seaborn

Python Data Science Handbook

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This is an excerpt from the Python Data Science Handbook by Jake VanderPlas; Jupyter notebooks are available on GitHub.

The text is released under the CC-BY-NC-ND license, and code is released under the MIT license. If you find this content useful, please consider supporting the work by buying the book!

Visualization with Seaborn

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< Geographic Data with Basemap | Contents | Further Resources >

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Matplotlib has proven to be an incredibly useful and popular visualization tool, but even avid users will admit it often leaves much to be desired. There are several valid complaints about Matplotlib that often come up:

Prior to version 2.0, Matplotlib's defaults are not exactly the best choices. It was based off of MATLAB circa 1999, and this often shows.
Matplotlib's API is relatively low level. Doing sophisticated statistical visualization is possible, but often requires a lot of boilerplate code.
Matplotlib predated Pandas by more than a decade, and thus is not designed for use with Pandas DataFrames. In order to visualize data from a Pandas DataFrame, you must extract each Series and often concatenate them together into the right format. It would be nicer to have a plotting library that can intelligently use the DataFrame labels in a plot.

An answer to these problems is Seaborn. Seaborn provides an API on top of Matplotlib that offers sane choices for plot style and color defaults, defines simple high-level functions for common statistical plot types, and integrates with the functionality provided by Pandas DataFrames.

To be fair, the Matplotlib team is addressing this: it has recently added the plt.style tools discussed in Customizing Matplotlib: Configurations and Style Sheets, and is starting to handle Pandas data more seamlessly. The 2.0 release of the library will include a new default stylesheet that will improve on the current status quo. But for all the reasons just discussed, Seaborn remains an extremely useful addon.

Seaborn Versus Matplotlib

Here is an example of a simple random-walk plot in Matplotlib, using its classic plot formatting and colors. We start with the typical imports:

In [1]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">import matplotlib.pyplot as plt
plt.style.use('classic')
%matplotlib inline
import numpy as np
import pandas as pd
</pre>

Now we create some random walk data:

In [2]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;"># Create some data
rng = np.random.RandomState(0)
x = np.linspace(0, 10, 500)
y = np.cumsum(rng.randn(500, 6), 0)
</pre>

And do a simple plot:

In [3]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;"># Plot the data with Matplotlib defaults
plt.plot(x, y)
plt.legend('ABCDEF', ncol=2, loc='upper left');
</pre>

[图片上传中...(image-54c657-1543748931675-22)]

Although the result contains all the information we'd like it to convey, it does so in a way that is not all that aesthetically pleasing, and even looks a bit old-fashioned in the context of 21st-century data visualization.

Now let's take a look at how it works with Seaborn. As we will see, Seaborn has many of its own high-level plotting routines, but it can also overwrite Matplotlib's default parameters and in turn get even simple Matplotlib scripts to produce vastly superior output. We can set the style by calling Seaborn's set() method. By convention, Seaborn is imported as sns:

In [4]:

Now let's rerun the same two lines as before:

In [5]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;"># same plotting code as above!
plt.plot(x, y)
plt.legend('ABCDEF', ncol=2, loc='upper left');
</pre>

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Ah, much better!

Exploring Seaborn Plots

The main idea of Seaborn is that it provides high-level commands to create a variety of plot types useful for statistical data exploration, and even some statistical model fitting.

Let's take a look at a few of the datasets and plot types available in Seaborn. Note that all of the following could be done using raw Matplotlib commands (this is, in fact, what Seaborn does under the hood) but the Seaborn API is much more convenient.

Histograms, KDE, and densities

Often in statistical data visualization, all you want is to plot histograms and joint distributions of variables. We have seen that this is relatively straightforward in Matplotlib:

In [6]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">data = np.random.multivariate_normal([0, 0], [[5, 2], [2, 2]], size=2000)
data = pd.DataFrame(data, columns=['x', 'y'])

for col in 'xy':
plt.hist(data[col], normed=True, alpha=0.5)
</pre>

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Rather than a histogram, we can get a smooth estimate of the distribution using a kernel density estimation, which Seaborn does with sns.kdeplot:

In [7]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">for col in 'xy':
sns.kdeplot(data[col], shade=True)
</pre>

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Histograms and KDE can be combined using distplot:

In [8]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">sns.distplot(data['x'])
sns.distplot(data['y']);
</pre>

