import pandas as pd
import numpy as np
from scipy import stats

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

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

data.head()

"""
Explanation: 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 to 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 when presented to the employer.
Exercises
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.
Write a story describing the statistical significance in the context or the original problem.
Does your analysis mean that race/name is the most important factor in callback success? Why or why not? If not, how would you amend your analysis?

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
End of explanation
"""


white = data[data['race'] == 'w']['call']
black = data[data['race'] == 'b']['call']

diff_of_means = np.abs(np.mean(white) - np.mean(black))

# assuming alpha = 0.05
SE = np.sqrt(np.std(white) ** 2 / len(white) + np.std(black) ** 2 / len(black))

margin_of_error = 1.96 * SE

confidence_interval = [diff_of_means - margin_of_error, diff_of_means + margin_of_error]

print('The margin of error is', margin_of_error)
print('The 95% confidence interval is', confidence_interval)

permutation_replicates = np.empty(100000)

for i in range(len(permutation_replicates)):
    permutation_samples = np.random.permutation(np.concatenate((white, black)))
    
    white_perm = permutation_samples[:len(white)]
    black_perm = permutation_samples[len(white):]
    
    permutation_replicates[i] = np.abs(np.mean(white_perm) - np.mean(black_perm))

p = np.sum(permutation_replicates > diff_of_means) / len(permutation_replicates)
print('p =', p)

"""
Explanation: 1) What test is appropriate for this problem? Does CLT apply?
we can perform a permutation test with the two samples. The Central Limit does apply.
2) What are the null and alternate hypotheses?
$H_0$: The race of a person has no bearing on whether he/she receives a callback.
$H_A$: The race of a person gives affects the callback rate.
3) Compute margin of error, confidence interval, and p-value.
End of explanation
"""


