def test_bootstrap_se_ci():
# Use treated mouse data from Table 2.1 and
# results from Table 2.2 and Table 13.1 in
# Bradley Efron and Robert Tibshirani,
# "An Introduction to the Bootstrap"
# (Chapman & Hall, 1993).
data = np.array([94, 197, 16, 38, 99, 141, 23], dtype=np.float64)
assert abs(np.mean(data) - 86.86) < 0.005 # this is just rounding error
bsd = bootstrap_se_ci(data, 123456789, 1000, np.mean, alpha=0.025)
# following comparisons are less precise because of r.n. stream differences
assert abs(bsd['se'] / 23.02 - 1) < 0.02
assert abs(bsd['cilo'] / 45.9 - 1) < 0.02
assert abs(bsd['cihi'] / 135.4 - 1) < 0.03
def test_bootstrap_se_ci():
# Use treated mouse data from Table 2.1 and
# results from Table 2.2 and Table 13.1 in
# Bradley Efron and Robert Tibshirani,
# "An Introduction to the Bootstrap"
# (Chapman & Hall, 1993).
data = np.array([94, 197, 16, 38, 99, 141, 23], dtype=np.float64)
assert abs(np.mean(data) - 86.86) < 0.005 # this is just rounding error
bsd = bootstrap_se_ci(data, 123456789, 1000, np.mean, alpha=0.025)
# following comparisons are less precise because of r.n. stream differences
assert abs(bsd['se'] / 23.02 - 1) < 0.02
assert abs(bsd['cilo'] / 45.9 - 1) < 0.02
assert abs(bsd['cihi'] / 135.4 - 1) < 0.03
def test_diff_count_precision():
"""
Estimate bootstrap standard error and confidence interval for count
statistics ('tax_cut' and 'tax_inc') in difference table generated
using puf.csv input data taking no account of tbi privacy fuzzing and
assuming all filing units in each bin have the same weight. These
assumptions imply that the estimates produced here are likely to
over-estimate the precision of the count statistics.
Background information on unweighted number of filing units by bin:
DECILE BINS:
0 16268
1 14897
2 13620
3 15760
4 16426
5 18070
6 18348
7 19352
8 21051
9 61733 <--- largest unweighted bin count
A 215525
WEBAPP BINS:
0 7081 <--- negative income bin is dropped in TaxBrain display
1 19355
2 22722
3 20098
4 17088
5 14515
6 24760
7 15875
8 25225
9 15123
10 10570 <--- smallest unweighted bin count
11 23113 <--- second largest unweighted WEBAPP bin count
A 215525
Background information on Trump2017.json reform used in TaxBrain run 16649:
WEBAPP bin 10 ($500-1000 thousand) has weighted count of 1179 thousand;
weighted count of units with tax increase is 32 thousand.
So, the mean weight for all units in WEBAPP bin 10 is 111.5421 and the
unweighted number with a tax increase is 287 assuming all units in that
bin have the same weight. (Note that 287 * 111.5421 is about 32,012.58,
which rounds to the 32 thousand shown in the TaxBrain difference table.)
WEBAPP bin 11 ($1000+ thousand) has weighted count of 636 thousand;
weighted count of units with tax increase is 27 thousand.
So, the mean weight for all units in WEBAPP bin 11 is about 27.517 and the
unweighted number with a tax increase is 981 assuming all units in that
bin have the same weight. (Note that 981 * 27.517 is about 26,994.18,
which rounds to the 27 thousand shown in the TaxBrain difference table.)
