

.. _sphx_glr_gallery_statistics_boxplot_demo.py:


========
Boxplots
========

Visualizing boxplots with matplotlib.

The following examples show off how to visualize boxplots with
Matplotlib. There are many options to control their appearance and
the statistics that they use to summarize the data.




.. code-block:: python

    import matplotlib.pyplot as plt
    import numpy as np
    from matplotlib.patches import Polygon


    # Fixing random state for reproducibility
    np.random.seed(19680801)

    # fake up some data
    spread = np.random.rand(50) * 100
    center = np.ones(25) * 50
    flier_high = np.random.rand(10) * 100 + 100
    flier_low = np.random.rand(10) * -100
    data = np.concatenate((spread, center, flier_high, flier_low), 0)

    fig, axs = plt.subplots(2, 3)

    # basic plot
    axs[0, 0].boxplot(data)
    axs[0, 0].set_title('basic plot')

    # notched plot
    axs[0, 1].boxplot(data, 1)
    axs[0, 1].set_title('notched plot')

    # change outlier point symbols
    axs[0, 2].boxplot(data, 0, 'gD')
    axs[0, 2].set_title('change outlier\npoint symbols')

    # don't show outlier points
    axs[1, 0].boxplot(data, 0, '')
    axs[1, 0].set_title("don't show\noutlier points")

    # horizontal boxes
    axs[1, 1].boxplot(data, 0, 'rs', 0)
    axs[1, 1].set_title('horizontal boxes')

    # change whisker length
    axs[1, 2].boxplot(data, 0, 'rs', 0, 0.75)
    axs[1, 2].set_title('change whisker length')

    fig.subplots_adjust(left=0.08, right=0.98, bottom=0.05, top=0.9,
                        hspace=0.4, wspace=0.3)

    # fake up some more data
    spread = np.random.rand(50) * 100
    center = np.ones(25) * 40
    flier_high = np.random.rand(10) * 100 + 100
    flier_low = np.random.rand(10) * -100
    d2 = np.concatenate((spread, center, flier_high, flier_low), 0)
    data.shape = (-1, 1)
    d2.shape = (-1, 1)
    # Making a 2-D array only works if all the columns are the
    # same length.  If they are not, then use a list instead.
    # This is actually more efficient because boxplot converts
    # a 2-D array into a list of vectors internally anyway.
    data = [data, d2, d2[::2, 0]]

    # Multiple box plots on one Axes
    fig, ax = plt.subplots()
    ax.boxplot(data)

    plt.show()





.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /gallery/statistics/images/sphx_glr_boxplot_demo_001.png
            :scale: 47

    *

      .. image:: /gallery/statistics/images/sphx_glr_boxplot_demo_002.png
            :scale: 47




Below we'll generate data from five different probability distributions,
each with different characteristics. We want to play with how an IID
bootstrap resample of the data preserves the distributional
properties of the original sample, and a boxplot is one visual tool
to make this assessment



.. code-block:: python


    numDists = 5
    randomDists = ['Normal(1,1)', ' Lognormal(1,1)', 'Exp(1)', 'Gumbel(6,4)',
                   'Triangular(2,9,11)']
    N = 500

    norm = np.random.normal(1, 1, N)
    logn = np.random.lognormal(1, 1, N)
    expo = np.random.exponential(1, N)
    gumb = np.random.gumbel(6, 4, N)
    tria = np.random.triangular(2, 9, 11, N)

    # Generate some random indices that we'll use to resample the original data
    # arrays. For code brevity, just use the same random indices for each array
    bootstrapIndices = np.random.random_integers(0, N - 1, N)
    normBoot = norm[bootstrapIndices]
    expoBoot = expo[bootstrapIndices]
    gumbBoot = gumb[bootstrapIndices]
    lognBoot = logn[bootstrapIndices]
    triaBoot = tria[bootstrapIndices]

    data = [norm, normBoot, logn, lognBoot, expo, expoBoot, gumb, gumbBoot,
            tria, triaBoot]

    fig, ax1 = plt.subplots(figsize=(10, 6))
    fig.canvas.set_window_title('A Boxplot Example')
    fig.subplots_adjust(left=0.075, right=0.95, top=0.9, bottom=0.25)

    bp = ax1.boxplot(data, notch=0, sym='+', vert=1, whis=1.5)
    plt.setp(bp['boxes'], color='black')
    plt.setp(bp['whiskers'], color='black')
    plt.setp(bp['fliers'], color='red', marker='+')

    # Add a horizontal grid to the plot, but make it very light in color
    # so we can use it for reading data values but not be distracting
    ax1.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',
                   alpha=0.5)

    # Hide these grid behind plot objects
    ax1.set_axisbelow(True)
    ax1.set_title('Comparison of IID Bootstrap Resampling Across Five Distributions')
    ax1.set_xlabel('Distribution')
    ax1.set_ylabel('Value')

