataframe to data. The name of the dataframe is provided by the user. 2. By default, R assumes that we will not give names to our columns. If the rst row in your table has column names, we need to add the argument header=true. 3. By default, R uses space to separate columns. We used tabs, so we add the argument sep="\t". For a CSV le, use sep="," 4. We can use the function names() to display the names of the columns of a dataframe. 5. R does not permit certain symbols for the names of a column, e.g. spaces. In all of those cases, the symbol is replaced by a dot. 6. Here we display the rst three rows of the dataframe data. > head(data,n=3) subject.id gender age..in.years. measured.response complient 1 1 Male Female Female Here we display the dimensions (# of rows & # of columns) of the dataframe data. > dim(data) [1] 6 5 > nrow(data) [1] 6 > ncol(data) [1] 5 8. Instead of giving the name of the le to import, we use use the file.choose() function. R will open a window to ask you the location of the le. > data<-read.table(file.choose(),header=true,sep="\t") Think of a vector, as a column in a dataframe. It is a homogeneous data structure. All of its elements are of the same type. Here are some common types: integer, double (often called numeric), boolean (often called logical), categorical (often called character or factor). Basically, a vector is either a numerical (quantitative) variable or a categorical (qualitative) variable. Reference to a vector in a dataframe: { with the column's name:

6 Intro to R Workshop - Psychology Statistics Club 6 > data$gender [1] Male Female Female Female Female Male Levels: Female Male Remark: R noticed that data$gender is categorical. So it also displayed its levels. { with the column's position: > data[,2] [1] Male Female Female Female Female Male Levels: Female Male Remark: We use square brackets for subsetting data with R. Here [,2] refers to the second column. [2,] refers to the second row and [2,3] refers to 2nd row and 3rd column. { Here we display the 2nd row in the dataframe data and, then, we ask R if it is a vector or a dataframe. A row is not a vector. > data[2,] subject.id gender age..in.years. measured.response complient 2 2 Female > is.data.frame(data[2,]) [1] TRUE > is.vector(data[2,]) [1] FALSE { Here we display the 3nd column in the dataframe data and, then, we ask R if it is a vector. > data[,3] [1] > is.vector(data[,3]) [1] TRUE A vector does not need to be a column of a dataframe. Just think of it as a list of elements of the same type. Examples of vectors: 1. The names of the dataframe is a character vector. > names(data) [1] "subject ID" "gender" "age (in years)" [4] "measured response" "complient" > is.vector(names(data)) [1] TRUE 2. We can construct vectors with function c() (which stands for combine). Here is a command to assign a character vector to names(data).

7 Intro to R Workshop - Psychology Statistics Club 7 names(data)<-c("subject ID","gender","age", "measured response","complient") We now redisplay the names of the columns in the dataframe data. > names(data) [1] "subject ID" "gender" "age" [4] "measured response" "complient" Comment: If you have a space in the name of a column, you must use quotes to refer to it by name. > data$`measured response` [1] Here are a few useful ways to build vectors. > # a numerical vector of zeros of size 6 > numeric(6) [1] > # build a vector by repeating a vector 4 times > rep(c(1,2),4) [1] > # an empty vector > c() NULL > # a numerical vector with the integers from 1 to 6 > 1:6 [1] > # a numerical vector with the integers from 10 to 20 > 10:20 [1] > # build a sequence of numbers with an increment of 0.5 > # starting at 1 and ending at 5. > seq(1,5,by=0.5) [1] Remark: We use the symbol # to write comments that R does not interpret. We can easily add a vector to a dataframe. > data<-data.frame(data,degree) > names(data) [1] "subject.id" "gender" "age" [4] "measured.response" "complient" "degree" We end this section by exporting a dataframe with the function read.table(). It will save the le in the working directory, unless you give it a path. write.table(data, file = "SavedExample.txt",sep = "\t", row.names = FALSE, col.names = TRUE)

8 Intro to R Workshop - Psychology Statistics Club 8 Comments: With the above command, we saved the dataframe data in the le `SavedExample.txt' in the working directory. R might modify the names of the columns, since some characters are not permitted, e.g. spaces. 8 Types, Test and Coercion / sapply / Factors Here are a few test functions: is.character(), is.logical(), is.numeric(), is.factor(). Here are a few coercion functions: as.character(), as.logical(), as.numeric(), as.factor(), factor(). Here is an example of testing that it is of type factor and then forcing it to be of type factor. > is.factor(data$complient) [1] FALSE > is.numeric(data$complient) [1] TRUE > data$complient<-factor(data$complient) > is.factor(data$complient) [1] TRUE > is.numeric(data$complient) [1] FALSE large Factors: Factors are categorical variables. They have levels, i.e. the categories. > levels(data$complient) [1] "1" "2" Here is a display of the vector: > data$complient [1] Levels: 1 2 We can change the labels of the levels, with the function factor by using a labels argument. The labels must be a vector as the same length as the levels. > data$complient<-factor(data$complient,labels=c("yes","no")) > data$complient [1] Yes Yes No No No No Levels: Yes No

