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matplotlib & pandas
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Python/matplotlab/gallery/statistics/boxplot_demo.md
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Python/matplotlab/gallery/statistics/boxplot_demo.md
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# 箱形图
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用matplotlib可视化箱形图。
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以下示例展示了如何使用Matplotlib可视化箱图。有许多选项可以控制它们的外观以及用于汇总数据的统计信息。
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```python
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import matplotlib.pyplot as plt
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import numpy as np
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from matplotlib.patches import Polygon
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# Fixing random state for reproducibility
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np.random.seed(19680801)
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# fake up some data
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spread = np.random.rand(50) * 100
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center = np.ones(25) * 50
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flier_high = np.random.rand(10) * 100 + 100
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flier_low = np.random.rand(10) * -100
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data = np.concatenate((spread, center, flier_high, flier_low))
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fig, axs = plt.subplots(2, 3)
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# basic plot
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axs[0, 0].boxplot(data)
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axs[0, 0].set_title('basic plot')
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# notched plot
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axs[0, 1].boxplot(data, 1)
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axs[0, 1].set_title('notched plot')
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# change outlier point symbols
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axs[0, 2].boxplot(data, 0, 'gD')
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axs[0, 2].set_title('change outlier\npoint symbols')
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# don't show outlier points
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axs[1, 0].boxplot(data, 0, '')
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axs[1, 0].set_title("don't show\noutlier points")
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# horizontal boxes
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axs[1, 1].boxplot(data, 0, 'rs', 0)
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axs[1, 1].set_title('horizontal boxes')
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# change whisker length
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axs[1, 2].boxplot(data, 0, 'rs', 0, 0.75)
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axs[1, 2].set_title('change whisker length')
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fig.subplots_adjust(left=0.08, right=0.98, bottom=0.05, top=0.9,
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hspace=0.4, wspace=0.3)
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# fake up some more data
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spread = np.random.rand(50) * 100
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center = np.ones(25) * 40
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flier_high = np.random.rand(10) * 100 + 100
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flier_low = np.random.rand(10) * -100
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d2 = np.concatenate((spread, center, flier_high, flier_low))
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data.shape = (-1, 1)
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d2.shape = (-1, 1)
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# Making a 2-D array only works if all the columns are the
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# same length. If they are not, then use a list instead.
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# This is actually more efficient because boxplot converts
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# a 2-D array into a list of vectors internally anyway.
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data = [data, d2, d2[::2, 0]]
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# Multiple box plots on one Axes
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fig, ax = plt.subplots()
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ax.boxplot(data)
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plt.show()
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```
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下面我们将从五个不同的概率分布生成数据，每个概率分布具有不同的特征。 我们想要了解数据的IID引导程序重采样如何保留原始样本的分布属性，并且箱形图是进行此评估的一种可视化工具。
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```python
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numDists = 5
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randomDists = ['Normal(1,1)', ' Lognormal(1,1)', 'Exp(1)', 'Gumbel(6,4)',
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'Triangular(2,9,11)']
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N = 500
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norm = np.random.normal(1, 1, N)
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logn = np.random.lognormal(1, 1, N)
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expo = np.random.exponential(1, N)
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gumb = np.random.gumbel(6, 4, N)
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tria = np.random.triangular(2, 9, 11, N)
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# Generate some random indices that we'll use to resample the original data
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# arrays. For code brevity, just use the same random indices for each array
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bootstrapIndices = np.random.random_integers(0, N - 1, N)
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normBoot = norm[bootstrapIndices]
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expoBoot = expo[bootstrapIndices]
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gumbBoot = gumb[bootstrapIndices]
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lognBoot = logn[bootstrapIndices]
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triaBoot = tria[bootstrapIndices]
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data = [norm, normBoot, logn, lognBoot, expo, expoBoot, gumb, gumbBoot,
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tria, triaBoot]
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fig, ax1 = plt.subplots(figsize=(10, 6))
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fig.canvas.set_window_title('A Boxplot Example')
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fig.subplots_adjust(left=0.075, right=0.95, top=0.9, bottom=0.25)
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bp = ax1.boxplot(data, notch=0, sym='+', vert=1, whis=1.5)
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plt.setp(bp['boxes'], color='black')
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plt.setp(bp['whiskers'], color='black')
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plt.setp(bp['fliers'], color='red', marker='+')
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# Add a horizontal grid to the plot, but make it very light in color
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# so we can use it for reading data values but not be distracting
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ax1.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',
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alpha=0.5)
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# Hide these grid behind plot objects
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ax1.set_axisbelow(True)
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ax1.set_title('Comparison of IID Bootstrap Resampling Across Five Distributions')
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ax1.set_xlabel('Distribution')
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ax1.set_ylabel('Value')
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# Now fill the boxes with desired colors
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boxColors = ['darkkhaki', 'royalblue']
