Chapter 10.3 · Two zooms

A deprivation index at two zooms

A county's percentile on a deprivation index follows the average of its tracts' percentiles, with a correlation of 0.96, yet 32.7% of residents live in a tract more than 25 percentile points from their county's percentile.

Author: Vishal Singh
Affiliation: NYU Stern
Published: 9 October 2026

A county's percentile on a deprivation index follows the average of its tracts' percentiles, with a correlation of 0.96 (95% CI 0.95 to 0.97) across counties, but the percentile of a resident's tract differs from the percentile of the resident's county by a median of 16.0 (95% CI 15.2 to 17.0) percentile points, and 32.7% (95% CI 30.9% to 34.4%) of residents live in a tract more than 25 points away. This chapter builds one index in two boxes, across 76,496 census tracts and across the counties that contain them, and compares what the two boxes say about the same 309.9 million residents. Chapter 10.2, The anatomy of a deprivation index takes the index apart measure by measure, Chapter 10.1, Gradients, slopes and variance splits the variance of tract measures between states, counties and tracts, and Chapter 10.4, Families of places groups tracts into families instead of ranking them.

One recipe in two boxes

The index is the first principal component of 14 census measures: the measures that Chapter 10.2, The anatomy of a deprivation index rebuilds from the American Community Survey (ACS) for 2019 to 2023, without the share of single-parent households. The staged tract file and the county file define that share differently, and in the median county outside Utah and Puerto Rico the county value is 1.52 times the resident-weighted mean of its tracts' values, so one recipe cannot use it in both boxes. Adding the tract version back to the tract index changes its ranking little, with a rank correlation of 0.996 between the two. The measures are 4 dollar amounts (family income, home value, rent and mortgage cost), the log of the ratio of low-income to high-income households, and shares of people, households or homes for the rest. Each box standardizes its measures, fits the component and signs it so that a higher score means more deprived. A box is the set of units that are compared. In the tract box the units are the 76,496 2020 census tracts that have a published Area Deprivation Index (ADI) rank, a population and all the measures, among them 779 tracts in Puerto Rico. In the county box they are the 3,205 of 3,222 rows of the county ACS pull (counties, Connecticut planning regions and Puerto Rico municipios) that have all the measures. Every measure in the county box is the county's own ACS estimate. A county's median family income is the median of its families and not an average of its tracts' medians, which is what an analyst gets from a county release of the survey.

A score becomes a percentile when it is ranked against a reference population. The usual practice ranks units, as the Neighborhood Atlas does for block groups.[1] Counties differ so much in size that this counts places and not people. The average resident lives in a county at the 26.5 (95% CI 24.5 to 28.8) percentile among counties. This chapter ranks by residents instead, so that a unit's percentile is the share of the box's residents who live in units that score lower. Tracts hold similar numbers of people, so for tracts the two conventions differ by 2.6 percentile points on average. The ranking by units returns below wherever it changes an answer.

The Neighborhood Atlas ranks block groups and not counties, so a county index has to be built, and the index here is not the ADI. It ranks tracts with a rank correlation of +0.78 (95% CI 0.73 to 0.82) with the published tract rank, because the ADI sums the measures in their own units, as Chapter 10.2, The anatomy of a deprivation index shows, and so follows home value.[2, 3] Applying the ADI formula to county estimates gives the same result: it ranks counties with a rank correlation of −0.99 (95% CI −0.99 to −0.99) with home value, negative because the formula scores low home values as more deprived, and +0.90 (95% CI 0.86 to 0.92) with the county index of this chapter. Fitting the county component by counting each county once, instead of weighting counties by residents, changes the county ranking little, with a rank correlation of +0.988 (95% CI 0.986 to 0.990) between the two.

