13.7 The R Statistical Analysis Tool

R is a powerful tool for statistical analysis, offering versatile functions for data manipulation and visualization. It allows users to create vectors, perform basic statistical operations, and generate informative plots with ease.

R's data structures, like data frames and matrices, enable efficient organization of complex datasets. Custom functions and packages expand R's capabilities, making it a flexible platform for various statistical tasks and data science projects.

Introduction to R for Statistical Analysis

Vector creation in R

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• Vectors store multiple elements of the same data type in a one-dimensional array
  • Numeric vectors store numbers (1, 2.5, -3)
  • Character vectors store strings ("apple", "banana", "cherry")
  • Logical vectors store TRUE or FALSE values
• Create vectors using the

  [c()](https://www.fiveableKeyTerm:c())

  function to combine elements

  • x <- c(1, 2, 3, 4, 5)

    creates a numeric vector with values 1, 2, 3, 4, and 5

  • y <- c("a", "b", "c")

    creates a character vector with values "a", "b", and "c"
• Generate sequences of numbers using the

  :

  operator

  • z <- 1:10

    creates a numeric vector with values 1, 2, 3, ..., 10

  • seq(from = 0, to = 1, by = 0.1)

    creates a sequence from 0 to 1 in increments of 0.1
• Assign vectors to variables using the assignment operator

  <-

  • prices <- c(10.99, 15.50, 8.75)

    assigns the vector to the variable

    prices

Basic R commands for statistics

• length(x)

  returns the number of elements in vector

  x

• sum(x)

  calculates the sum of all elements in numeric vector

  x

• mean(x)

  calculates the arithmetic mean of numeric vector

  x

• median(x)

  calculates the median value of numeric vector

  x

• min(x)

  and

  max(x)

  return the minimum and maximum values in numeric vector

  x

• var(x)

  and

  sd(x)

  calculate the variance and standard deviation of numeric vector

  x

• summary(x)

  provides a summary of the distribution of vector

  x

  , including minimum, maximum, median, and quartile values
• Perform arithmetic operations on vectors element-wise

  • x + y

    adds corresponding elements of vectors

    x

    and

    y

  • x * 2

    multiplies each element of vector

    x

    by 2
• Subset vectors using logical operations based on conditions

  • x[x > 3]

    returns a vector containing only the elements of

    x

    greater than 3

  • y[y == "a"]

    returns a vector containing only the elements of

    y

    equal to "a"

Statistical plots with R functions

• Create basic scatter plots using the

  [plot()](https://www.fiveableKeyTerm:plot())

  function

  • plot(x, y)

    creates a scatter plot with

    x

    values on the x-axis and

    y

    values on the y-axis
  • Customize plots using arguments like

    main

    ,

    xlab

    ,

    ylab

    ,

    col

    ,

    pch

• Generate histograms of a numeric vector using the

  [hist()](https://www.fiveableKeyTerm:hist())

  function

  • hist(x)

    creates a histogram of the values in vector

    x

  • Adjust number of bins, colors, and labels with arguments like

    breaks

    ,

    col

    ,

    main

• Create box plots of a numeric vector or grouped by a factor variable using the

  [boxplot()](https://www.fiveableKeyTerm:boxplot())

  function

  • boxplot(x)

    creates a box plot of the values in vector

    x

  • boxplot(x ~ f)

    creates box plots of

    x

    grouped by the levels of factor

    f

• Arrange multiple plots in a grid using the

  [par()](https://www.fiveableKeyTerm:par())

  function with

  mfrow

  or

  mfcol

  argument

  • par(mfrow = c(2, 2))

    creates a 2x2 grid of plots
  • Subsequent plotting functions will fill the grid in row-wise or column-wise order

Data structures and functions in R

• Data frames are two-dimensional structures that can hold different types of data in columns
  • Create data frames using the

    data.frame()

    function
  • Access columns using the

    $

    operator or by name with square brackets
• Matrices are two-dimensional structures that hold data of the same type
  • Create matrices using the

    [matrix](https://www.fiveableKeyTerm:Matrix)()

    function or by combining vectors
• Factors are used to represent categorical data with predefined levels
  • Convert vectors to factors using the

    factor()

    function
• Functions are reusable blocks of code that perform specific tasks
  • Create custom functions using the

    function()

    keyword
• Packages extend R's functionality with additional functions and data sets
  • Install packages using

    install.packages()

    and load them with

    library()

• RStudio is an integrated development environment (IDE) for R that provides a user-friendly interface for coding, data analysis, and visualization