Q3: Disparities in Outcomes - Racial Justice Act Examples

When looking at disposed of (i.e. closed/not pending) shooting cases in which someone was shot, how do outcomes and sentences compare for Latino defendants versus for white or non-Latino defendants?

import pandas as pd
from cryptorandom.cryptorandom import SHA256
from scipy.stats import fisher_exact
from scipy.stats.contingency import odds_ratio
import numpy as np
import seaborn as sns

sns.set_theme()

import os
os.chdir('../')
from utils import chi2, permutation

seed = 98066
prng = SHA256(seed)

# data loading
df = pd.read_csv("example-1/example_1_data_sanitized.csv")

df_filtered = df[(df["Open  = 0; Closed =1"]==1) & (df["Someone shot? (0=no, 1=yes)"]==1) & (df["Exclude?"].isnull()) ].reset_index(drop=True)

prison = lambda row: row["State prison Prison?"] # returns 1 if they went to county or state prison

# filter for sentenced, race
df_filtered["prison"] = df_filtered.apply(prison, axis=1).astype(int)
df_filtered = df_filtered[["Docket", "prison", "Probation", "Dismissal?", "Prison in months", "Race"]]

df_white_hispanic = df_filtered[df_filtered["Race"].isin(["W", "H"])].reset_index(drop=True)
df_non_hispanic = df_filtered
df_non_hispanic["race"] = [ "H" if race == "H" else "NH" for race in df_non_hispanic["Race"].to_list()]

In disposed of cases, are Latino defendants more frequently sentenced to prison compared to white or non-latino defendants?¶

Tests: fishers/permutation, risk ratio, odds ratio

Latino v White¶

df_race_prison_white_hispanic = df_white_hispanic[["Race", "prison", "Docket"]]

contingency_white_hispanic = pd.crosstab(df_race_prison_white_hispanic["Race"], df_race_prison_white_hispanic["prison"])
contingency_white_hispanic

# risk ratio
(contingency_white_hispanic.at["H", 1]  / (contingency_white_hispanic.at["H", 0] + contingency_white_hispanic.at["H", 1] ))/ \
(contingency_white_hispanic.at["W", 1]  / (contingency_white_hispanic.at["W", 0] + contingency_white_hispanic.at["W", 1] ))

np.float64(1.7894736842105263)

# odds ratio
table = contingency_white_hispanic[[1,0]].T # reformat to gets odds of prison
result = odds_ratio(table)
print(f"The odds of a Hispanic defendant who shot someone to be sentenced to prison is {round(result.statistic,3)} \n \
      times higher than a White defendant who also shot someone")

The odds of a Hispanic defendant who shot someone to be sentenced to prison is 7.944 
       times higher than a White defendant who also shot someone

# fishers exact 
# null hypothesis: hispanics and whites are sentenced to prison at the same rate
# alternative hypothesis: hispanics are sentenced to prison at a greater rate than whites
res = fisher_exact(table, alternative='greater')
print(f"p-value: {round(res.pvalue,5)}, test stat: {res.statistic}")

p-value: 0.01322, test stat: 8.5

# permutation proportion - assumption under null is race can be randomly selected
# null hypothesis: hispanics and whites are sentenced to prison at the same proportion
# alternative hypothesis: hispanics are sentenced to prison at a greater proportion than whites
h_prison, w_prison = permutation.get_lists(df_race_prison_white_hispanic, "Race", "H", "W", "prison")
_ = permutation.t_test(h_prison, w_prison, "greater", prng=prng, title="Sentenced to Prison")

/opt/anaconda3/envs/rja/lib/python3.12/site-packages/scipy/stats/_axis_nan_policy.py:586: RuntimeWarning: Precision loss occurred in moment calculation due to catastrophic cancellation. This occurs when the data are nearly identical. Results may be unreliable.
  res = hypotest_fun_out(*samples, **kwds)

p-value: 0.0149, test stat: 2.77746

# n_h = len(df_race_prison_white_hispanic[df_race_prison_white_hispanic["Race"]=="H"]) # number we sample in each step
# obs_stat = contingency_white_hispanic.at["H", 1]/n_h # proportion of hispanics sentenced to prison
# def test_stat(df): 
#     return df["prison"].mean()
# _, _ = permutation.prop_test(n_h, df_race_prison_white_hispanic, test_stat, obs_stat, prng=prng, plot_title="Sentenced to Prison", tail="greater")

