2 Descriptive Statistics

Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.

Descriptive statistics are typically distinguished from inferential statistics. With descriptive statistics you are simply describing what is or what the data shows. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what’s going on in our data.

2.1 Summary Statistics in R

We’ll use the dataset iris throughout this example. This dataset is imported by default in R, you only need to load it by running iris in the command line. Here, we load the iris dataset and rename it to df

df <- iris # This is a common name for a single data frame

2.1.1 Preview

Below, a preview of the dataset:

head(df) # first 6 observations

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa

2.1.2 Data Frame Structure

Below, a preview of the dataset’s structure:

str(df) # structure of a dataset

## '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 ...

2.1.3 Summary

To get the summary statistics for each column, you can use the summary function.

summary(df)

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

2.2 Plots

For this section, we are going to use Hadley Wickham’s ggplot2 package, which is a widely adopted library for plotting in R.
It uses an approach to plotting heavily inspired by Leland Wilkinson’s Grammar of Graphics.

2.2.1 Bar Chart

ggplot(data = df,
       mapping = aes(x = Species,
                     fill = Species)) +
  geom_bar()

2.3 Histogram

ggplot(data = df,
       mapping = aes(x = Sepal.Length)) +
  geom_histogram() +
  labs(
    title = "Histogram of Sepal Length",
    x = "Sepal Length"
  )

## `stat_bin()` using `bins = 30`. Pick better value with
## `binwidth`.

2.3.1 Density Function

ggplot(data = df,
       mapping = aes(x = Sepal.Length)) +
  geom_density(fill = "red",
               col = "red",
               alpha = .5) +
  labs(
    title = "Density of Sepal Length",
    x = "Sepal Length",
    y = "Probability"
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(hjust = .5,
                              face = "bold")
  )

2.3.2 Scatterplot

ggplot(data = df,
       mapping = aes(x = Sepal.Length,
                     y = Petal.Width,
                     col = Petal.Width)) +
  geom_point() +
  guides(col = "none")

2.3.3 Jitter Plot

A Jitter plot is simply a scatterplot with a certain offset.

ggplot(data = df,
       mapping = aes(x = Sepal.Length,
                     y = Petal.Width,
                     col = Petal.Width)) +
  geom_jitter() + #scatterplot with offset
  guides(col = "none")

2.3.4 Regression Line

We can add a regression line to the last jitter plot by adding a call to geom_smooth, as in:

ggplot(data = df,
       mapping = aes(x = Sepal.Length,
                     y = Petal.Width,
                     col = Petal.Width)) +
  geom_jitter() +
  geom_smooth(method = "lm",
              formula = y ~ x) + ## Simple Linear Regression, regressing y over x
  guides(col = "none")

There’s also a couple of things more that you can do, but this is just a template.