Figure 1 compares the weights. The first component carries 40.6% (95% CI 39.3% to 42.3%) of the variance of the measures in the tract box and 44.2% (95% CI 42.2% to 46.8%) in the county box, and the second component carries 18.3% (95% CI 16.4% to 20.0%) and 29.3% (95% CI 25.1% to 32.8%). 8 of the 14 weights differ by less than 0.05 between the boxes. Homeownership has a weight of −0.18 (95% CI −0.20 to −0.16) in the tract box and 0.03 (95% CI −0.06 to 0.10) in the county box, and crowding goes from 0.14 (95% CI 0.12 to 0.15) to −0.05 (95% CI −0.12 to 0.03); both county intervals include zero. The weight on adults with little schooling falls from 0.21 (95% CI 0.20 to 0.22) to 0.09 (95% CI 0.01 to 0.15), and the weight on income disparity rises from 0.27 (95% CI 0.26 to 0.27) to 0.34 (95% CI 0.31 to 0.36). The recipe carries over from tracts to counties, and the measures that rank tracts are not all the measures that rank counties.

Figure 1

Homeownership has a weight of −0.18 in the tract index and 0.03 in the county index, and crowding goes from 0.14 to −0.05

Weights of the 14 standardized measures in the first principal component, tract box (76,496 tracts) and county box (3,205 counties), ACS 2019 to 2023

Measure

Tract box
County box

Show data

Data for Homeownership has a weight of −0.18 in the tract index and 0.03 in the county index, and crowding goes from 0.14 to −0.05
box	conf_high	conf_low	measure	n	weight
Tract box	−0.366	−0.379	Family income	76,496	−0.374
County box	−0.368	−0.383	Family income	3,205	−0.377
Tract box	−0.322	−0.339	White-collar jobs	76,496	−0.331
County box	−0.290	−0.319	White-collar jobs	3,205	−0.307
Tract box	−0.281	−0.312	Mortgage cost	76,496	−0.297
County box	−0.270	−0.344	Mortgage cost	3,205	−0.317
Tract box	−0.279	−0.300	Gross rent	76,496	−0.289
County box	−0.299	−0.354	Gross rent	3,205	−0.333
Tract box	−0.254	−0.288	Home value	76,496	−0.271
County box	−0.257	−0.324	Home value	3,205	−0.297
Tract box	−0.161	−0.198	Homeownership	76,496	−0.182
County box	0.101	−0.059	Homeownership	3,205	0.028
Tract box	0.191	0.077	No vehicle	76,496	0.133
County box	0.108	−0.061	No vehicle	3,205	0.013
Tract box	0.155	0.120	Crowding	76,496	0.138
County box	0.034	−0.122	Crowding	3,205	−0.051
Tract box	0.184	0.169	No plumbing	76,496	0.177
County box	0.278	0.245	No plumbing	3,205	0.264
Tract box	0.195	0.177	Unemployment	76,496	0.186
County box	0.219	0.116	Unemployment	3,205	0.171
Tract box	0.217	0.196	Under 9 years of school	76,496	0.207
County box	0.154	0.012	Under 9 years of school	3,205	0.086
Tract box	0.272	0.259	Income disparity	76,496	0.266
County box	0.356	0.311	Income disparity	3,205	0.338
Tract box	0.349	0.338	Poverty	76,496	0.344
County box	0.358	0.309	Poverty	3,205	0.337
Tract box	0.376	0.364	Below 150% of poverty	76,496	0.371
County box	0.373	0.331	Below 150% of poverty	3,205	0.355

The two bars of a measure are close for most measures, and they part for homeownership and crowding, whose county bars are close to zero, and for schooling, income disparity and incomplete plumbing. Each bar is the weight of a measure in the first component of the standardized measures in its box, signed so that the poverty rate is positive, with a 95% interval from a bootstrap over counties. Bars to the left measure advantage and bars to the right measure hardship.Note: Each box standardizes its measures with population-weighted means and standard deviations, fits the component to the population-weighted correlation matrix of its units (tracts weighted by residents in the tract box, counties weighted by residents in the county box) and signs it so that the poverty rate has a positive weight.Note: The county box takes every measure from the county's own ACS estimate, not from an average of its tracts. Counties include Connecticut planning regions and Puerto Rico municipios.Source: ACS 2019-2023 five-year estimates (tracts and counties); population-weighted