    # Now fill the boxes with desired colors
    boxColors = ['darkkhaki', 'royalblue']
    numBoxes = numDists*2
    medians = list(range(numBoxes))
    for i in range(numBoxes):
        box = bp['boxes'][i]
        boxX = []
        boxY = []
        for j in range(5):
            boxX.append(box.get_xdata()[j])
            boxY.append(box.get_ydata()[j])
        boxCoords = list(zip(boxX, boxY))
        # Alternate between Dark Khaki and Royal Blue
        k = i % 2
        boxPolygon = Polygon(boxCoords, facecolor=boxColors[k])
        ax1.add_patch(boxPolygon)
        # Now draw the median lines back over what we just filled in
        med = bp['medians'][i]
        medianX = []
        medianY = []
        for j in range(2):
            medianX.append(med.get_xdata()[j])
            medianY.append(med.get_ydata()[j])
            ax1.plot(medianX, medianY, 'k')
            medians[i] = medianY[0]
        # Finally, overplot the sample averages, with horizontal alignment
        # in the center of each box
        ax1.plot([np.average(med.get_xdata())], [np.average(data[i])],
                 color='w', marker='*', markeredgecolor='k')

    # Set the axes ranges and axes labels
    ax1.set_xlim(0.5, numBoxes + 0.5)
    top = 40
    bottom = -5
    ax1.set_ylim(bottom, top)
    ax1.set_xticklabels(np.repeat(randomDists, 2),
                        rotation=45, fontsize=8)

    # Due to the Y-axis scale being different across samples, it can be
    # hard to compare differences in medians across the samples. Add upper
    # X-axis tick labels with the sample medians to aid in comparison
    # (just use two decimal places of precision)
    pos = np.arange(numBoxes) + 1
    upperLabels = [str(np.round(s, 2)) for s in medians]
    weights = ['bold', 'semibold']
    for tick, label in zip(range(numBoxes), ax1.get_xticklabels()):
        k = tick % 2
        ax1.text(pos[tick], top - (top*0.05), upperLabels[tick],
                 horizontalalignment='center', size='x-small', weight=weights[k],
                 color=boxColors[k])

    # Finally, add a basic legend
    fig.text(0.80, 0.08, str(N) + ' Random Numbers',
             backgroundcolor=boxColors[0], color='black', weight='roman',
             size='x-small')
    fig.text(0.80, 0.045, 'IID Bootstrap Resample',
             backgroundcolor=boxColors[1],
             color='white', weight='roman', size='x-small')
    fig.text(0.80, 0.015, '*', color='white', backgroundcolor='silver',
             weight='roman', size='medium')
    fig.text(0.815, 0.013, ' Average Value', color='black', weight='roman',
             size='x-small')

    plt.show()




.. image:: /gallery/statistics/images/sphx_glr_boxplot_demo_003.png
    :align: center




Here we write a custom function to bootstrap confidence intervals.
We can then use the boxplot along with this function to show these intervals.



.. code-block:: python



    def fakeBootStrapper(n):
        '''
        This is just a placeholder for the user's method of
        bootstrapping the median and its confidence intervals.

        Returns an arbitrary median and confidence intervals
        packed into a tuple
        '''
        if n == 1:
            med = 0.1
            CI = (-0.25, 0.25)
        else:
            med = 0.2
            CI = (-0.35, 0.50)

        return med, CI

    inc = 0.1
    e1 = np.random.normal(0, 1, size=(500,))
    e2 = np.random.normal(0, 1, size=(500,))
    e3 = np.random.normal(0, 1 + inc, size=(500,))
    e4 = np.random.normal(0, 1 + 2*inc, size=(500,))

    treatments = [e1, e2, e3, e4]
    med1, CI1 = fakeBootStrapper(1)
    med2, CI2 = fakeBootStrapper(2)
    medians = [None, None, med1, med2]
    conf_intervals = [None, None, CI1, CI2]

    fig, ax = plt.subplots()
    pos = np.array(range(len(treatments))) + 1
    bp = ax.boxplot(treatments, sym='k+', positions=pos,
                    notch=1, bootstrap=5000,
                    usermedians=medians,
                    conf_intervals=conf_intervals)

    ax.set_xlabel('treatment')
    ax.set_ylabel('response')
    plt.setp(bp['whiskers'], color='k', linestyle='-')
    plt.setp(bp['fliers'], markersize=3.0)
    plt.show()



.. image:: /gallery/statistics/images/sphx_glr_boxplot_demo_004.png
    :align: center




**Total running time of the script:** ( 0 minutes  0.723 seconds)



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     :download:`Download Python source code: boxplot_demo.py <boxplot_demo.py>`



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     :download:`Download Jupyter notebook: boxplot_demo.ipynb <boxplot_demo.ipynb>`

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