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If we pass the full two-dimensional dataset to kdeplot, we will get a two-dimensional visualization of the data:

In [9]:

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We can see the joint distribution and the marginal distributions together using sns.jointplot. For this plot, we'll set the style to a white background:

In [10]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">with sns.axes_style('white'):
sns.jointplot("x", "y", data, kind='kde');
</pre>

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There are other parameters that can be passed to jointplot—for example, we can use a hexagonally based histogram instead:

In [11]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">with sns.axes_style('white'):
sns.jointplot("x", "y", data, kind='hex')
</pre>

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Pair plots

When you generalize joint plots to datasets of larger dimensions, you end up with pair plots. This is very useful for exploring correlations between multidimensional data, when you'd like to plot all pairs of values against each other.

We'll demo this with the well-known Iris dataset, which lists measurements of petals and sepals of three iris species:

In [12]:

Out[12]:

	sepal_length	sepal_width	petal_length	petal_width	species
0	5.1	3.5	1.4	0.2	setosa
1	4.9	3.0	1.4	0.2	setosa
2	4.7	3.2	1.3	0.2	setosa
3	4.6	3.1	1.5	0.2	setosa
4	5.0	3.6	1.4	0.2	setosa

Visualizing the multidimensional relationships among the samples is as easy as calling sns.pairplot:

In [13]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">sns.pairplot(iris, hue='species', size=2.5);
</pre>

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Faceted histograms

Sometimes the best way to view data is via histograms of subsets. Seaborn's FacetGrid makes this extremely simple. We'll take a look at some data that shows the amount that restaurant staff receive in tips based on various indicator data:

In [14]:

Out[14]:

	total_bill	tip	sex	smoker	day	time	size
0	16.99	1.01	Female	No	Sun	Dinner	2
1	10.34	1.66	Male	No	Sun	Dinner	3
2	21.01	3.50	Male	No	Sun	Dinner	3
3	23.68	3.31	Male	No	Sun	Dinner	2
4	24.59	3.61	Female	No	Sun	Dinner	4

In [15]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">tips['tip_pct'] = 100 * tips['tip'] / tips['total_bill']

grid = sns.FacetGrid(tips, row="sex", col="time", margin_titles=True)
grid.map(plt.hist, "tip_pct", bins=np.linspace(0, 40, 15));
</pre>

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Factor plots

Factor plots can be useful for this kind of visualization as well. This allows you to view the distribution of a parameter within bins defined by any other parameter:

In [16]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">with sns.axes_style(style='ticks'):
g = sns.factorplot("day", "total_bill", "sex", data=tips, kind="box")
g.set_axis_labels("Day", "Total Bill");
</pre>

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Joint distributions

Similar to the pairplot we saw earlier, we can use sns.jointplot to show the joint distribution between different datasets, along with the associated marginal distributions:

In [17]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">with sns.axes_style('white'):
sns.jointplot("total_bill", "tip", data=tips, kind='hex')
</pre>

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The joint plot can even do some automatic kernel density estimation and regression:

In [18]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">sns.jointplot("total_bill", "tip", data=tips, kind='reg');
</pre>

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Bar plots

Time series can be plotted using sns.factorplot. In the following example, we'll use the Planets data that we first saw in Aggregation and Grouping:

In [19]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">planets = sns.load_dataset('planets')
planets.head()
</pre>

Out[19]:

	method	number	orbital_period	mass	distance	year
0	Radial Velocity	1	269.300	7.10	77.40	2006
1	Radial Velocity	1	874.774	2.21	56.95	2008
2	Radial Velocity	1	763.000	2.60	19.84	2011
3	Radial Velocity	1	326.030	19.40	110.62	2007
4	Radial Velocity	1	516.220	10.50	119.47	2009

In [20]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">with sns.axes_style('white'):
g = sns.factorplot("year", data=planets, aspect=2,
kind="count", color='steelblue')
g.set_xticklabels(step=5)
</pre>

[图片上传中...(image-ce7061-1543748931674-9)]

We can learn more by looking at the method of discovery of each of these planets:

In [21]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">with sns.axes_style('white'):
g = sns.factorplot("year", data=planets, aspect=4.0, kind='count',
hue='method', order=range(2001, 2015))
g.set_ylabels('Number of Planets Discovered')
</pre>

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For more information on plotting with Seaborn, see the Seaborn documentation, a tutorial, and the Seaborn gallery.

