Violin & Box Plots

Violin

There are a few ways of plotting the relationship between one quantitative and one qualitative variable, that demonstrate the data at different levels of abstraction. The violin plot is on the lower level of abstraction. For each level of the categorical variable, a distribution of the values on the numeric variable is plotted. The distribution is plotted as a kernel density estimate, something like a smoothed histogram. There is an extra section at the end of the previous lesson that provides more insight into kernel density estimates.

Seaborn's violinplot function can be used to create violin plots combined with box plots – we'll discuss box plots on the next page.

sb.violinplot(data = df, x = 'cat_var', y = 'num_var')

Here, you can see that the numeric data takes on a different shape in each categorical level: Some bimodality is suggested in group Alpha, a relatively high variance is observed in Beta, and Gamma and Delta are skewed negatively and positively, respectively. You can also see that each level has been rendered in a different color, like how the plain countplot was in the previous lesson. We can set the "color" parameter to make each curve the same color if it is not meaningful.

Inside each curve, there is a black shape with a white dot inside. This is the miniature box plot mentioned above. A further discussion of box plots will be performed on the next page. If you'd like to remove the box plot, you can set the inner = None parameter in the violinplot call to simplify the look of the final visualization.

base_color = sb.color_palette()[0]
sb.violinplot(data = df, x = 'cat_var', y = 'num_var', color = base_color,
              inner = None)

Additional Variation

Much like how the bar chart could be rendered with horizontal bars, the violin plot can also be rendered horizontally. Seaborn is smart enough to make an appropriate inference on which orientation is requested, depending on whether "x" or "y" receives the categorical variable. But if both variables are numeric (e.g., one is discretely-valued) then the "orient" parameter can be used to specify the plot orientation.

base_color = sb.color_palette()[0]
sb.violinplot(data = df, x = 'num_var', y = 'cat_var', color = base_color,
              inner = None)

Box

For explanatory data viz, boxplot is easier to understand quickly.

A box plot is another way of showing the relationship between a numeric variable and a categorical variable. Compared to the violin plot, the box plot leans more on summarization of the data, primarily just reporting a set of descriptive statistics for the numeric values on each categorical level. A box plot can be created using seaborn's boxplot function.

plt.figure(figsize = [10, 5])
base_color = sb.color_palette()[0]

# left plot: violin plot
plt.subplot(1, 2, 1)
ax1 = sb.violinplot(data = df, x = 'cat_var', y = 'num_var', color = base_color)

# right plot: box plot
plt.subplot(1, 2, 2)
sb.boxplot(data = df, x = 'cat_var', y = 'num_var', color = base_color)
plt.ylim(ax1.get_ylim()) # set y-axis limits to be same as left plot

Note that the "color" parameter is being used here to make each box the same color. In order to provide a better comparison of the violin and box plots, a ylim expression has been added to the second plot to match the two plots' y-axis limits. The Axes object returned by violinplot is assigned to a variable, ax1 is used to programmatically obtain those limit values.

(Documentation: Axes objects)

The inner boxes and lines in the violin plot match up with the boxes and whiskers in the box plot. In a box plot, the central line in the box indicates the median of the distribution, while the top and bottom of the box represent the third and first quartiles of the data, respectively. Thus, the height of the box is the interquartile range (IQR). From the top and bottom of the box, the whiskers indicate the range from the first or third quartiles to the minimum or maximum value in the distribution. Typically, a maximum range is set on whisker length; by default this is 1.5 times the IQR. For the Gamma level, there are points below the lower whisker that indicate individual outlier points that are more than 1.5 times the IQR below the first quartile.

Comparing the two plots, the box plot is a cleaner summary of the data than the violin plot. It's easier to compare statistics between the groups with a box plot. This makes a box plot worth more consideration if you have a lot of groups to compare, or if you are building explanatory plots. You can clearly see from the box plot that the Delta group has the lowest median. On the other hand, the box plot lacks as nuanced a depiction of distributions as the violin plot: you can't see the slight bimodality present in the Alpha level values. The violin plot may be a better option for exploration, especially since seaborn's implementation also includes the box plot by default.

Additional Variations

As with violinplot, boxplot can also render horizontal box plots by setting the numeric and categorical features to the appropriate arguments.

base_color = sb.color_palette()[0]
sb.boxplot(data = df, x = 'num_var', y = 'cat_var', color = base_color)

In violinplot, there is an additional option for plotting summary statistics in the violin, beyond the default mini box plot. By setting inner = 'quartile', three lines will be plotted within each violin area for the three middle quartiles. The line with thick dashes indicates the median, and the two lines with shorter dashes on either side the first and third quartiles.

base_color = sb.color_palette()[0]
sb.violinplot(data = df, x = 'cat_var', y = 'num_var', color = base_color,
              inner = 'quartile')