Latino v Non-Latino¶

# filter for sentenced, race
df_race_prison_non_hispanic = df_non_hispanic[["race", "prison", "Docket"]]

contingency_non_hispanic = pd.crosstab(df_race_prison_non_hispanic["race"], df_race_prison_non_hispanic["prison"])
contingency_non_hispanic

# risk ratio
(contingency_non_hispanic.at["H", 1]  / (contingency_non_hispanic.at["H", 0] + contingency_non_hispanic.at["H", 1] ))/ \
(contingency_non_hispanic.at["NH", 1]  / (contingency_non_hispanic.at["NH", 0] + contingency_non_hispanic.at["NH", 1] ))

np.float64(1.7231968810916178)

# odds ratio
table = contingency_non_hispanic[[1,0]].T # reformat to gets odds of prison
result = odds_ratio(table)
print(f"The odds of a Hispanic defendant who shot someone to be sentenced to prison is {round(result.statistic,3)} \n \
      times higher than a Non-Hispanic defendant who also shot someone")

The odds of a Hispanic defendant who shot someone to be sentenced to prison is 7.674 
       times higher than a Non-Hispanic defendant who also shot someone

# fishers exact 
# null hypothesis: hispanics and non-hispanics are sentenced to prison at the same rate
# alternative hypothesis: hispanics are sentenced to prison at a greater rate than non-hispanics
res = fisher_exact(table, alternative='greater')
print(f"p-value: {round(res.pvalue,5)}, test stat: {res.statistic}")

p-value: 0.00312, test stat: 7.87037037037037

# permutation proportion - assumption under null is race can be randomly selected
# null hypothesis: hispanics and non-hispanics are sentenced to prison at the same proportion
# alternative hypothesis: hispanics are sentenced to prison at a greater proportion than non-hispanics
h_prison, nh_prison = permutation.get_lists(df_race_prison_non_hispanic, "race", "H", "NH", "prison")
_ = permutation.t_test(h_prison, nh_prison, "greater", prng=prng, title="Sentenced to Prison")

p-value: 0.0019, test stat: 3.02759

# def test_stat(df): 
#     return df["prison"].mean()
# n_h = len(df_race_prison_non_hispanic[df_race_prison_non_hispanic["race"]=="H"]) # number we sample in each step
# obs_stat = contingency_non_hispanic.at["H", 1]/n_h # proportion of hispanics sentenced to prison
#_, _ = permutation.prop_test(n_h, df_race_prison_non_hispanic, test_stat, obs_stat, prng=prng, plot_title="Sentenced to Prison", tail="greater")

In disposed of cases, are Latino defendants less frequently sentenced to probation compared to white or non-latino defendants?¶

Tests: fishers/permutation proportion, risk ratio

Latino v White¶

df_race_prob_white_hispanic = df_white_hispanic[["Race", "Probation", "Docket"]]

contingency_white_hispanic = pd.crosstab(df_race_prob_white_hispanic["Race"], df_race_prob_white_hispanic["Probation"])
contingency_white_hispanic

# risk ratio
(contingency_white_hispanic.at["H", 1]  / (contingency_white_hispanic.at["H", 0] + contingency_white_hispanic.at["H", 1] ))/ \
(contingency_white_hispanic.at["W", 1]  / (contingency_white_hispanic.at["W", 0] + contingency_white_hispanic.at["W", 1] ))

np.float64(0.3368421052631579)

# risk ratio
(contingency_white_hispanic.at["H", 0]  / (contingency_white_hispanic.at["H", 0] + contingency_white_hispanic.at["H", 1] ))/ \
(contingency_white_hispanic.at["W", 0]  / (contingency_white_hispanic.at["W", 0] + contingency_white_hispanic.at["W", 1] ))

np.float64(1.3014354066985645)

# odds ratio
table = contingency_white_hispanic.T # reformat to gets odds of probation
result = odds_ratio(table)
print(f"The odds of a Hispanic defendant who shot someone to not be sentenced to probation is {round(result.statistic,3)} \n \
      times higher than a White defendant who also shot someone")

The odds of a Hispanic defendant who shot someone to not be sentenced to probation is 3.714 
       times higher than a White defendant who also shot someone

table.reindex([1.0, 0.0])