"""
dump = False # setting to True implies results printed and test fails
seed = 123456789
bs_samples = 1000
alpha = 0.025 # implies 95% confidence interval
# compute stderr and confidence interval for WEBAPP bin 10 increase count
data_list = [111.5421] * 287 + [0.0] * (10570 - 287)
assert len(data_list) == 10570
data = np.array(data_list)
assert (data > 0).sum() == 287
data_estimate = np.sum(data) * 1e-3
assert abs((data_estimate / 32) - 1) < 0.0005
bsd = bootstrap_se_ci(data, seed, bs_samples, np.sum, alpha)
stderr = bsd['se'] * 1e-3
cilo = bsd['cilo'] * 1e-3
cihi = bsd['cihi'] * 1e-3
if dump:
res = '{}EST={:.1f} B={} alpha={:.3f} se={:.2f} ci=[ {:.2f} , {:.2f} ]'
print(
res.format('WEBAPP-BIN10: ', data_estimate, bs_samples, alpha,
stderr, cilo, cihi))
assert abs((stderr / 1.90) - 1) < 0.0008
# NOTE: a se of 1.90 thousand implies that when comparing the difference
# in the weighted number of filing units in WEBAPP bin 10 with a
# tax increase, the difference statistic has a bigger se (because
# the variance of the difference is the sum of the variances of the
# two point estimates). So, in WEBAPP bin 10 if the point estimates
# both had se = 1.90, then the difference in the point estimates has
# has a se = 2.687. This means that the difference would have to be
# over 5 thousand in order for there to be high confidence that the
# difference was different from zero in a statistically significant
# manner.
# Or put a different way, a difference of 1 thousand cannot be
# accurately detected while a difference of 10 thousand can be
# accurately detected.
assert abs((cilo / 28.33) - 1) < 0.0012
assert abs((cihi / 35.81) - 1) < 0.0012
# compute stderr and confidence interval for WEBAPP bin 11 increase count
data_list = [27.517] * 981 + [0.0] * (23113 - 981)
assert len(data_list) == 23113
data = np.array(data_list)
assert (data > 0).sum() == 981
data_estimate = np.sum(data) * 1e-3
assert abs((data_estimate / 27) - 1) < 0.0005
bsd = bootstrap_se_ci(data, seed, bs_samples, np.sum, alpha)
stderr = bsd['se'] * 1e-3
cilo = bsd['cilo'] * 1e-3
cihi = bsd['cihi'] * 1e-3
if dump:
res = '{}EST={:.1f} B={} alpha={:.3f} se={:.2f} ci=[ {:.2f} , {:.2f} ]'
print(
res.format('WEBAPP-BIN11: ', data_estimate, bs_samples, alpha,
stderr, cilo, cihi))
assert abs((stderr / 0.85) - 1) < 0.0040
# NOTE: a se of 0.85 thousand implies that when comparing the difference
# in the weighted number of filing units in WEBAPP bin 11 with a
# tax increase, the difference statistic has a bigger se (because
# the variance of the difference is the sum of the variances of the
# two point estimates). So, in WEBAPP bin 11 if the point estimates
# both had se = 0.85, then the difference in the point estimates has
# has a se = 1.20. This means that the difference would have to be
# over 2.5 thousand in order for there to be high confidence that the
# difference was different from zero in a statistically significant
# manner.
# Or put a different way, a difference of 1 thousand cannot be
# accurately detected while a difference of 10 thousand can be
# accurately detected.
assert abs((cilo / 25.37) - 1) < 0.0012
assert abs((cihi / 28.65) - 1) < 0.0012
# fail if doing dump
assert not dump
def test_diff_count_precision():
"""
Estimate bootstrap standard error and confidence interval for count
statistics ('tax_cut' and 'tax_inc') in difference table generated
using puf.csv input data taking no account of tbi privacy fuzzing and
assuming all filing units in each bin have the same weight. These
assumptions imply that the estimates produced here are likely to
over-estimate the precision of the count statistics.
Background information on unweighted number of filing units by bin:
DECILE BINS:
0 16268
1 14897
2 13620
3 15760
4 16426
5 18070
6 18348
7 19352
8 21051
9 61733 <--- largest unweighted bin count
A 215525
STANDARD BINS:
0 7081 <--- negative income bin was dropped in TaxBrain display
1 19355
2 22722
3 20098
4 17088
5 14515
6 24760
7 15875
8 25225
9 15123
10 10570 <--- smallest unweighted bin count
11 23113 <--- second largest unweighted WEBAPP bin count
A 215525
Background information on Trump2017.json reform used in TaxBrain run 16649:
STANDARD bin 10 ($500-1000 thousand) has weighted count of 1179 thousand;
weighted count of units with tax increase is 32 thousand.