Example: Exploring Marathon Finishing Times

Here we'll look at using Seaborn to help visualize and understand finishing results from a marathon. I've scraped the data from sources on the Web, aggregated it and removed any identifying information, and put it on GitHub where it can be downloaded (if you are interested in using Python for web scraping, I would recommend Web Scraping with Python by Ryan Mitchell). We will start by downloading the data from the Web, and loading it into Pandas:

In [22]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;"># !curl -O https://raw.githubusercontent.com/jakevdp/marathon-data/master/marathon-data.csv
</pre>

In [23]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">data = pd.read_csv('marathon-data.csv')
data.head()
</pre>

Out[23]:

	age	gender	split	final
0	33	M	01:05:38	02:08:51
1	32	M	01:06:26	02:09:28
2	31	M	01:06:49	02:10:42
3	38	M	01:06:16	02:13:45
4	31	M	01:06:32	02:13:59

By default, Pandas loaded the time columns as Python strings (type object); we can see this by looking at the dtypes attribute of the DataFrame:

In [24]:

Out[24]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: black; word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: 0px; border-radius: 0px; vertical-align: baseline;">age int64
gender object
split object
final object
dtype: object</pre>

Let's fix this by providing a converter for the times:

In [25]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">def convert_time(s):
h, m, s = map(int, s.split(':'))
return pd.datetools.timedelta(hours=h, minutes=m, seconds=s)

data = pd.read_csv('marathon-data.csv',
converters={'split':convert_time, 'final':convert_time})
data.head()
</pre>

Out[25]:

	age	gender	split	final
0	33	M	01:05:38	02:08:51
1	32	M	01:06:26	02:09:28
2	31	M	01:06:49	02:10:42
3	38	M	01:06:16	02:13:45
4	31	M	01:06:32	02:13:59

In [26]:

Out[26]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: black; word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: 0px; border-radius: 0px; vertical-align: baseline;">age int64
gender object
split timedelta64[ns]
final timedelta64[ns]
dtype: object</pre>

That looks much better. For the purpose of our Seaborn plotting utilities, let's next add columns that give the times in seconds:

In [27]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">data['split_sec'] = data['split'].astype(int) / 1E9
data['final_sec'] = data['final'].astype(int) / 1E9
data.head()
</pre>

Out[27]:

	age	gender	split	final	split_sec	final_sec
0	33	M	01:05:38	02:08:51	3938.0	7731.0
1	32	M	01:06:26	02:09:28	3986.0	7768.0
2	31	M	01:06:49	02:10:42	4009.0	7842.0
3	38	M	01:06:16	02:13:45	3976.0	8025.0
4	31	M	01:06:32	02:13:59	3992.0	8039.0

To get an idea of what the data looks like, we can plot a jointplot over the data:

In [28]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">with sns.axes_style('white'):
g = sns.jointplot("split_sec", "final_sec", data, kind='hex')
g.ax_joint.plot(np.linspace(4000, 16000),
np.linspace(8000, 32000), ':k')
</pre>

[图片上传中...(image-87fe97-1543748931673-7)]

The dotted line shows where someone's time would lie if they ran the marathon at a perfectly steady pace. The fact that the distribution lies above this indicates (as you might expect) that most people slow down over the course of the marathon. If you have run competitively, you'll know that those who do the opposite—run faster during the second half of the race—are said to have "negative-split" the race.

Let's create another column in the data, the split fraction, which measures the degree to which each runner negative-splits or positive-splits the race:

In [29]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">data['split_frac'] = 1 - 2 * data['split_sec'] / data['final_sec']
data.head()
</pre>

Out[29]:

	age	gender	split	final	split_sec	final_sec	split_frac
0	33	M	01:05:38	02:08:51	3938.0	7731.0	-0.018756
1	32	M	01:06:26	02:09:28	3986.0	7768.0	-0.026262
2	31	M	01:06:49	02:10:42	4009.0	7842.0	-0.022443
3	38	M	01:06:16	02:13:45	3976.0	8025.0	0.009097
4	31	M	01:06:32	02:13:59	3992.0	8039.0	0.006842

Where this split difference is less than zero, the person negative-split the race by that fraction. Let's do a distribution plot of this split fraction:

In [30]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">sns.distplot(data['split_frac'], kde=False);
plt.axvline(0, color="k", linestyle="--");
</pre>

[图片上传中...(image-8f5d6a-1543748931673-6)]

In [31]:

Out[31]:

Out of nearly 40,000 participants, there were only 250 people who negative-split their marathon.

