Understanding Histograms and Density Plots

[duttashi]

A collection of self curated notes to understand data visualization techniques.

[duttashi]

Feature to Look For Some things to keep an eye out for when looking at data on a numeric variable:

• skewness, multimodality
• gaps, outliers
• rounding, e.g. to integer values, or heaping, i.e. a few particular values occur very frequently
• impossible or suspicious value

Histograms

Histogram Basics

• Historams are constructed by binning the data and counting the number of observations in each bin.
• The objective is usually to visualize the shape of the distribution.
• The number of bins needs to be
  • large enough to reveal interesting features;
  • small enough not to be too noisy.
• A very small bin width can be used to look for rounding or heaping.
• Common choices for the vertical scale are
  • bin counts, or frequencies
  • counts per unit, or densities
• The count scale is more intepretable for lay viewers.
• The density scale is more suited for comparison to mathematical density models.
• Constructing histograms with unequal bin widths is possible but rarely a good idea.

Histograms in R There are many ways to plot histograms in R:

• the hist function in the base graphics package;
• truehist in package MASS
• histogram in package lattice
• geom_histogram in package ggplot2

Superimposing a Density A histogram can be used to compare the data distribution to a theoretical model, such as a normal distribution. This requires using a density scale for the vertical axis.

Density Plots

Density Plot Basics

• Density plots can be thought of as plots of smoothed histograms.
• The smoothness is controlled by a bandwidth parameter that is analogous to the histogram binwidth.
• Most density plots use a kernel density estimate, but there are other possible strategies; qualitatively the particular strategy rarely matters.

Using base graphics, a density plot of the geyser duration variable with default bandwidth plot(density(geyser$duration))

Grouping and Faceting Both ggplot and lattice make it easy to show multiple densities for different subgroups in a single plot. lattice uses the group argument.

library(lattice)
densityplot(~ yield | site, data = barley)

In ggplot you can map the group variable to an aesthetic, such as color: ggplot(barley) + geom_density(aes(x = yield, color = site)) Using fill and alpha can also be useful ggplot(barley) + geom_density(aes(x = yield, fill = site), alpha = 0.2)

Often a more effective approach is to use the idea of small multiples, collections of charts designed to facilitate comparisons. For this we can use the lattice package. Lattice uses the term lattice plots or trellis plots. These plots are specified using the | operator in a formula. densityplot(~ yield | site, data = barley) Comparison is facilitated by using common axes. These ideas can be combined: densityplot(~ yield | site, group = year, data = barley, auto.key = TRUE)

Whereas, ggplot uses the notion of faceting ggplot(barley) + geom_density(aes(x = yield)) + facet_wrap(~site) Again this can be combined with the color aesthetic: ggplot(barley) + geom_density(aes(x = yield, color = year)) + facet_wrap(~site)

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