9 Intro to R Workshop - Psychology Statistics Club 9 sapply: It is good practice to verify the type of all the columns in a dataframe. This can be time consuming to verify the type one column at a time. We can use the function sapply to apply the function is.factor on all the columns of a dataframe. It returns a logical vector. > sapply(data,is.factor) subject.id gender age FALSE TRUE FALSE measured.response complient degree FALSE TRUE TRUE We identify which columns are numerical. > sapply(data,is.numeric) subject.id gender age TRUE FALSE TRUE measured.response complient degree TRUE FALSE FALSE 9 Functions of a numerical vector (Descriptive Statistics) / Group statistics Let x be a numerical vector. For example, consider the following assignment. x<-c(16,15,14,16,13,12,14,13,10) By using the command summary(x), we obtain some descriptive statistics for x. > summary(x) Min. 1st Qu. Median Mean 3rd Qu. Max Here are some descriptives for the age of the subjects in the dataframe data. > summary(data$age) Min. 1st Qu. Median Mean 3rd Qu. Max Here is a list of some common statistics. sum(x) mean(x) var(x) sd(x) min(x) max(x) median(x) # sum of the components # mean # variance # standard deviation # min # max # median

10 Intro to R Workshop - Psychology Statistics Club 10 quantile(x) # 5-number summary (min,q1,median,q3,max) length(x) # number of components sort(x) # arrange values in ascending order rank(x) # rank the values from 1 to length(x) Let us use the sapply function to get the mean for each column in the dataframe data. > sapply(data,mean) subject.id gender age NA measured.response complient degree NA NA Warning messages: 1: In mean.default(x[[i]],...) : argument is not numeric or logical: returning NA 2: In mean.default(x[[i]],...) : argument is not numeric or logical: returning NA 3: In mean.default(x[[i]],...) : argument is not numeric or logical: returning NA Comments: R is warning us that it cannot compute the mean of a non-numerical vector. If we know that a certain command will display warnings, we can suppress warnings before using the command. It is good practice, > # suppress warnings > options(warn=-1) > sapply(data,mean) subject.id gender age NA measured.response complient degree NA NA > # put warnings back on > options(warn=0) Recall that we use square brackets for subsetting. We could extract the numerical columns and only compute the mean for each of these columns. > numericcol<-sapply(data,is.numeric) > sapply(data[,numericcol],mean) subject.id age measured.response Group Statistics:

11 Intro to R Workshop - Psychology Statistics Club 11 We can use the aggregate function to get group statistics for a numerical vector y according to the levels of another variable x in a dataframe data. fun is the descriptive statistic that you want to compute. Its usage is aggregate(y~x,data,fun) Here are the mean age for the subjects in the dataframe data according to the levels of gender. > Mean<-aggregate(age~gender,data,mean) > Mean gender age 1 Female Male Here we build a dataframe with a few descriptive statistics for the age for the subjects in the dataframe data according to the levels of gender. > Mean<-aggregate(age~gender,data,mean) > SD<-aggregate(age~gender,data,sd) > n<-aggregate(age~gender,data,length) > AgeStats<-data.frame(Mean,SD[,2],n[,2]) > names(agestats)<-c("gender","mean","std dev","n") > AgeStats Gender Mean Std dev n 1 Female Male Remark: The discussion in this section assumes that there are no missing values. > mean(c(na,0,1)) [1] NA Missing values can cause some problems. R could not compute the mean of the vector, since there was a missing value. 10 Missing values / User build functions Consider the data in the le OmitExample.txt. We import the data and assign it to the dataframe data1. > data1<-read.table("omitexample.txt",header=true,sep="\t") > data1 subject.id gender age..in.years. measured.response complient 1 1 Male Female 45 NA Female Female NA 1.8 2