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numBoxes = numDists*2
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medians = list(range(numBoxes))
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for i in range(numBoxes):
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box = bp['boxes'][i]
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boxX = []
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boxY = []
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for j in range(5):
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boxX.append(box.get_xdata()[j])
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boxY.append(box.get_ydata()[j])
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boxCoords = np.column_stack([boxX, boxY])
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# Alternate between Dark Khaki and Royal Blue
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k = i % 2
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boxPolygon = Polygon(boxCoords, facecolor=boxColors[k])
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ax1.add_patch(boxPolygon)
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# Now draw the median lines back over what we just filled in
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med = bp['medians'][i]
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medianX = []
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medianY = []
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for j in range(2):
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medianX.append(med.get_xdata()[j])
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medianY.append(med.get_ydata()[j])
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ax1.plot(medianX, medianY, 'k')
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medians[i] = medianY[0]
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# Finally, overplot the sample averages, with horizontal alignment
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# in the center of each box
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ax1.plot([np.average(med.get_xdata())], [np.average(data[i])],
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color='w', marker='*', markeredgecolor='k')
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# Set the axes ranges and axes labels
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ax1.set_xlim(0.5, numBoxes + 0.5)
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top = 40
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bottom = -5
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ax1.set_ylim(bottom, top)
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ax1.set_xticklabels(np.repeat(randomDists, 2),
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rotation=45, fontsize=8)
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# Due to the Y-axis scale being different across samples, it can be
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# hard to compare differences in medians across the samples. Add upper
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# X-axis tick labels with the sample medians to aid in comparison
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# (just use two decimal places of precision)
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pos = np.arange(numBoxes) + 1
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upperLabels = [str(np.round(s, 2)) for s in medians]
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weights = ['bold', 'semibold']
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for tick, label in zip(range(numBoxes), ax1.get_xticklabels()):
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k = tick % 2
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ax1.text(pos[tick], top - (top*0.05), upperLabels[tick],
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horizontalalignment='center', size='x-small', weight=weights[k],
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color=boxColors[k])
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# Finally, add a basic legend
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fig.text(0.80, 0.08, str(N) + ' Random Numbers',
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backgroundcolor=boxColors[0], color='black', weight='roman',
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size='x-small')
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fig.text(0.80, 0.045, 'IID Bootstrap Resample',
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backgroundcolor=boxColors[1],
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color='white', weight='roman', size='x-small')
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fig.text(0.80, 0.015, '*', color='white', backgroundcolor='silver',
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weight='roman', size='medium')
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fig.text(0.815, 0.013, ' Average Value', color='black', weight='roman',
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size='x-small')
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plt.show()
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```
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在这里，我们编写一个自定义函数来引导置信区间。然后我们可以使用boxplot和此函数来显示这些间隔。
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```python
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def fakeBootStrapper(n):
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'''
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This is just a placeholder for the user's method of
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bootstrapping the median and its confidence intervals.
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Returns an arbitrary median and confidence intervals
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packed into a tuple
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'''
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if n == 1:
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med = 0.1
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CI = (-0.25, 0.25)
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else:
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med = 0.2
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CI = (-0.35, 0.50)
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return med, CI
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inc = 0.1
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e1 = np.random.normal(0, 1, size=(500,))
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e2 = np.random.normal(0, 1, size=(500,))
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e3 = np.random.normal(0, 1 + inc, size=(500,))
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e4 = np.random.normal(0, 1 + 2*inc, size=(500,))
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treatments = [e1, e2, e3, e4]
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med1, CI1 = fakeBootStrapper(1)
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med2, CI2 = fakeBootStrapper(2)
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medians = [None, None, med1, med2]
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conf_intervals = [None, None, CI1, CI2]
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fig, ax = plt.subplots()
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pos = np.array(range(len(treatments))) + 1
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bp = ax.boxplot(treatments, sym='k+', positions=pos,
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notch=1, bootstrap=5000,
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usermedians=medians,
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conf_intervals=conf_intervals)
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ax.set_xlabel('treatment')
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ax.set_ylabel('response')
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plt.setp(bp['whiskers'], color='k', linestyle='-')
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plt.setp(bp['fliers'], markersize=3.0)
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plt.show()
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```
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## 下载这个示例
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- [下载python源码: boxplot_demo.py](https://matplotlib.org/_downloads/boxplot_demo.py)
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- [下载Jupyter notebook: boxplot_demo.ipynb](https://matplotlib.org/_downloads/boxplot_demo.ipynb)
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