Let's see whether there is any correlation between this split fraction and other variables. We'll do this using a pairgrid, which draws plots of all these correlations:

In [32]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">g = sns.PairGrid(data, vars=['age', 'split_sec', 'final_sec', 'split_frac'],
hue='gender', palette='RdBu_r')
g.map(plt.scatter, alpha=0.8)
g.add_legend();
</pre>

[图片上传中...(image-f67ccc-1543748931673-5)]

It looks like the split fraction does not correlate particularly with age, but does correlate with the final time: faster runners tend to have closer to even splits on their marathon time. (We see here that Seaborn is no panacea for Matplotlib's ills when it comes to plot styles: in particular, the x-axis labels overlap. Because the output is a simple Matplotlib plot, however, the methods in Customizing Ticks can be used to adjust such things if desired.)

The difference between men and women here is interesting. Let's look at the histogram of split fractions for these two groups:

In [33]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">sns.kdeplot(data.split_frac[data.gender=='M'], label='men', shade=True)
sns.kdeplot(data.split_frac[data.gender=='W'], label='women', shade=True)
plt.xlabel('split_frac');
</pre>

[图片上传中...(image-6dfc69-1543748931673-4)]

The interesting thing here is that there are many more men than women who are running close to an even split! This almost looks like some kind of bimodal distribution among the men and women. Let's see if we can suss-out what's going on by looking at the distributions as a function of age.

A nice way to compare distributions is to use a violin plot

In [34]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">sns.violinplot("gender", "split_frac", data=data,
palette=["lightblue", "lightpink"]);
</pre>

[图片上传中...(image-2f5681-1543748931673-3)]

This is yet another way to compare the distributions between men and women.

Let's look a little deeper, and compare these violin plots as a function of age. We'll start by creating a new column in the array that specifies the decade of age that each person is in:

In [35]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">data['age_dec'] = data.age.map(lambda age: 10 * (age // 10))
data.head()
</pre>

Out[35]:

	age	gender	split	final	split_sec	final_sec	split_frac	age_dec
0	33	M	01:05:38	02:08:51	3938.0	7731.0	-0.018756	30
1	32	M	01:06:26	02:09:28	3986.0	7768.0	-0.026262	30
2	31	M	01:06:49	02:10:42	4009.0	7842.0	-0.022443	30
3	38	M	01:06:16	02:13:45	3976.0	8025.0	0.009097	30
4	31	M	01:06:32	02:13:59	3992.0	8039.0	0.006842	30

In [36]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">men = (data.gender == 'M')
women = (data.gender == 'W')

with sns.axes_style(style=None):
sns.violinplot("age_dec", "split_frac", hue="gender", data=data,
split=True, inner="quartile",
palette=["lightblue", "lightpink"]);
</pre>

[图片上传中...(image-6c3e8c-1543748931672-2)]

Looking at this, we can see where the distributions of men and women differ: the split distributions of men in their 20s to 50s show a pronounced over-density toward lower splits when compared to women of the same age (or of any age, for that matter).

Also surprisingly, the 80-year-old women seem to outperform everyone in terms of their split time. This is probably due to the fact that we're estimating the distribution from small numbers, as there are only a handful of runners in that range:

In [38]:

Out[38]:

Back to the men with negative splits: who are these runners? Does this split fraction correlate with finishing quickly? We can plot this very easily. We'll use regplot, which will automatically fit a linear regression to the data:

In [37]:

<pre style="box-sizing: border-box; overflow: auto; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 13px; display: block; padding: 0px; margin: 0px; line-height: 1.42857; color: rgb(51, 51, 51); word-break: break-all; overflow-wrap: break-word; background-color: transparent; border: none; border-radius: 4px;">g = sns.lmplot('final_sec', 'split_frac', col='gender', data=data,
markers=".", scatter_kws=dict(color='c'))
g.map(plt.axhline, y=0.1, color="k", ls=":");
</pre>

[图片上传中...(image-454ae4-1543748931670-1)]

Apparently the people with fast splits are the elite runners who are finishing within ~15,000 seconds, or about 4 hours. People slower than that are much less likely to have a fast second split.