# fishers exact 
# null hypothesis: hispanics and whites are sentenced to probation at the same rate
# alternative hypothesis: hispanics are sentenced to probation at a lesser rate than whites
res = fisher_exact(table.reindex([1.0, 0.0]), alternative='less')
print(f"p-value: {round(res.pvalue,5)}, test stat: {round(res.statistic, 5)}")

p-value: 0.1354, test stat: 0.25882

# permutation proportion - assumption under null is race can be randomly selected
# null hypothesis: hispanics and whites are sentenced to probation at the same proportion
# alternative hypothesis: hispanics are sentenced to probation at a lesser rate than whites
h_prob, w_prob = permutation.get_lists(df_race_prob_white_hispanic, "Race", "H", "W", "Probation")
_ = permutation.t_test(h_prob, w_prob, "less", prng=prng, title="Sentenced to Probation")

p-value: 0.13119, test stat: -1.53462

# def test_stat(df): 
#     return df["Probation"].mean()

# n_h = len(df_race_prob_white_hispanic[df_race_prob_white_hispanic["Race"]=="H"]) # number we sample in each step
# obs_stat = contingency_white_hispanic.at["H", 1]/n_h # proportion of hispanics sentenced to prison
# _, _ = permutation.prop_test(n_h, df_race_prob_white_hispanic, test_stat, obs_stat, prng=prng, plot_title="Sentenced to Probation", tail="less")

Latino v Non-Latino¶

# filter for sentenced, race
df_race_prob_non_hispanic = df_non_hispanic[["race", "Probation", "Docket"]]

contingency_non_hispanic = pd.crosstab(df_race_prob_non_hispanic["race"], df_race_prob_non_hispanic["Probation"])
contingency_non_hispanic

# risk ratio
(contingency_non_hispanic.at["H", 0]  / (contingency_non_hispanic.at["H", 0] + contingency_non_hispanic.at["H", 1] ))/ \
(contingency_non_hispanic.at["NH", 0]  / (contingency_non_hispanic.at["NH", 0] + contingency_non_hispanic.at["NH", 1] ))

np.float64(1.2243767313019391)

# risk ratio
(contingency_non_hispanic.at["H", 1]  / (contingency_non_hispanic.at["H", 0] + contingency_non_hispanic.at["H", 1] ))/ \
(contingency_non_hispanic.at["NH", 1]  / (contingency_non_hispanic.at["NH", 0] + contingency_non_hispanic.at["NH", 1] ))

np.float64(0.39097744360902253)

# odds ratio
table = contingency_non_hispanic.T # reformat to gets odds of prison
result = odds_ratio(table)
print(f"The odds of a Hispanic defendant who shot someone to not be sentenced to probation is {round(result.statistic,3)} \n \
      times higher than a Non-Hispanic defendant who also shot someone")

The odds of a Hispanic defendant who shot someone to not be sentenced to probation is 3.089 
       times higher than a Non-Hispanic defendant who also shot someone

# fishers exact 
# null hypothesis: hispanics and non-hispanics are sentenced to probation at the same rate
# alternative hypothesis: hispanics are sentenced to probation at a lesser rate than non-hispanics
res = fisher_exact(table.reindex([1.0, 0.0]), alternative='less')
print(f"p-value: {round(res.pvalue,5)}, test stat: {res.statistic}")

p-value: 0.12431, test stat: 0.31932773109243695

# permutation proportion - assumption under null is race can be randomly selected
# null hypothesis: hispanics and non-hispanics get probation at the same proportion
# alternative hypothesis: hispanics are sentenced to probation at a lesser proportion than non-hispanics
h_prob, nh_prob = permutation.get_lists(df_race_prob_non_hispanic, "race", "H", "NH", "Probation")
_ = permutation.t_test(h_prob, nh_prob, "less", prng=prng, title="Sentenced to Probation")

p-value: 0.11799, test stat: -1.46546

# def test_stat(df): 
#     return df["Probation"].mean()
# n_h = len(df_race_prob_non_hispanic[df_race_prob_non_hispanic["race"]=="H"]) # number we sample in each step
# obs_stat = contingency_non_hispanic.at["H", 1]/n_h # proportion of hispanics sentenced to prison
# _, _ = permutation.prop_test(n_h, df_race_prob_non_hispanic, test_stat, obs_stat, prng=prng, plot_title="Sentenced to Probation", tail="less")

