Examining racial discrimination in the US job market

Background

Racial discrimination continues to be pervasive in cultures throughout the world. Researchers examined the level of racial discrimination in the United States labor market by randomly assigning identical résumés black-sounding or white-sounding names and observing the impact on requests for interviews from employers.

Data

In the dataset provided, each row represents a resume. The 'race' column has two values, 'b' and 'w', indicating black-sounding and white-sounding. The column 'call' has two values, 1 and 0, indicating whether the resume received a call from employers or not.

Note that the 'b' and 'w' values in race are assigned randomly to the resumes.

Exercise

You will perform a statistical analysis to establish whether race has a significant impact on the rate of callbacks for resumes.

Answer the following questions in this notebook below and submit to your Github account.

What test is appropriate for this problem? Does CLT apply?
What are the null and alternate hypotheses?
Compute margin of error, confidence interval, and p-value.
Discuss statistical significance.

You can include written notes in notebook cells using Markdown:

In the control panel at the top, choose Cell > Cell Type > Markdown
Markdown syntax: http://nestacms.com/docs/creating-content/markdown-cheat-sheet

Resources

Experiment information and data source: http://www.povertyactionlab.org/evaluation/discrimination-job-market-united-states
Scipy statistical methods: http://docs.scipy.org/doc/scipy/reference/stats.html
Markdown syntax: http://nestacms.com/docs/creating-content/markdown-cheat-sheet



In [1]:

    
%matplotlib inline
import pandas as pd
import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(color_codes=True)
from IPython.core.display import HTML
css = open('style-table.css').read() + open('style-notebook.css').read()
HTML('<style>{}</style>'.format(css))









    Out[1]:



In [2]:

    
data = pd.io.stata.read_stata('data/us_job_market_discrimination.dta')



In [3]:

    
# number of callbacks for black-sounding names
sum(data[data.race=='b'].call)









    Out[3]:





157.0



In [5]:

    
#number of callbacks for white-sounding names
sum(data[data.race=='w'].call)









    Out[5]:





235.0

Does the central limit theorem apply? What statistical test is appropriate?

In this case we are not dealing with a sufficiently large range of indendent random variables. As we increase our sample size, our data remains categorical. This means it can take on only a small subset of defined values. The CLT will not apply in this case, as no amount of smoothing out will lead us to see a normal distribution.

Because of this, the appropriate statistical test would be a $\chi^{2}$ test.



In [ ]:



In [ ]:

    
white_called =sum(data[data.race=='w'].call)
black_called = sum(data[data.race=='b'].call)
black_nocall = sum(data[])