• Basics of object-oriented programming in R

• Simple R data structures

• Simple descriptive statistics, (some) inferential statistics, and plotting with Base R

• (A few) programming best practices

Open source programming language, with a particular focus on statistical programming.

History: Originally (in 1993) an implementation of the S programming language (Bell Labs), by Ross Ihaka and Robert Gentleman (hence R) at University of Auckland.

Currently the R Foundation for Statistical Computing is based in Vienna. Development is distributed globally.

RStudio:

RStudio is an Integrated Developer Environment (IDE) that makes using R and other reproducible research tools easier.

R can be easily expanded by user created packages hosted on GitHub and/or CRAN.

citation()

## 
## To cite R in publications use:
## 
##   R Core Team (2016). R: A language and environment for
##   statistical computing. R Foundation for Statistical Computing,
##   Vienna, Austria. URL https://www.R-project.org/.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {R: A Language and Environment for Statistical Computing},
##     author = {{R Core Team}},
##     organization = {R Foundation for Statistical Computing},
##     address = {Vienna, Austria},
##     year = {2016},
##     url = {https://www.R-project.org/},
##   }
## 
## We have invested a lot of time and effort in creating R, please
## cite it when using it for data analysis. See also
## 'citation("pkgname")' for citing R packages.

Like many other popular programming languages, R is object-oriented.

Objects are R's nouns. They include (not exhaustive):

• character strings (e.g. words)

• numbers

• vectors of numbers or character strings

• matrices

• data frames

• lists

2 + 3

## [1] 5

2 - 3

## [1] -1

2 * 3

## [1] 6

2 / 3

## [1] 0.6666667

You use the assignment operator (<-) to assign character strings, numbers, vectors, etc. to object names

## Assign the number 10 to an object called number
number <- 10

number

## [1] 10

# Assign Hello World to an object called words
words <- "Hello World"

words

## [1] "Hello World"

You can assign almost anything to an object. For example, the output of a maths operation:

divided <- 2 / 3

divided

## [1] 0.6666667

You can also use the equality sign (=):

number = 10

number

## [1] 10

Note: it has a slightly different meaning.

See StackOverflow discussion.

• NA: not available, missing

• NULL: does not exist, is undefined

• TRUE, T: logical true. Logical is also an object class.

• FALSE, F: logical false

absent <- NA
is.na(absent)

## [1] TRUE

Objects have distinct classes.

# Find the class of number
class(number)

## [1] "numeric"

# Find the class of absent
class(absent)

## [1] "logical"

• Object names cannot have spaces

  • Use CamelCase, name_underscore, or name.period

• Avoid creating an object with the same name as a function (e.g. c and t) or special value (NA, NULL, TRUE, FALSE).

• Use descriptive object names!

  • Not: obj1, obj2

• Each object name must be unique in an environment.

  • Assigning something to an object name that is already in use will overwrite the object's previous contents.

# Find objects in your workspace
ls()

## [1] "absent"   "divided"  "number"   "searches" "words"

Or the Environment tab in RStudio

As with natural language writing, it is a good idea to stick to one style guide with your R code:

• Google's R Style Guide

• Hadely Wickham's R Style Guide

A vector is an ordered collection of numbers, characters, etc. of the same type.

Vectors can be created with the c (combine) function.

# Create numeric vector
numeric_vector <- c(1, 2, 3)

# Create character vector
character_vector <- c('Albania', 'Botswana', 'Cambodia')

Categorical variables are called factors in R.

# Create numeric vector
fruits <- c(1, 1, 2)

# Create character vector for factor labels
fruit_names <- c('apples', 'mangos')

# Convert to labelled factor
fruits_factor <- factor(fruits, labels = fruit_names)

summary(fruits_factor)

## apples mangos 
##      2      1

Matrices are collections of vectors with the same length and class.

# Combine numeric_vector and character_vector into a matrix
combined <- cbind(numeric_vector, character_vector)

combined

##      numeric_vector character_vector
## [1,] "1"            "Albania"       
## [2,] "2"            "Botswana"      
## [3,] "3"            "Cambodia"

Note (1): R coerced numeric_vector into a character vector.

Note (2): You can rbind new rows onto a matrix.

Data frames are collections of vectors with the same length.

Each column (vector) can be of a different class.

# Combine numeric_vector and character_vector into a data frame
combined_df <- data.frame(numeric_vector, character_vector,
                          stringsAsFactors = FALSE)

combined_df

##   numeric_vector character_vector
## 1              1          Albania
## 2              2         Botswana
## 3              3         Cambodia

A list is an object containing other objects that can have different lengths and classes.