In disposed of cases, do Latino defendants less frequently obtain a dismissal of their case as compare to white or non-Latino defendants?¶

Tests: chi-squares/fishers/permutation, risk ratio

Latino v White¶

df_race_dis_white_hispanic = df_white_hispanic[["Race", "Dismissal?", "Docket"]]

contingency_white_hispanic = pd.crosstab(df_race_dis_white_hispanic["Race"], df_race_dis_white_hispanic["Dismissal?"])
contingency_white_hispanic

# risk ratio
(contingency_white_hispanic.at["H", 0]  / (contingency_white_hispanic.at["H", 0] + contingency_white_hispanic.at["H", 1] ))/ \
(contingency_white_hispanic.at["W", 0]  / (contingency_white_hispanic.at["W", 0] + contingency_white_hispanic.at["W", 1] ))

np.float64(1.2307692307692308)

# odds ratio
table = contingency_white_hispanic.T # reformat to gets odds of probation
result = odds_ratio(table)
print(f"The odds of a Hispanic defendant who shot someone to not be dismissed is {round(result.statistic,3)} \n \
      times higher than a Hispanic defendant who also shot someone")

The odds of a Hispanic defendant who shot someone to not be dismissed is inf 
       times higher than a Hispanic defendant who also shot someone

# fishers exact 
# null hypothesis: hispanics and whites are dismissed at the same rate
# alternative hypothesis: hispanics are dismissed at a lesser rate than whites
res = fisher_exact(table.reindex([1.0, 0.0]), alternative='less')
print(f"p-value: {round(res.pvalue,5)}, test stat: {round(res.statistic, 5)}")

p-value: 0.08556, test stat: 0.0

# permutation proportion - assumption under null is race can be randomly selected
# null hypothesis: hispanics and whites are dismissed at the same proportion
# alternative hypothesis: hispanics are dismissed at a lesser rate than whites
h_dis, w_dis = permutation.get_lists(df_race_dis_white_hispanic, "Race", "H", "W", "Dismissal?")
_ = permutation.t_test(h_dis, w_dis, "less", prng=prng, title="Dismissed")

p-value: 0.08689, test stat: -2.03324

# n_h = len(df_race_dis_white_hispanic[df_race_prob_white_hispanic["Race"]=="H"]) # number we sample in each step
# obs_stat = contingency_white_hispanic.at["H", 1]/n_h # proportion of hispanics sentenced to prison
# def test_stat(df): 
#     return df["Dismissal?"].mean()
# _, _ = permutation.prop_test(n_h, df_race_dis_white_hispanic, test_stat, obs_stat, prng=prng, plot_title="Dismissed", tail="less")

Latino v Non-Latino¶

# filter for sentenced, race
df_race_dis_non_hispanic = df_non_hispanic[["race", "Dismissal?", "Docket"]]

contingency_non_hispanic = pd.crosstab(df_race_dis_non_hispanic["race"], df_race_dis_non_hispanic["Dismissal?"])
contingency_non_hispanic

# risk ratio
(contingency_non_hispanic.at["H", 0]  / (contingency_non_hispanic.at["H", 0] + contingency_non_hispanic.at["H", 1] ))/ \
(contingency_non_hispanic.at["NH", 0]  / (contingency_non_hispanic.at["NH", 0] + contingency_non_hispanic.at["NH", 1] ))

np.float64(1.2380952380952381)

contingency_non_hispanic.T

# odds ratio
table = contingency_non_hispanic.T # reformat to gets odds of prison
result = odds_ratio(table) # issue bc 0 in denom
print(f"The odds of a Hispanic defendant who shot someone to be dismissed is {round(result.statistic,3)} \n \
      times higher than a Non-Hispanic defendant who also shot someone")

The odds of a Hispanic defendant who shot someone to be dismissed is inf 
       times higher than a Non-Hispanic defendant who also shot someone