The county ranking follows the average of its neighborhoods

Set each county's own percentile against the population-weighted mean of the percentiles of its tracts. Across counties the two correlate 0.96 (95% CI 0.95 to 0.97) when counties are weighted by residents and 0.96 (95% CI 0.95 to 0.96) when each county counts once. The tract box covers only tracts that have all the measures, so a county's tracts in the frame may hold only part of its residents. Among counties where they hold at least 90% of residents the correlation is 0.96 (95% CI 0.95 to 0.97), and 605 counties, with 25.5% of residents, fall below that cutoff. Ranking counties on the mean tract score, instead of the mean tract percentile, gives a rank correlation of 0.99 (95% CI 0.98 to 0.99) with the county's own percentile. For a question about counties as units, the county file and the tract file give nearly the same order.

The agreement is in order and not in level. The county's own percentile lies farther from the middle of the scale than the mean of its tracts' percentiles in counties that hold 96.3% (95% CI 94.1% to 98.0%) of residents, and in 96.7% (95% CI 96.0% to 97.3%) of counties counted once. Across counties, each additional point of county percentile goes with 0.57 (95% CI 0.55 to 0.59) points of average tract percentile when counties are weighted by residents and 0.68 (95% CI 0.68 to 0.69) points when each county counts once. A county at an end of the county ranking has, on average, neighborhoods that are less extreme than the county itself.

Residents sit far from their county's percentile

Give each resident two numbers, the percentile of their tract and the percentile of their county. Figure 2 plots the difference. Ranking by residents, the median absolute difference is 16.0 (95% CI 15.2 to 17.0) percentile points, 32.7% (95% CI 30.9% to 34.4%) of residents are more than 25 points from their county's percentile and 14.1% (95% CI 12.9% to 15.4%) are more than 40. Among counties where the frame holds at least 90% of residents the share more than 25 points away is 32.4% (95% CI 30.3% to 34.5%). Across residents the two percentiles correlate 0.57 (95% CI 0.54 to 0.61). The sign is close to even, with 46.8% (95% CI 44.9% to 48.6%) of residents living in a tract that ranks as more deprived than their county.

The ranking convention changes the picture. Ranking each tract and each county once, as is usual, the median difference is 19.4 (95% CI 18.7 to 20.2) points, 40.7% (95% CI 39.1% to 42.2%) of residents are more than 25 points away and 22.8% (95% CI 21.1% to 24.6%) are more than 40, and 81.5% (95% CI 80.3% to 82.6%) live in a tract that ranks as more deprived than their county. That lean follows from the reference population. Counted by units, the average resident lives in a county at the 26.5 percentile, below the middle of the county ranking, while the average resident's tract sits near the middle of the tract ranking.

Figure 2

Counted among residents, 32.7% of people live in a tract more than 25 percentile points from their county's percentile, and 40.7% when tracts and counties are ranked as units

Population-weighted distribution of a resident's tract percentile minus the resident's county percentile, in bins of five percentile points, 309.9 million residents of 76,496 tracts, ACS 2019 to 2023