# Create a list with three objects of different lengths
test_list <- list(countries = character_vector, not_there = c(NA, NA),
                  more_numbers = 1:10)
test_list

## $countries
## [1] "Albania"  "Botswana" "Cambodia"
## 
## $not_there
## [1] NA NA
## 
## $more_numbers
##  [1]  1  2  3  4  5  6  7  8  9 10

Functions do things to/with objects. Functions are like R's verbs.

When using functions to do things to objects, they are always followed by parentheses (). The parentheses contain the arguments. Arguments are separated by commas.

# Summarise combined_df
summary(combined_df, digits = 2)

##  numeric_vector character_vector  
##  Min.   :1.0    Length:3          
##  1st Qu.:1.5    Class :character  
##  Median :2.0    Mode  :character  
##  Mean   :2.0                      
##  3rd Qu.:2.5                      
##  Max.   :3.0

Use ? to find out what arguments a function can take.

?summary

The help page will also show the function's default argument values.

The $ is known as the component selector. It selects a component of an object.

combined_df$character_vector

## [1] "Albania"  "Botswana" "Cambodia"

You can use subscripts [] to also select components.

For data frames they have a [row, column] pattern.

# Select the second row and first column of combined_df
combined_df[2, 1]

## [1] 2

# Select the first two rows
combined_df[c(1, 2), ]

##   numeric_vector character_vector
## 1              1          Albania
## 2              2         Botswana

# Select the character_vector column
combined_df[, 'character_vector']

## [1] "Albania"  "Botswana" "Cambodia"

You can use assignment with parts of objects. For example:

combined_df$character_vector[3] <- 'China'
combined_df$character_vector

## [1] "Albania"  "Botswana" "China"

You can even add new variables:

combined_df$new_var <- 1:3
combined_df

##   numeric_vector character_vector new_var
## 1              1          Albania       1
## 2              2         Botswana       2
## 3              3            China       3

You can greatly expand the number of functions by installing and loading user-created packages.

# Install dplyr package
install.packages('dplyr')

# Load dplyr package
library(dplyr)

You can also call a function directly from a specific package with the double colon operator (::).

Grouped <- dplyr::group_by(combined_df, character_vector)

List internal data sets:

data()

Load swiss data set:

data(swiss)

Find data description:

?swiss

Find variable names:

names(swiss)

## [1] "Fertility"        "Agriculture"      "Examination"     
## [4] "Education"        "Catholic"         "Infant.Mortality"

See the first three rows and four columns

head(swiss[1:3, 1:4])

##              Fertility Agriculture Examination Education
## Courtelary        80.2        17.0          15        12
## Delemont          83.1        45.1           6         9
## Franches-Mnt      92.5        39.7           5         5

Note: not all of R's built-in data sets are data frames.

For Assignment 1, try to focus on data sets that are either data frames or matrices.

Pipe: pass a value forward to a function call.

Why?

• Faster compilation.

• Enhanced code readability.

In R use %>% from the dplyr package.

%>% passes a value to the first argument of the next function call.

Not piped:

values <- rnorm(1000, mean = 10)
value_mean <- mean(values)
round(value_mean, digits = 2)

## [1] 9.95

Piped:

library(dplyr)

rnorm(1000, mean = 10) %>% mean() %>% round(digits = 2)

## [1] 10.03

You can create a function to find the sample mean (\(\bar{x} = \frac{\sum x}{n}\)) of a vector.

fun_mean <- function(x){
    sum(x) / length(x)
}

## Find the mean
fun_mean(x = swiss$Examination)

## [1] 16.48936

Functions:

• Simplify your code if you do repeated tasks.

• Lead to fewer mistakes.

• Are easier to understand.

• Save time over the long run–a general solution to problems in different contexts.

Descriptive Statistics: describe samples

Stats 101: describe sample distributions with appropriate measure of:

• central tendancy

• variability

hist(swiss$Examination)

hist(swiss$Examination,
     main = 'Swiss Canton Draftee Examination Scores (1888)',
     xlab = '% receiving highest mark on army exam')

(or use the mean function in base R)

mean(swiss$Examination)

## [1] 16.48936

If you have missing values (NA):

mean(swiss$Examination, na.rm = TRUE)

You can 'loop' through the data set to find the mean for each column

for (i in 1:length(names(swiss))) {
    swiss[, i] %>%
    mean() %>%
    round(digits = 1) %>%
    paste(names(swiss)[i], ., '\n') %>%  # the . directs the pipe
    cat()
}

## Fertility 70.1 
## Agriculture 50.7 
## Examination 16.5 
## Education 11 
## Catholic 41.1 
## Infant.Mortality 19.9

Median

median(swiss$Examination)

## [1] 16

Mode

mode is not an R function to find the statistical mode.