12 Intro to R Workshop - Psychology Statistics Club Female Male degree 1 yes 2 no 3 no 4 yes 5 yes 6 yes There is a missing value in the third column and also in the fourth column. So we will have diculties compute the mean for each of these columns. > numericcol<-sapply(data1,is.numeric) > sapply(data1[,numericcol],mean) subject.id age..in.years. measured.response NA NA complient We can omit the missing values with the function na.omit. However, it will delete all rows with a missing value. > na.omit(data1) subject.id gender age..in.years. measured.response complient 1 1 Male Female Female Male degree 1 yes 3 no 5 yes 6 yes User dened function: Another solution is to build our own function to compute the mean of a vector after omitting missing values in this vector. mean.na<-function(x) { x<-x[!is.na(x)] # keep value if not NA return(mean(x)) } We use our user dened function to compute the mean of the numerical vectors in the dataframe data1. > sapply(data1[,numericcol],mean.na) subject.id age..in.years. measured.response

13 Intro to R Workshop - Psychology Statistics Club complient R does not have a sample size function. We can use the function length, but it gives the number of components in the vector (including missing values). > length(data1$age..in.years.) [1] 6 > data1$age..in.years. [1] NA We dene functions to count the number of missing values in a vector and to count the number of non-missing values in a vector. numna<-function(x) { return(length(x[is.na(x)])) } SampleSize<-function(x) { return(length(x)-numna(x)) } We use our functions on the vector age..in.years. in the dataframe data1. > SampleSize(data1$age..in.years.) [1] 5 > numna(data1$age..in.years.) [1] 1 11 To source an R script We will want to save our user dened R functions. Steps to save your functions: 1. In the RStudio menu, select File! New File! New R script. 2. In the new editor window, enter your functions. 3. Save the current editor window. I saved it as myfunctions.r. 2 ways to Access your functions: 1. In the RStudio menu, select File! Open File. Browse for myfunctions.r. 2. Alternatively, we can source the le. R will interpret all commands in the le that have been sourced. I am assuming that myfunctions.r is in the working directory. > source("myfunctions.r")

14 Intro to R Workshop - Psychology Statistics Club Applying our new skills Exercises to try in class. 1. Consider a company that produces items made from glass. The data is in the le glassworks.txt. (Source: Applied Linear Models, by Kutner et al.). A large company is studying the eects of the length of special training for new employees on the quality of work. Employees are randomly assigned to have either 6, 8, 10, or 12 hours of training. After the special training, each employee is given the same amount of material. The response variable is the number of acceptable pieces. (a) Compute the number of subjects per group. Is it a balanced study (i.e. same # of observations per group)? (b) Compute the mean response and the standard deviation of the response for each group. 2. Consider the data in the le FinalGrades.txt. (a) For each assignment, compute the mean and the standard deviation. (b) For the nal exam, compute the mean according to the levels of the faculty.

15 Intro to R Workshop - Psychology Statistics Club Logical vectors / Table of frequencies / Convert a numerical vector into a factor It is easy to compute the proportion of statistical units in a dataframe that satisfy a certain condition. We use logical operators. Operator Description < less than <= less than or equal to > greater than >= greater than or equal to == exactly equal to!= not equal to!x Not x x j y x&y istrue(x) x OR y x AND y test if x is TRUE What proportion of the subjects in data are over 60? > data$age>60 [1] FALSE FALSE TRUE FALSE FALSE FALSE R considers FALSE as 0 and TRUE as 1. So by computing the mean, we get the proportion of TRUE values: > mean(data$age>60) [1] So 16.7% of the subjects are over 60. What proportion of the subjects in data are male? > data$gender=="male" [1] TRUE FALSE FALSE FALSE FALSE TRUE > mean(data$gender=="male") [1] So 33.3% of the subjects are male. What proportion of the subjects in data are female and at most 30? > (data$gender=="female")&(data$age<=30) [1] FALSE FALSE FALSE TRUE TRUE FALSE > mean((data$gender=="female")&(data$age<=30)) [1] So 33.3% of the subjects are female and at most 30. Table of frequencies: We can use the function table to obtain a table of frequencies for a categorical vector.