So, the mean weight for all units in STANDARD bin 10 is 111.5421 and the
unweighted number with a tax increase is 287 assuming all units in that
bin have the same weight. (Note that 287 * 111.5421 is about 32,012.58,
which rounds to the 32 thousand shown in the TaxBrain difference table.)
STANDARD bin 11 ($1000+ thousand) has weighted count of 636 thousand;
weighted count of units with tax increase is 27 thousand.
So, the mean weight for all units in STANDARD bin 11 is about 27.517 and
the unweighted number with a tax increase is 981 assuming all units in
that bin have the same weight. (Note that 981 * 27.517 is about 26,994.18,
which rounds to the 27 thousand shown in the TaxBrain difference table.)
"""
dump = False # setting to True implies results printed and test fails
seed = 123456789
bs_samples = 1000
alpha = 0.025 # implies 95% confidence interval
# compute stderr and confidence interval for STANDARD bin 10 increase count
data_list = [111.5421] * 287 + [0.0] * (10570 - 287)
assert len(data_list) == 10570
data = np.array(data_list)
assert (data > 0).sum() == 287
data_estimate = np.sum(data) * 1e-3
assert abs((data_estimate / 32) - 1) < 0.0005
bsd = bootstrap_se_ci(data, seed, bs_samples, np.sum, alpha)
stderr = bsd['se'] * 1e-3
cilo = bsd['cilo'] * 1e-3
cihi = bsd['cihi'] * 1e-3
if dump:
res = '{}EST={:.1f} B={} alpha={:.3f} se={:.2f} ci=[ {:.2f} , {:.2f} ]'
print(
res.format('STANDARD-BIN10: ',
data_estimate, bs_samples, alpha, stderr, cilo, cihi)
)
assert abs((stderr / 1.90) - 1) < 0.0008
# NOTE: a se of 1.90 thousand implies that when comparing the difference
# in the weighted number of filing units in STANDARD bin 10 with a
# tax increase, the difference statistic has a bigger se (because
# the variance of the difference is the sum of the variances of the
# two point estimates). So, in STANDARD bin 10 if the point
# estimates both had se = 1.90, then the difference in the point
# estimates has has a se = 2.687. This means that the difference
# would have to be over 5 thousand in order for there to be high
# confidence that the difference was different from zero in a
# statistically significant manner.
# Or put a different way, a difference of 1 thousand cannot be
# accurately detected while a difference of 10 thousand can be
# accurately detected.
assert abs((cilo / 28.33) - 1) < 0.0012
assert abs((cihi / 35.81) - 1) < 0.0012
# compute stderr and confidence interval for STANDARD bin 11 increase count
data_list = [27.517] * 981 + [0.0] * (23113 - 981)
assert len(data_list) == 23113
data = np.array(data_list)
assert (data > 0).sum() == 981
data_estimate = np.sum(data) * 1e-3
assert abs((data_estimate / 27) - 1) < 0.0005
bsd = bootstrap_se_ci(data, seed, bs_samples, np.sum, alpha)
stderr = bsd['se'] * 1e-3
cilo = bsd['cilo'] * 1e-3
cihi = bsd['cihi'] * 1e-3
if dump:
res = '{}EST={:.1f} B={} alpha={:.3f} se={:.2f} ci=[ {:.2f} , {:.2f} ]'
print(
res.format('STANDARD-BIN11: ',
data_estimate, bs_samples, alpha, stderr, cilo, cihi)
)
assert abs((stderr / 0.85) - 1) < 0.0040
# NOTE: a se of 0.85 thousand implies that when comparing the difference
# in the weighted number of filing units in STANDARD bin 11 with a
# tax increase, the difference statistic has a bigger se (because
# the variance of the difference is the sum of the variances of the
# two point estimates). So, in STANDARD bin 11 if point estimates
# both had se = 0.85, then the difference in the point estimates has
# has a se = 1.20. This means that the difference would have to be
# over 2.5 thousand in order for there to be high confidence that the
# difference was different from zero in a statistically significant
# manner.
# Or put a different way, a difference of 1 thousand cannot be
# accurately detected while a difference of 10 thousand can be
# accurately detected.
assert abs((cilo / 25.37) - 1) < 0.0012
assert abs((cihi / 28.65) - 1) < 0.0012
# fail if doing dump
assert not dump
