summary statistics

Look at summary statistics of a variable. There are two types of summary statistics: location (mean, median, mode) and range/scale (min, max, variance).

median(data$totalsal)

## [1] 59342

max(data$totalsal)

## [1] 819069

A summary statistic compresses all \(N\) observations you have into a single number. These numbers can be informative, but you lose information. Visualizing your data can often provide more insight that the summary statistics alone.

point plot

For one variable the most simple visualization is to just plot the raw data.

# plot each data point
ggplot(data=data) +
    geom_point(aes(x=totalsal, y=0)) +
    ylim(-10, 10)

jitter plot

One problem with the above plot is that data points lie on top of each other. A better version of this plot is a jitter plot

# same plot as above but with random y values
ggplot(data=data) +
    geom_jitter(aes(x=totalsal, y=0)) +
    ylim(-10, 10)

A jitter plot adds a small amount of random noise to the data so the points no longer overlap.

boxplot

A plot with all the data points has a lot of information in it. To gain insight it can be useful to compress the information. For example you might make a box plot.

ggplot(data=data) +
    geom_boxplot(aes(x=0, y=totalsal))

histogram

Or a histogram

ggplot(data=data) +
    geom_histogram(aes(x=totalsal), bins = 30)

binwidth

Histograms have an important parameter: the bin width (or equivalently the number of bins). ggplot2 defaults to 30 bins (divides the range of the data equally). Warning: histograms can look dramatically different depending on the binwidth. There is not necessarily one “correct” bin width. You should use a range of bin-widths and use your judgement.

This is probably too many bins

ggplot(data=data) +
    geom_histogram(aes(x=totalsal), bins = 10000)

Probably too few bins

ggplot(data=data) +
    geom_histogram(aes(x=totalsal), bins = 2)

A reasonable number of bins

ggplot(data=data) +
    geom_histogram(aes(x=totalsal), bins = 100)

Many data data are multimodal. Finding modes can be some of the most important discoveries. Setting the bin-width too wide will miss modes. Setting the bin-width too small will show modes that don’t exist.

This simulated data has two modes. Depending on the bin-width you might see one, two, three (or more?) modes. “Objectively” answering: is that mode really there is non-trivial (e.g. see SiZer)

set.seed(342)
mix <- tibble(val=c(rnorm(n=200, mean=0, sd=1), 
                  rnorm(n=200, mean=.5, sd=1)))

# wide binwidth
ggplot(data=mix) +
    geom_histogram(aes(x=val), bins = 10)

# moderate binwidth
ggplot(data=mix) +
    geom_histogram(aes(x=val), bins = 30)

# small binwidth
ggplot(data=mix) +
    geom_histogram(aes(x=val), bins = 100)

kernel density estimate

A histogram reduces your N data points into a discrete distribution. A Kernel Density Estimate(KDE) reduces your data to a continuous density.

# geom_density with its default values
ggplot(data=data) +
    geom_density(aes(x=totalsal), kernel="gaussian", adjust=1)

As with a histogram, a KDE as parameter(s) that control the level of data compression. You can read more about the details in the geom_density documentation or on Wikipedia. ggplot will use “smart defaults” but its worth playing around with this parameter. Warning: always be wary of “smart defaults”. No one default value will work well in every (or even a majority of) situations.

# geom_density with a fat window
ggplot(data=data) +
    geom_density(aes(x=totalsal), kernel="gaussian", adjust=10)

# geom_density with a skinny window
ggplot(data=data) +
    geom_density(aes(x=totalsal), kernel="gaussian", adjust=.1)

combining the plots

Best practice for exploratory analysis is to include the raw points with a histogram and/or KDE

ggplot(data=data) +
    geom_histogram(aes(x=totalsal), bins=100) +
    geom_point(aes(x=totalsal, y=0), shape='|', color='red') # use vertical points or jitter