Inference and Gender Gaps

Allen Downey

MIT License

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

gss = pd.read_hdf('gss_feminism_2022.hdf', key='gss')

Here are the 10 fe variables and the text of the questions.

fechld

A. A working mother can establish just as warm and secure a relationship with her children as a mother who does not work.

fefam

D. It is much better for everyone involved if the man is the achiever outside the home and the woman takes care of the home and family.

fehelp

B. It is more important for a wife to help her husband’s career than to have one herself.

fehire

Because of past discrimination, employers should make special efforts to hire and promote qualified women.

fehome

Women should take care of running their homes and leave running the country up to men.

fejobaff

Some people say that because of past discrimination, women should be given preference in hiring and promotion. Others say that such preference in hiring and promotion of women is wrong because it discriminates against men. What about your opinion - are you for or against preferential hiring and promotion of women? IF FOR:Do you favor preference in hiring and promotion strongly or not strongly? IF AGAINST:Do you oppose preference in hiring and promotion strongly or not strongly?

fepol

A. Tell me if you agree or disagree with this statement: Most men are better suited emotionally for politics than are most women.

fepres

If your party nominated a woman for President, would you vote for her if she were qualified for the job?

fepresch

C. A preschool child is likely to suffer if his or her mother works.

fework

Do you approve or disapprove of a married woman earning money in business or industry if she has a husband capable of supporting her?

fe_columns = [x for x in gss.columns if x.startswith('fe')]
fe_columns

['fechld',
 'fefam',
 'fehelp',
 'fehire',
 'fehome',
 'fejobaff',
 'fepol',
 'fepres',
 'fepresch',
 'fework']

from utils import decorate

grouped = gss.groupby('year')
intervals = pd.DataFrame(columns=['first', 'last', '# years'], dtype=int)

for column in fe_columns:
    counts = grouped[column].count()
    nonzero = counts.replace(0, np.nan).dropna()
    n_years = len(nonzero)
    first, last = nonzero.index.min(), nonzero.index.max()
    intervals.loc[column] = first, last, n_years

intervals

	first	last	# years
fechld	1977	2022	23
fefam	1977	2022	23
fehelp	1977	1998	11
fehire	1996	2022	13
fehome	1974	1998	16
fejobaff	1996	2022	13
fepol	1974	2022	27
fepres	1972	2010	19
fepresch	1977	2022	23
fework	1972	1998	17

current_columns = intervals.query('last==2022').index.values
current_columns

array(['fechld', 'fefam', 'fehire', 'fejobaff', 'fepol', 'fepresch'],
      dtype=object)

For each variable, I’ll select “agree” and “strongly agree”, except for fework, where I’ve selected “approve”.

agree_responses = {
    'fechld': [1, 2],
    'fefam': [1, 2],
    'fehelp': [1, 2],
    'fehire': [1, 2],
    'fehome': [1],
    'fejobaff': [1, 2],
    'fepol': [1],
    'fepres': [1],
    'fepresch': [1, 2],
    'fework': [1],
}

Resampling

resample_by_year uses weighted bootstrap resampling to simultaneously correct for stratified sampling and estimate error bounds on a year-by year basis.

from utils import resample_by_year

np.random.seed(17)
samples = [resample_by_year(gss, "wtssall") for i in range(101)]

def make_series(data, query, column):
    subset = data.query(query)
    xtab = pd.crosstab(subset['year'], subset[column], normalize='index')
    series = xtab[agree_responses[column]].sum(axis=1)
    return series * 100

from utils import make_lowess

def make_smooth_series(data, query, column):
    series = make_series(data, query, column)
    smooth = make_lowess(series)
    return smooth

plot_percentiles plots the median of the resampled estimates as a line and a 90% confidence interval as a shaded area.

def percentile_rows(series_seq, ps):
    """Computes percentiles from aligned series.

    series_seq: list of sequences
    ps: cumulative probabilities

    returns: NumPy array
    """
    array = np.array(series_seq)
    rows = np.percentile(array, ps, axis=0)
    return rows

def plot_percentiles(series_seq, ps=None, **options):
    """Plot the low, median, and high percentiles.

    series_seq: sequence of Series
    options: options passed plt.plot and plt.fill_between
    """
    label = options.pop('label', '')
    ps = [5, 50, 95]
    xs = series_seq[0].index
    low, med, high = percentile_rows(series_seq, ps)
    plt.plot(xs, med, alpha=0.5, **options)
    plt.fill_between(xs, low, high, linewidth=0, alpha=0.2, **options)
    
    offset = adjust_map.get((column, label), 0)
    x = xs[0] - 0.5
    y = med[0] + offset
    plt.text(x, y, label, ha='right', va='center')

def plot_median(series_seq, column, **options):
    """Plot the low, median, and high percentiles.