16 Intro to R Workshop - Psychology Statistics Club 16 > table(data$gender) Female Male 4 2 > # expressed as a percentage > table(data$gender)/length(data$gender)*100 Female Male Cut a numeric vector into intervals: We can use the function cut to break a numerical vector into intervals. It has an argument called break. It can be a number for the number of breaks or a numeric vector for the values of the breaks. > cut(data$age,breaks=3) [1] (33.3,47.7] (33.3,47.7] (47.7,62] (19,33.3] (19,33.3] [6] (33.3,47.7] Levels: (19,33.3] (33.3,47.7] (47.7,62] > cut(data$age,breaks=c(19,30,40,65)) [1] (30,40] (40,65] (40,65] <NA> (19,30] (40,65] Levels: (19,30] (30,40] (40,65] > agecat<-cut(data$age,breaks=c(19,30,40,65)) Here we have a two-way contingency table for the joint distribution of gender and age. > table(data$gender,agecat) agecat (19,30] (30,40] (40,65] Female Male Logical vector for subsetting: We can use a logical vector to obtain a subset a dataframe. Suppose that we only want to retain the female subjects. > datafemale <- data[data$gender=="female",] > datafemale subject.id gender age measured.response complient degree 2 2 Female Yes no 3 3 Female No no 4 4 Female No yes 5 5 Female No yes Comment: [data$gender=="female",] means that we want to retain the rows that correspond to females, but keep all of the columns.

17 Intro to R Workshop - Psychology Statistics Club Operations on numerical vectors R has a few arithmetic operators. Operator Description + addition subtraction multiplication = division ^ or exponentiation x%%y modulus (x mod y) 5%%2 is 1 x%=%y integer division 5%=%2 is 2 Operations are done component-wise. Here are a few examples. > x<-c(1,2,3) > y<-c(-1,0,1) > x+y [1] > x-y [1] > x*y [1] > x/y [1] -1 Inf 3 > 2+x [1] > 2*x [1] > x/2 [1] > x^2 [1] Here are a few other functions that might be useful. > sqrt(x) ## square root [1] > log(x) ## natural logarithm [1] > exp(x) ## exponential of base e [1] > w<-c(1.2,4.5,7.8) > w<-c(1.2,4.5,-7.8) > ceiling(w) ## round up [1] > floor(w) ## round down [1] 1 4-8

18 Intro to R Workshop - Psychology Statistics Club 18 > round(w) ## round [1] > abs(w) ## absolute value [1] We can apply an arithmetic operations in the presence of missing values. result will be NA. The > z<-c(na,1,1) > x+z [1] NA 3 4 Grades Example: We import the data from the le SmallClass.txt and display the names of the columns. > grades<-read.table("smallclass.txt",header=true,sep="\t") > names(grades) [1] "Student.ID" "Assignment1..Total.Pts..20." [3] "Assignment2..Total.Pts..30." "Test...Total.Pts..12." [5] "Assignment3..Total.Pts..50." "Assignment4..Total.Pts..20." [7] "FinalExam..Total.Pts..100." We will build a dataframe just for the assignments. > assignments<-grades[,c(2,3,5,6)] > names(assignments) [1] "Assignment1..Total.Pts..20." "Assignment2..Total.Pts..30." [3] "Assignment3..Total.Pts..50." "Assignment4..Total.Pts..20." We will convert each assignment into a percentage. > assignments<-grades[,c(2,3,5,6)] > assignments[,1]<-assignments[,1]/20*100 > assignments[,2]<-assignments[,2]/30*100 > assignments[,3]<-assignments[,3]/50*100 > assignments[,4]<-assignments[,4]/20*100 > names(assignments)<-c("hw1","hw2","hw3","hw4") > sapply(assignments,mean) hw1 hw2 hw3 hw Remark: There are no NA in the means. This means that there are no missing assignments. Say that we would like to keep that best 3 of 4 assignments. function that does the following We will build a For each student (i.e. each statistical unit), we construct a numeric vector of the four marks and convert any NA to a zero.

19 Intro to R Workshop - Psychology Statistics Club 19 We sort the four assignments and keep the best 3 of the four. We add the row of the best 3 of 4 assignments to a dataframe and we compute the average of the three marks. We use the function rbind to add a row to a dataframe. The result of the function will be a list containing a dataframe and a vector. BestOf <- function(x,n) { nstudents<-nrow(x) nassignments<-ncol(x) # empty dataframe BestMarks<-data.frame(NULL) # initialize a vector for the averages Avg<-numeric(nStudents) for (i in 1:nStudents) { best<-sort(as.numeric(x[i,]),decreasing=true)[1:n] best[best==na]<-0 Avg[i]<-mean(best) BestMarks<-rbind(BestMarks,best) } names(bestmarks)<-paste0("best",1:n) } return(list(bestmarks=bestmarks,mean=avg)) We are ready to get the best 3 assignment for each student. > BestOf(assignments,3) $BestMarks Best1 Best2 Best $Mean [1] We will add these means to the original dataframe. > grades<-data.frame(grades,bestof(assignments,3)$mean)