Instead use summary for factor nominal variables or make a bar chart.

devtools::source_url('http://bit.ly/OTWEGS')
plot(MortalityGDP$region, xlab = 'Region')

Variation is "perhaps the most important quantity in statistical analysis. The greater the variability in the data, the greater will be our uncertainty in the values of the parameters estimated . . . and the lower our ability to distinguish between competing hypotheses" (Crawley 2005, 33)

Range:

range(swiss$Examination)

## [1]  3 37

Quartiles:

summary(swiss$Examination)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    3.00   12.00   16.00   16.49   22.00   37.00

Interquartile Range (\(IQR = Q_{3} - Q_{1}\)):

IQR(swiss$Examination)

## [1] 10

Boxplots:

boxplot(swiss$Examination, main = '% of Draftees with Highest Mark')

Sum of squares (summing deviations from the mean):

\[\mathrm{Sum\:of\:Squares} = \sum(x - \bar{x})^2\]

• But sum of squares always gets bigger with a larger sample size.

  • Unless the new values exactly equal the mean.

Degrees of freedom (number of values that are free to vary):

For the mean:

\[\mathrm{df} = n - 1\]

Why?

For a given mean and sample size, \(n - 1\) values can vary, but the \(n\)th value must always be the same. See Crawley (2005, 36-37).

We can use degrees of freedom to create an "unbiased" measure of variability that is not dependent on the sample size.

Variance (\(s^2\)):

\[ s^2 = \frac{\mathrm{Sum\:of\:Squares}}{\mathrm{Degrees\:of\:Freedom}} = \frac{\sum(x - \bar{x})^2}{n - 1} \]

But this is not in the same units as the mean, so it can be confusing to interpret.

Use standard deviation (\(s\)) to put variance in terms of the mean:

\[s = \sqrt{s^2}\]

The standard error of the mean:

If we think of the variation around a central tendency as a measure of the unreliability of an estimate (mean) in a population, then we want the measure to decrease as the sample size goes up.

\[ \mathrm{SE}_{\bar{x}} = \sqrt{\frac{s^{2}}{n}} \]

Note: \(\sqrt{}\) so that the dimensions of the measure of unreliability and the parameter whose variability is being measured are the same.

Good overview of variance, degrees of freedom, and standard errors in Crawley (2005, Ch. 4).

Variance:

var(swiss$Examination)

## [1] 63.64662

Standard Deviation:

sd(swiss$Examination)

## [1] 7.977883

Standard Error:

sd_error <- function(x) {
    sd(x) / sqrt(length(x))
}

sd_error(swiss$Examination)

## [1] 1.163694

Simulated normally distributed data with SD of 30 and mean 50

Normal30 <- rnorm(1e+6, mean = 50, sd = 30)

Highly skewed data can be transformed to have a normal distribution.

Helps correct two violations of key assumptions in linear regression (see later in the course): (a) non-linearity and (b) heteroskedasticity.

hist(swiss$Education, main = '')

log(swiss$Education) %>% hist(main = "Swiss Education")

The natural log transformation is only useful for data that does not contain zeros.

See http://robjhyndman.com/hyndsight/transformations/ for suggestions on other transformations such as Box-Cox and Inverse Hyperbolic Sine.

plot(log(swiss$Education), swiss$Examination)

cor.test(log(swiss$Education), swiss$Examination)

## 
##  Pearson's product-moment correlation
## 
## data:  log(swiss$Education) and swiss$Examination
## t = 6.4313, df = 45, p-value = 7.133e-08
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.5053087 0.8168779
## sample estimates:
##       cor 
## 0.6920531

ggplot2::ggplot(swiss, aes(log(Education), Examination)) +
    geom_point() + geom_smooth() + theme_bw()

Always close!

In R this means closing:

• ()

• []

• {}

• ''

• ""

There are usually many ways to acheive the same goal, but . .

make your code as simple as possible.

• Easier to read.

• Easier to write (ultimately).

• Easier to find mistakes.

• Often computationally more efficient.

One way to do this is to define things once–e.g. use variables to contain values and custom functions to contain multiple sequential function calls.

Bad

mean(rnorm(1000))

## [1] -0.003707504

sd(rnorm(1000))

## [1] 0.9980258

Good

rand_sample <- rnorm(1000)

mean(rand_sample)

## [1] 0.0003898685

sd(rand_sample)

## [1] 0.9768

Test your code early and often. Do the results meet your expectations?

• Easier to find errors.

• For an advanced discussion see Wickham, Testing R Packages.

• Save your work in a new .R source file. You will need it for the next seminar.

• Create a data frame with four columns. The data set should have one of each: character strings, numeric, logical, and factor variables.

• Access R data sets.

• Explore the data and find ways to numerically/graphically describe it.

• Find and use R functions that were not covered in the lecture for exploring and transforming your data.

• Create your own function (what it does is open to you).