1 Setup

library(tibble)           # special type of data frame
library(magrittr)         # pipes
library(dplyr)            # data manipulation
library(ggplot2)          # pretty plots
library(tidyr)            # reshape data frames; mostly for ggplots

2 Introduction

This is a very simple streamlined set of exmple code to describe some basic summary statistics and graphs to facilitate preliminary data exploration.

3 The Iris Data Set

We will be using a few data sets during the course, one of the classic statistical learning data sets is the iris data set which comes with any standard installation of R. This famous (Fisher’s or Anderson’s) iris data set gives the measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for 50 flowers from each of 3 species of iris. The species are Iris setosa, versicolor, and virginica.

?iris        # open help file for the object
dim(iris)        # get dimensions of data

[1] 150   5

class(iris)  # a data frame class object

[1] "data.frame"

The first goal for any analysis is to understand the dimensions and structure of the data set you are working with. Here are some simple commands to understand the general structure of your data set, typically in the form of a data.frame (or nowadays tibble) class object:

dim(iris)            # dimensions (rows, columns)

[1] 150   5

str(iris)            # structure of the data frame object

'data.frame':   150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

iris[1:5, ]          # echo the first 5 rows

names(iris)          # what are the column names

[1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"     

sapply(iris, class)  # what are the classes of each column (very important!); feature vs. class data

Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species 
   "numeric"    "numeric"    "numeric"    "numeric"     "factor" 

table(iris$Species)  # once you know which column contains the classes, what are the class counts?

    setosa versicolor  virginica 
        50         50         50 

The summary function is a special class of generic functions (called S3) that perform specific operations depending on the class object they are performing on … in this case a data.frame class object. The default is to summarize the columns, reporting a different summary for each:

summary(iris)

  Sepal.Length    Sepal.Width     Petal.Length    Petal.Width          Species  
 Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100   setosa    :50  
 1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300   versicolor:50  
 Median :5.800   Median :3.000   Median :4.350   Median :1.300   virginica :50  
 Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199                  
 3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800                  
 Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500                  

However, it is often more useful from a classification perspective to know the feature means by class, which can be accomplished via the tapply function:

sapply(iris[, -5], function(x)
  tapply(x, iris$Species, mean))   # feature means split by Species

           Sepal.Length Sepal.Width Petal.Length Petal.Width
setosa            5.006       3.428        1.462       0.246
versicolor        5.936       2.770        4.260       1.326
virginica         6.588       2.974        5.552       2.026

There is a new syntax that has become quite popular in recent years, referred to simply as tidy data analysis, spearheaded by Hadley Wickham. Here is how you would get to the same answer using this syntax:

iris %>% 
  tibble::as.tibble() %>%    # make 'iris' a `tibble` data frame
  dplyr::group_by(Species) %>%
  dplyr::summarise_all(funs(mean))

4 Splitting Data

All of the following commands produce exactly the same output:

split(iris$Sepal.Length, iris$Species)

$setosa
 [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1 5.7 5.1 5.4 5.1 4.6
[24] 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8
[47] 5.1 4.6 5.3 5.0

$versicolor
 [1] 7.0 6.4 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1 6.3
[24] 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5 5.5 6.1 5.8 5.0 5.6 5.7
[47] 5.7 6.2 5.1 5.7

$virginica
 [1] 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.0 6.9 5.6 7.7
[24] 6.3 6.7 7.2 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8 6.7 6.7
[47] 6.3 6.5 6.2 5.9

split(iris[["Sepal.Length"]], iris$Species)

$setosa
 [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1 5.7 5.1 5.4 5.1 4.6
[24] 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8
[47] 5.1 4.6 5.3 5.0

$versicolor
 [1] 7.0 6.4 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1 6.3
[24] 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5 5.5 6.1 5.8 5.0 5.6 5.7
[47] 5.7 6.2 5.1 5.7

$virginica
 [1] 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.0 6.9 5.6 7.7
[24] 6.3 6.7 7.2 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8 6.7 6.7
[47] 6.3 6.5 6.2 5.9

split(iris[[1L]], iris$Species)

$setosa
 [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1 5.7 5.1 5.4 5.1 4.6
[24] 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8
[47] 5.1 4.6 5.3 5.0

$versicolor
 [1] 7.0 6.4 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1 6.3
[24] 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5 5.5 6.1 5.8 5.0 5.6 5.7
[47] 5.7 6.2 5.1 5.7

$virginica
 [1] 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.0 6.9 5.6 7.7
[24] 6.3 6.7 7.2 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8 6.7 6.7
[47] 6.3 6.5 6.2 5.9

split(iris[[which(names(iris) == "Sepal.Length")]], iris$Species)

$setosa
 [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1 5.7 5.1 5.4 5.1 4.6
[24] 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8
[47] 5.1 4.6 5.3 5.0

$versicolor
 [1] 7.0 6.4 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1 6.3
[24] 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5 5.5 6.1 5.8 5.0 5.6 5.7
[47] 5.7 6.2 5.1 5.7

$virginica
 [1] 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.0 6.9 5.6 7.7
[24] 6.3 6.7 7.2 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8 6.7 6.7
[47] 6.3 6.5 6.2 5.9

split(iris, iris$Species)

5 Plotting

par(mfrow = c(2, 2))                          # make 2x2 grid for plots
par(mgp = c(2, 0.75, 0), mar = c(3, 4, 3, 1)) # graphics settings; squeeze margins
purrr::walk(names(iris)[-5], function(class)  # purrr::walk() suppresses output; side effects only
  boxplot(split(iris[[class]], iris$Species), main = class, col = 1:3))

6 Plotting via ggplot2

df <- iris %>% 
  tidyr::gather(key = "Feature", value = "cm", -Species) %>%  # re-arrange to long format
  dplyr::mutate(Feature = gsub("\\.", " ", Feature)) %>%   # remove dot in name
  tibble::as.tibble()     # make tibble for easy viewing

df

df %>% 
ggplot(aes(y = cm, x = Species, fill = Species)) +
  geom_boxplot(color = "#1F3552", alpha = 0.75, size = 0.5) +
  scale_x_discrete(name = "Species") +
  ggtitle("Overall Title") +
  theme(plot.title = element_text(hjust = 0.5)) +
  facet_wrap(~Feature, ncol = 2) 

7 Pairwise plots

Very useful for visually inspecting variables for patterns of interest. You will typically need to know your outcome of interest a priori, i.e. supervised analysis, or you will not know how to color the points.

plot(iris[, -5], col = iris$Species)

iris %>% 
  ggplot(aes(x = Sepal.Length, y = Sepal.Width, color = Species)) +
    geom_point(alpha = 0.5, size = 2.5) +
    ggtitle("Title Goes Here") +
    # this is a useful trick; add `NULL` as last line
    # you then don't need to manage the `+` signs above when building the layers
    NULL  

Created on 2018-09-03 by the Rmarkdown package (v1.10) and R version 3.5.1 (2018-07-02).