# fishers exact 
# null hypothesis: hispanics and non-hispanics have cases dismissed at the same rate
# alternative hypothesis: hispanics cases are dismissed at a lower rate than non-hispanics
res = fisher_exact(table.reindex([1.0, 0.0]), alternative='less')
print(f"p-value: {round(res.pvalue,5)}, test stat: {res.statistic}")

p-value: 0.03426, test stat: 0.0

# permutation proportion - assumption under null is race can be randomly selected
# null hypothesis: hispanics and non-hispanics are dismissed at the same proportion
# alternative hypothesis: hispanics are dismissed at a lower proportion than non-hispanics
h_dis, nh_dis = permutation.get_lists(df_race_dis_non_hispanic, "race", "H", "NH", "Dismissal?")
_ = permutation.t_test(h_dis, nh_dis, "less", prng=prng, title="Dismissed")

p-value: 0.0354, test stat: -2.09675

# n_h = len(df_race_prison_non_hispanic[df_race_dis_non_hispanic["race"]=="H"]) # number we sample in each step
# obs_stat = contingency_non_hispanic.at["H", 1]/n_h # proportion of hispanics sentenced to prison
# def test_stat(df): 
#     return df["Dismissal?"].mean()
# _, _ = permutation.prop_test(n_h, df_race_dis_non_hispanic, test_stat, obs_stat, prng=prng, plot_title="Dismissed", tail="less")

On average, are Latino defendants sentenced to prison sentenced to a longer prison term compared to white defendants sentenced to prison?¶

Tests: 2 - permutation

prison_sentences = df_white_hispanic[df_race_prison_white_hispanic["prison"]==1][["Race", "Prison in months"]]

white = prison_sentences[prison_sentences["Race"]=="W"]["Prison in months"].tolist()
hispanic = prison_sentences[prison_sentences["Race"]=="H"]["Prison in months"].tolist()
print(len(hispanic))
_,_,_ = permutation.t_test(hispanic, white, "greater", prng=prng)

p-value: 0.07589, test stat: 1.47004

print(f"On averages, Whites sentenced to prison are sentanced for {round(np.mean(white),3)} months and Hispanics sentenced to prison are sentenced for {round(np.mean(hispanic),3)} months")

On averages, Whites sentenced to prison are sentanced for 82.5 months and Hispanics sentenced to prison are sentenced for 126.941 months

prison_sentences = df_white_hispanic[["Race", "Prison in months"]]
white = prison_sentences[prison_sentences["Race"]=="W"]["Prison in months"].tolist()
hispanic = prison_sentences[prison_sentences["Race"]=="H"]["Prison in months"].tolist()
_,_,_ = permutation.t_test(hispanic, white, "greater", prng=prng)
print(f"On averages, Whites sentenced to prison are sentanced for {round(np.mean(white),3)} months and Hispanics sentenced to prison are sentenced for {round(np.mean(hispanic),3)} months")

p-value: 0.0029, test stat: 2.96635
On averages, Whites sentenced to prison are sentanced for 41.25 months and Hispanics sentenced to prison are sentenced for 113.579 months

How does the average sentence for Latino defendants charged with a shooting compare to the average sentence for white or non-Latino defendants charged with a shooting?¶

might need clarification on this question vs the previous

Tests: 2 - permutation

prison_sentences = df_non_hispanic[df_race_prison_non_hispanic["prison"]==1][["race", "Prison in months"]]

non_hispanic = prison_sentences[prison_sentences["race"]=="NH"]["Prison in months"].tolist()
hispanic = prison_sentences[prison_sentences["race"]=="H"]["Prison in months"].tolist()
_,_,_ = permutation.t_test(hispanic, non_hispanic, "greater", prng=prng)

p-value: 0.66173, test stat: -0.42069

print(f"On averages, Non-Hispanics sentenced to prison are sentanced for {round(np.mean(non_hispanic),3)} months and Hispanics sentenced to prison are sentenced for {round(np.mean(hispanic),3)} months")

On averages, Non-Hispanics sentenced to prison are sentanced for 136.0 months and Hispanics sentenced to prison are sentenced for 126.941 months

prison_sentences = df_non_hispanic[["race", "Prison in months"]]

non_hispanic = prison_sentences[prison_sentences["race"]=="NH"]["Prison in months"].tolist()
hispanic = prison_sentences[prison_sentences["race"]=="H"]["Prison in months"].tolist()
_,_,_ = permutation.t_test(hispanic, non_hispanic, "greater", prng=prng)

p-value: 0.0309, test stat: 1.92255

print(f"On averages, Non-Hispanics sentenced to prison are sentanced for {round(np.mean(non_hispanic),3)} months and Hispanics sentenced to prison are sentenced for {round(np.mean(hispanic),3)} months")

On averages, Non-Hispanics sentenced to prison are sentanced for 71.077 months and Hispanics sentenced to prison are sentenced for 113.579 months