    series_seq: sequence of Series
    ps: percentiles to use for low, medium and high
    label: string label for the median line
    options: options passed plt.plot and plt.fill_between
    """
    label = options.pop('label', '')
    xs = series_seq[0].index
    med = percentile_rows(series_seq, 50)
    plt.plot(xs, med, alpha=0.5, **options)

    offset = adjust_map.get((column, label), 0)
    x = xs[0] - 0.5
    y = med[0] + offset
    plt.text(x, y, label, ha='right', va='center')

def plot_series_bounds(column, query1, query2):
    male_series_seq = [make_series(sample, query1, column) 
                       for sample in samples]
    female_series_seq = [make_series(sample, query2, column) 
                         for sample in samples]
    plot_percentiles(male_series_seq, label='male')
    plot_percentiles(female_series_seq, label='female')
    decorate(ylabel='Percent agree/approve', 
             xlim=[1971, 2023],
             title=column)

def plot_four_series(column, smooth=False, bounds=False):
    queries = ['sex==1 & age<30', 'sex==1 & age>=30', 
               'sex==2 & age<30', 'sex==2 & age>=30']
    colors = ['C0', 'C0', 'C1', 'C1']
    styles = ['-', '--', '-', '--']
    short_labels = ['M<30', 'M≥30', 'F<30', 'F≥30']
    long_labels = ['Male <30', 'Male ≥30', 'Female <30', 'Female ≥30']
    
    for i, query in enumerate(queries):
        if smooth:
            series_seq = [make_smooth_series(sample, query, column) 
                          for sample in samples]
        else:
            series_seq = [make_series(sample, query, column) 
                          for sample in samples]
            
        options = dict(color=colors[i], ls=styles[i], label=short_labels[i])
        if bounds:
            plot_percentiles(series_seq, **options)
        else:
            plot_median(series_seq, column, **options)
            
    decorate(ylabel='Percent agree', 
             xlim=[1971, 2023])

Plot without smoothing

adjust_map = {('fejobaff', 'M<30'): -1.3,
              ('fejobaff', 'M≥30'): -0.65,
              ('fepol', 'F≥30'): 1,
             }

smooth = False

title = """A working mother can establish just as warm and secure a
relationship with her children as a mother who does not work
"""
plot_four_series('fechld', smooth=smooth)
plt.title(title, loc='left');

title = """It is much better for everyone involved if the man is the achiever 
outside the home and the woman takes care of the home and family
"""
plot_four_series('fefam', smooth=smooth)
plt.title(title, loc='left');

title = """Because of past discrimination, employers should make 
special efforts to hire and promote qualified women
"""
plot_four_series('fehire', smooth=smooth)
plt.title(title, loc='left');

title = """Some people say that because of past discrimination, 
women should be given preference in hiring and promotion. 
Others say that such preference in hiring and promotion of 
women  is wrong because it discriminates against men. 
What about your opinion - are you for or against 
preferential hiring and promotion of women?
"""
plot_four_series('fejobaff', smooth=smooth)
plt.title(title, loc='left')
plt.ylabel('Percent in favor');

title = """Most men are better suited emotionally
for politics than are most women
"""
plot_four_series('fepol', smooth=smooth)
plt.title(title, loc='left')
plt.xlim([1968, 2023]);

title = """A preschool child is likely to suffer if his or her mother works
"""
plot_four_series('fepresch', smooth=smooth)
plt.title(title, loc='left');

Plot with smoothing

adjust_map = {('fepresch', 'F≥30'): 1,
             }

smooth = True

title = """A working mother can establish just as warm and secure a
relationship with her children as a mother who does not work
"""
plot_four_series('fechld', smooth=smooth)
plt.title(title, loc='left');

title = """It is much better for everyone involved if the man is the achiever 
outside the home and the woman takes care of the home and family
"""
plot_four_series('fefam', smooth=smooth)
plt.title(title, loc='left');

title = """Because of past discrimination, employers should make 
special efforts to hire and promote qualified women
"""
plot_four_series('fehire', smooth=smooth)
plt.title(title, loc='left');

title = """Some people say that because of past discrimination, 
women should be given preference in hiring and promotion. 
Others say that such preference in hiring and promotion of 
women  is wrong because it discriminates against men. 
What about your opinion - are you for or against 
preferential hiring and promotion of women?
"""
plot_four_series('fejobaff', smooth=smooth)
plt.title(title, loc='left')
plt.ylabel('Percent in favor');

title = """Most men are better suited emotionally
for politics than are most women
"""
plot_four_series('fepol', smooth=smooth)
plt.title(title, loc='left')
plt.xlim([1968, 2023]);

title = """A preschool child is likely to suffer if his or her mother works
"""
plot_four_series('fepresch', smooth=smooth)
plt.title(title, loc='left');