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The vote for the Civil Rights Act in 1964

The Civil Rights Act of 1964 was one of the most important pieces of legislation ever passed in the USA. Excluding "present" and "abstain" votes, 153 House Democrats and 136 Republicans voted yea. However, 91 Democrats and 35 Republicans voted nay. Did party affiliation make a difference in the vote?

To answer this question, you will evaluate the hypothesis that the party of a House member has no bearing on his or her vote. You will use the fraction of Democrats voting in favor as your test statistic and evaluate the probability of observing a fraction of Democrats voting in favor at least as small as the observed fraction of 153/244. (That's right, at least as small as. In 1964, it was the Democrats who were less progressive on civil rights issues.) To do this, permute the party labels of the House voters and then arbitrarily divide them into "Democrats" and "Republicans" and compute the fraction of Democrats voting yea.

This exercise is part of the course

Statistical Thinking in Python (Part 2)

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Exercise instructions

  • Construct Boolean arrays, dems and reps that contain the votes of the respective parties; e.g., dems has 153 True entries and 91 False entries.
  • Write a function, frac_yea_dems(dems, reps) that returns the fraction of Democrats that voted yea. The first input is an array of Booleans, Two inputs are required to use your draw_perm_reps() function, but the second is not used.
  • Use your draw_perm_reps() function to draw 10,000 permutation replicates of the fraction of Democrat yea votes.
  • Compute and print the p-value.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Construct arrays of data: dems, reps
dems = np.array([True] * 153 + [False] * 91)
reps = ____

def frac_yea_dems(dems, reps):
    """Compute fraction of Democrat yea votes."""
    frac = ____ / ____
    return frac

# Acquire permutation samples: perm_replicates
perm_replicates = ____(____, ____, frac_yea_dems, ____)

# Compute and print p-value: p
p = np.sum(____ <= 153/244) / len(____)
print('p-value =', p)
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