20 Intro to R Workshop - Psychology Statistics Club 20 > names(grades) [1] "Student.ID" "Assignment1..Total.Pts..20." [3] "Assignment2..Total.Pts..30." "Test...Total.Pts..12." [5] "Assignment3..Total.Pts..50." "Assignment4..Total.Pts..20." [7] "FinalExam..Total.Pts..100." "BestOf.assignments..3..Mean" We are ready to compute the nal grades with the following scheme. Best 3 of 4 assignments 20% Max(Test,Final) 25% Final Exam 55% If the student did not write the nal exam, it should remain an NA. > test<-grades[,4]/12*100 > test[test==na]<-0 > exam<-grades[,7] > exam [1] > hw<-grades[,8] > FinalGrade<-.2*hw+.25*max(exam,test)+.55*exam > FinalGrade [1] Cut Functions Revisited We are now ready to compute the alpha grades, i.e. convert a numeric vector into a factor. We use the cut function as follows. ## letter grades: ##90-100=A+; 85-89=A; 80-84=A-; ##75-79=B; 70-74=B-; ##65-69=C; 60-64=C-; ##55-59=D; 50-54=D-; ##40-49=E; 0-39=F; letters=c("f","e","d-","d","c-","c","b-","b","a","a-","a+") # right-hand limits are not included alpha.grade<-cut(finalgrade, c(0,40,50,55,60,65,70,75,80,85,90,inf), right=false, labels=letters ) Here are the alpha grades for the 5 students and a corresponding table of frequency. > alpha.grade [1] B- B- C A- A Levels: F E D- D C- C B- B A A- A+ > table(alpha.grade) alpha.grade F E D- D C- C B- B A A- A

21 Intro to R Workshop - Psychology Statistics Club Plot a one numerical variable (Boxplot & Histogram) / Installing an R package To produce a boxplot of x and a histogram of x, we use boxplot(x) and hist(x), respectively. > par(mfrow=c(1,2)) # graphics window of 1 row, 2 columns > hist(finalgrade) > boxplot(finalgrade) The result is Installing an R package: R has a very large community of contributes that are developing packages that are freely available through CRAN (The Comprehensive R Archive Network). We will install the package packhv with the following command: install.packages("packhv") Comments: You only need to install the package once onto your computer. If you do not have administrator privileges on the computer, then you might not be able to install a package in the default location for packages. If that is the case, then create a new directory on the computer, say C:/myPackages. You should be able to install in this location : install.packages("packhv",lib="c:/mypackages") To use a package during a session, we must load it by using the function library. For example: > library(packhv) > # you can also give the location of the package on your computer > library(packhv,lib.loc="c:/mypackages") We can now use the function hist_boxplot from the package packhv par(mfrow=c(1,1)) # graphics window of 1 row, 1 column hist_boxplot(finalgrade,col="lightblue",freq=true, ylab="frequency", xlab="final Grade (in percentage)", main="distribution of the Final Grades",

22 Intro to R Workshop - Psychology Statistics Club 22 cex.lab=1.15) # increase the font size on both axes axis(2,cex.axis=1.05) axis(1,cex.axis=1.15) Now this is where R shines. We can easily modify a graph. For example, we can add text to the plot with the function text. text(85,1.7,"mean = 76, sd = 6.7, n = 5",cex=1.15) The result is 17 Applying our new skills { Part II Exercises to try in class. 1. Consider a company that produces items made from glass. The data is in the le glassworks.txt. (Source: Applied Linear Models, by Kutner et al.). A large company is studying the eects of the length of special training for new employees on the quality of work. Employees are randomly assigned to have either 6, 8, 10, or 12 hours of training. After the special training, each employee is given the same amount of material. The response variable is the number of acceptable pieces. (a) Compute comparative boxplots to describe the number of acceptable pieces according to the amount of training. Hint: try boxplot(y~x,data) 2. Consider the data in the le FinalGrades.txt. (a) Compute the nal grades with the following distribution. Convert the nal grades to alpha grades and produce a frequency table for the alpha grades. Best 2 of 4 assignments 15% Max(Test,Final) 15% Final Exam 60% (b) Produce a plot to describe the distribution of the nal grades. (c) What is the failure rate? That is, what proportion of the students have a nal grade lower than 50%?

23 Intro to R Workshop - Psychology Statistics Club Saving the workspace You can save objects to retrieve in the future. Here we saved the objects Cereal and methadone. > # save specific objects to a file > # if you don't specify the path, the cwd is assumed > save(cereal,methadone,file="myfile.rdata") To retrieve the saved objects, use the function load. # load a workspace into the current session # if you don't specify the path, the cwd is assumed load("myfile.rdata")