Lecture 2 - Basics of Descriptive Statistics

Review of R basics

• Basic algebraic operators in R: +, -, *, /, ^, %%, %/%

• Basic assignment operators in R: ->, <-

• Basic atomic data types in R: integer, double, character and logical

• Basic Logical values and operators: TRUE, FALSE, ==, !=, >=, <=, >, <, &&, ||, &, |

• Create atomic vectors in R: c(), seq()

• Help documentation: use ? or help()

• Use functions in R: positional arguments and keyword arguments.

Lab Exercise

1. Compute \[ \left( \frac{2206 \sqrt{2}}{99^2} \right)^{-1} \]

2. What is the result of the following code (don’t execute it, tell by inspection):

x <- 1
2 <- y
(x == y) | (x < y)

3. Create a vector containing 1,3,5,7,9 in three different ways

4. Use the help documentation, find the factorial function and the inverse sine function in R.

R Basics - Atomic Vectors

We have learned how to create vectors that contain multiple values of the same type with The c() function. These vectors are called atomic vectors, of which there are six types: logical, integer, double, character, complex, and raw. Integer and double vectors are collectively known as numeric vectors. In this course we won’t use complex and raw vectors so we ignore them here.

We can use typeof function to check the type of a vector. Try the following code in your console.

typeof(c(1,2,3))
typeof(c(1L, 2L, 3L))
typeof(c("a", "b", "c"))
typeof(c(T, F, TRUE, FALSE))

Two Key Properties for Vectors

Every vector has two key properties:

• Its type, which you can determine with typeof().

typeof(letters)
typeof(1:10)

• Its length, which you can determine with length().

x <- seq(1, 20, by = 3)
length(x)

There’s one other related object: NULL. NULL is often used to represent the absence of a vector (as opposed to NA which is used to represent the absence of a value in a vector). NULL typically behaves like a vector of length 0.

length(NULL)

Names for Vector Elements

In a vector, each element can be assigned a label, for example

grades <- c(James = 79, Jane = 85, Jack = 91)
grades

## James  Jane  Jack 
##    79    85    91

Here the values in grades are the numbers 79, 85, 91, but now each value is assigned with a student name. The labels of a vector is another character vector. We can retrieve them by the function names:

names(grades)

## [1] "James" "Jane"  "Jack"

Its type is character.

student_names <- names(grades)
typeof(student_names)

## [1] "character"

Functions basics in R

To use a function, we need to understand the following basic concepts:

• Argument: inputs of a function

• Required Argument: If a required argument is missing, the function will print an error message

• Optional Argument: One doesn’t have to input an optional argument; if it is missing, a default value will be taken.

• Positional Argument: Arguments that have to input in a specific order

• Keyword Argument: Arguments that are specified by a keyword (usually optional with a default value)

Example

my_data <- c(1, 2, 2, 5, 10, NA)
mean(my_data, trim = 0, na.rm = TRUE)

## [1] 4

In the example above, we call the function mean() to computer the data average. Let’s check the help documentation of the function mean():

help("mean")

So we see that there are a few arguments for the function:

• x keyword - the input data: This is the first argument; this argument is required and there is no default value.

• trim keyword - the fraction of observations to be trimmed from each end of x before the mean is computed: This is the second argument, with the default value of being 0

• na.rm keyword - a logical value being TRUE of FALSE indicating whether NA values are removed before the mean is computed: This is the third argument, with the default value of being FALSE.

Lab Exercise

Try the following code and see what it gives to you. Can you explain why the result is what you observed?

mean(trim = 0, na.rm = T)
mean(my_data)
mean(my_data, trim = 0.2)
mean(my_data, trim = 0.2, na.rum = T)

R Basics - List

To create a “vector” mixed with different data types in R, we need to create a list using the list() function:

my_list <- list(student_name = c('James', 'Jane', 'Jack'), student_grade = c(79, 85, 91))

Here the first element in the list is a character vector, with the label student_name. The second element in the list is a double vector, with the label student_grade. To retrieve an element in a list, we usually use the $ along with the label.

my_list$student_name

## [1] "James" "Jane"  "Jack"

my_list$student_grade

## [1] 79 85 91