Draw a Double Box Plot Chart (2-Axes Box Plot; Box Plot Correlation Diagram) in Python

Question

I want to plot the distribution of two variables using box plot on both x and y axes. Examples of the kind of chart I am looking to obtain are available on this site but they are using R.

I am wondering if it is possible to obtain the same result in Python with matlplotlib.pyplot for example. The boxplot function doesn't seem to work for this kind of chart.

I tried something like this for two groups :

import matplotlib.pyplot as plt
x1 = [x11, x12, ..., x1n]
x2 = [x21, x22, ..., x2n]
y1 = [y11, y12, ..., y1n]
y2 = [y21, y22, ..., y2n]

data = [list(zip(x1,y1)), list(zip(x2,y2))]
fig, ax = plt.subplots()
ax.boxplot(data)

The results is the following one : Instead of something like this :

Answer 1

Here's a rough attempt at solving the problem using numpys percentile method and Rectangles and Line2Ds for the actual plotting:

from matplotlib import pyplot as plt
from matplotlib.patches import Rectangle
from matplotlib.lines import Line2D

import numpy as np

def boxplot_2d(x,y, ax, whis=1.5):
    xlimits = [np.percentile(x, q) for q in (25, 50, 75)]
    ylimits = [np.percentile(y, q) for q in (25, 50, 75)]

    ##the box
    box = Rectangle(
        (xlimits[0],ylimits[0]),
        (xlimits[2]-xlimits[0]),
        (ylimits[2]-ylimits[0]),
        ec = 'k',
        zorder=0
    )
    ax.add_patch(box)

    ##the x median
    vline = Line2D(
        [xlimits[1],xlimits[1]],[ylimits[0],ylimits[2]],
        color='k',
        zorder=1
    )
    ax.add_line(vline)

    ##the y median
    hline = Line2D(
        [xlimits[0],xlimits[2]],[ylimits[1],ylimits[1]],
        color='k',
        zorder=1
    )
    ax.add_line(hline)

    ##the central point
    ax.plot([xlimits[1]],[ylimits[1]], color='k', marker='o')

    ##the x-whisker
    ##defined as in matplotlib boxplot:
    ##As a float, determines the reach of the whiskers to the beyond the
    ##first and third quartiles. In other words, where IQR is the
    ##interquartile range (Q3-Q1), the upper whisker will extend to
    ##last datum less than Q3 + whis*IQR). Similarly, the lower whisker
    ####will extend to the first datum greater than Q1 - whis*IQR. Beyond
    ##the whiskers, data are considered outliers and are plotted as
    ##individual points. Set this to an unreasonably high value to force
    ##the whiskers to show the min and max values. Alternatively, set this
    ##to an ascending sequence of percentile (e.g., [5, 95]) to set the
    ##whiskers at specific percentiles of the data. Finally, whis can
    ##be the string 'range' to force the whiskers to the min and max of
    ##the data.
    iqr = xlimits[2]-xlimits[0]

    ##left
    left = np.min(x[x > xlimits[0]-whis*iqr])
    whisker_line = Line2D(
        [left, xlimits[0]], [ylimits[1],ylimits[1]],
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_line)
    whisker_bar = Line2D(
        [left, left], [ylimits[0],ylimits[2]],
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_bar)

    ##right
    right = np.max(x[x < xlimits[2]+whis*iqr])
    whisker_line = Line2D(
        [right, xlimits[2]], [ylimits[1],ylimits[1]],
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_line)
    whisker_bar = Line2D(
        [right, right], [ylimits[0],ylimits[2]],
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_bar)

    ##the y-whisker
    iqr = ylimits[2]-ylimits[0]

    ##bottom
    bottom = np.min(y[y > ylimits[0]-whis*iqr])
    whisker_line = Line2D(
        [xlimits[1],xlimits[1]], [bottom, ylimits[0]], 
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_line)
    whisker_bar = Line2D(
        [xlimits[0],xlimits[2]], [bottom, bottom], 
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_bar)

    ##top
    top = np.max(y[y < ylimits[2]+whis*iqr])
    whisker_line = Line2D(
        [xlimits[1],xlimits[1]], [top, ylimits[2]], 
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_line)
    whisker_bar = Line2D(
        [xlimits[0],xlimits[2]], [top, top], 
        color = 'k',
        zorder = 1
    )
    ax.add_line(whisker_bar)

    ##outliers
    mask = (x<left)|(x>right)|(y<bottom)|(y>top)
    ax.scatter(
        x[mask],y[mask],
        facecolors='none', edgecolors='k'
    )

#the figure and axes
fig,(ax1,ax2) = plt.subplots(ncols=2)

#some fake data
x = np.random.rand(1000)**2
y = np.sqrt(np.random.rand(1000))
#x = np.random.rand(1000)
#y = np.random.rand(1000)

#plotting the original data
ax1.scatter(x,y,c='r', s=1)

#doing the box plot
boxplot_2d(x,y,ax=ax2, whis=1)

plt.show()

This could of course still be made much nicer by allowing for keyword arguments that could then be forwarded to the Rectangle and Line2D calls. The final result looks something like this:

The left side shows the actual data as a scatter plot and the right side shows the resulting 2D box plot. Hope this helps.