Examining Categorical Data

After learning the basics of data and examining numerical data a bit more closely, today we'll jump into a closer look at categorical data. This is mostly section 1.7 of our text, which is the last section that we'll do in chapter 1.

A little data

Let's start small today by taking a look at our class data:

Gender Age Height Eye Color Major
f 18 5.333333 green market
f 18 5.083333 brown Bio
m 31 6.250000 brown Acct
m 20 6.583333 blue Comm
m 31 6.166667 blue Mgmt
m 20 5.750000 hazel Geo & Eco
m 49 5.916667 hazel Mechatronics
f 28 5.666667 green Anthro & Health
f 22 5.583333 brown Psychology

Recall that this comes from our class forum question; I updated our Scraping our class data demo to clean this up, too.

Frequency tables and bar plots

A simple way to get a handle on one categorical variable is through a frequency table. Here's the frequency table for Eye Color in this data frame:

Green Brown Blue Hazel
2 3 2 2

Sometimes, it's easier to visualize this with a picture called a bar plot:

Note that bar plots look a lot like histograms but it's important to keep them distinct. A bar plot represents counts of categorical data while a histogram represents counts in some range of numerical data.

Contingency tables

If we'd like to explore any possible relationship between two categorical variables, we can use a contingency table. Here's the contingency table for gender and eye color:

G\EC blue brown green hazel
f 0 2 2 0
m 2 1 0 2

Often, it's useful to include row and column sums as margins:

G\EC blue brown green hazel All
f 0 2 2 0 4
m 2 1 0 2 5
All 2 3 2 2 9

We could even use proportions, as we'll see in just a bit.

Stacked bar plots

We can expand the bar plot idea to account for and visualize two categorical variables. This is called a stacked bar plot:

Mosaic plots

Another tools to visualize a pair of categorical variables that is more tightly tied to contingency tables is calles a mosaic plot:

A lotta data

Now let's examine the same stuff for a lot of data. We'll do so by applying Python to our CDC dataset.

Here's our basic imports:

In [1]:
%matplotlib inline
import pandas as pd

We'll compute a couple more special tools when we need them.

Getting the data

Recall that we can import our CDC data right off of the web:

In [2]:
df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
genhlth exerany hlthplan smoke100 height weight wtdesire age gender
0 good 0 1 0 70 175 175 77 m
1 good 0 1 1 64 125 115 33 f
2 good 1 1 1 60 105 105 49 f
3 good 1 1 0 66 132 124 42 f
4 very good 0 1 0 61 150 130 55 f

A contingency table and bar plot

Here's how to generate a frequency table for the genhlth variable:

In [3]:
value_counts = df['genhlth'].value_counts()
very good    6972
good         5675
excellent    4657
fair         2019
poor          677
Name: genhlth, dtype: int64

We can go straight from the value_counts to the corresponding bar plot:

In [4]:
value_counts.plot('bar', edgecolor='black', rot=0);

A contingency table

Pandas has a crosstab function designed specifically to generate a contingency table.

In [5]:
cont = pd.crosstab(df.genhlth, df.smoke100)
smoke100 0 1
excellent 2879 1778
fair 911 1108
good 2782 2893
poor 229 448
very good 3758 3214

You might want to reorder the rows, place the row and column sums in the margins, and/or indicate proportions, rather than counts:

In [6]:
cont = pd.crosstab(df.genhlth, df.smoke100, normalize=True, margins=True)
cont = cont.reindex(['excellent', 'very good', 'good', 'fair', 'poor', 'All'])
smoke100 0 1 All
excellent 0.14395 0.08890 0.23285
very good 0.18790 0.16070 0.34860
good 0.13910 0.14465 0.28375
fair 0.04555 0.05540 0.10095
poor 0.01145 0.02240 0.03385
All 0.52795 0.47205 1.00000

It's very easy to generate a stacked bar chart directly from a contingency table.

In [7]:
cont = pd.crosstab(df.genhlth, df.smoke100)
cont = cont.reindex(['excellent', 'very good', 'good', 'fair', 'poor'])
cont.plot(kind='bar', stacked=True, rot=0, edgecolor='black');

There's also a function in the statsmodels library that makes it very easy to generate a mosaic plot:

In [8]:
from statsmodels.graphics.mosaicplot import mosaic
mosaic(df, ['genhlth', 'smoke100']);

It's actually quite tricky to reorder and style that result, though.

In [10]:
from seaborn import palplot, color_palette as pl

df2 = df[df.genhlth == 'excellent']
df2 = df2.append(df[df.genhlth == 'very good'])
df2 = df2.append(df[df.genhlth == 'good'])
df2 = df2.append(df[df.genhlth == 'fair'])
df2 = df2.append(df[df.genhlth == 'poor'])

def color(key):
    if key == ('excellent', '0'):
        return {'color': pl()[2]}
    elif key == ('excellent', '1'):
        return {'color': pl()[8]}
    elif key == ('very good', '0'):
        return {'color': pl()[0]}
    elif key == ('very good', '1'):
        return {'color': pl()[9]}
    elif key == ('good', '0'):
        return {'color': pl()[4]}
    elif key == ('good', '1'):
        return {'color': pl()[6]}
    elif key == ('fair', '0'):
        return {'color': pl()[1]}
    elif key == ('fair', '1'):
        return {'color': pl()[3]}
    elif key == ('poor', '1'):
        return {'color': pl()[7]}
        return {'color': 'gray'}

mosaic(df2, ['genhlth', 'smoke100'], gap=(0.02,0.02), 
       properties=color, labelizer=lambda key: "");