Show data

Data for Counted among residents, 32.7% of people live in a tract more than 25 percentile points from their county's percentile, and 40.7% when tracts and counties are ranked as units
conf_high	conf_low	convention	n	share	x0	x1
0.024	0	Among residents	5	0.009	−95	−90
0.025	0.003	Among residents	12	0.013	−90	−85
0.095	0.019	Among residents	48	0.053	−85	−80
0.136	0.045	Among residents	72	0.086	−80	−75
0.220	0.096	Among residents	119	0.153	−75	−70
0.424	0.196	Among residents	241	0.300	−70	−65
0.651	0.324	Among residents	345	0.465	−65	−60
0.841	0.534	Among residents	535	0.680	−60	−55
1.24	0.808	Among residents	750	1.02	−55	−50
1.70	1.16	Among residents	1,050	1.42	−50	−45
2.12	1.59	Among residents	1,366	1.85	−45	−40
2.77	2.19	Among residents	1,801	2.48	−40	−35
3.62	2.97	Among residents	2,451	3.29	−35	−30
4.81	3.93	Among residents	3,246	4.34	−30	−25
5.52	4.75	Among residents	3,941	5.13	−25	−20
6.41	5.69	Among residents	4,717	6.04	−20	−15
7.58	6.71	Among residents	5,618	7.11	−15	−10
9.10	8.06	Among residents	6,675	8.57	−10	−5
10.88	9.51	Among residents	7,779	10.17	−5	0
9.69	8.27	Among residents	6,783	8.94	0	5
7.31	6.53	Among residents	5,316	6.91	5	10
6.16	5.57	Among residents	4,464	5.86	10	15
5.00	4.48	Among residents	3,656	4.74	15	20
4.12	3.60	Among residents	3,006	3.87	20	25
3.82	3.16	Among residents	2,664	3.49	25	30
3.01	2.48	Among residents	2,102	2.75	30	35
2.50	1.96	Among residents	1,678	2.24	35	40
2.15	1.54	Among residents	1,475	1.85	40	45
1.90	1.32	Among residents	1,214	1.61	45	50
1.60	1.01	Among residents	981	1.30	50	55
1.37	0.768	Among residents	765	1.04	55	60
1.16	0.542	Among residents	575	0.800	60	65
1.03	0.453	Among residents	521	0.697	65	70
0.380	0.208	Among residents	217	0.287	70	75
0.352	0.148	Among residents	164	0.240	75	80
0.192	0.067	Among residents	83	0.122	80	85
0.113	0.033	Among residents	47	0.068	85	90
0.028	0.005	Among residents	11	0.015	90	95
0.004	0	Among residents	2	0.001	95	100
0.002	0	Among tracts and counties	1	0.001	−85	−80
0.009	0	Among tracts and counties	2	0.003	−80	−75
0.042	0.002	Among tracts and counties	11	0.017	−75	−70
0.035	0	Among tracts and counties	11	0.013	−70	−65
0.078	0.019	Among tracts and counties	43	0.045	−65	−60
0.118	0.033	Among tracts and counties	62	0.072	−60	−55
0.175	0.066	Among tracts and counties	104	0.115	−55	−50
0.245	0.103	Among tracts and counties	138	0.166	−50	−45
0.337	0.184	Among tracts and counties	210	0.255	−45	−40
0.501	0.304	Among tracts and counties	310	0.392	−40	−35
0.687	0.410	Among tracts and counties	424	0.538	−35	−30
1.06	0.666	Among tracts and counties	667	0.845	−30	−25
1.37	0.961	Among tracts and counties	921	1.16	−25	−20
1.99	1.46	Among tracts and counties	1,352	1.72	−20	−15
2.81	2.18	Among tracts and counties	1,940	2.49	−15	−10
4.20	3.52	Among tracts and counties	3,023	3.85	−10	−5
7.19	6.48	Among tracts and counties	5,226	6.83	−5	0
11.42	9.67	Among tracts and counties	7,717	10.46	0	5
9.77	8.76	Among tracts and counties	6,789	9.26	5	10
9.05	8.27	Among tracts and counties	6,399	8.65	10	15
8.16	7.40	Among tracts and counties	5,885	7.78	15	20
7.48	6.71	Among tracts and counties	5,425	7.09	20	25
6.37	5.85	Among tracts and counties	4,652	6.10	25	30
5.63	5.14	Among tracts and counties	4,208	5.39	30	35
4.84	4.38	Among tracts and counties	3,597	4.60	35	40
4.13	3.67	Among tracts and counties	3,044	3.89	40	45
3.70	3.26	Among tracts and counties	2,730	3.48	45	50
3.25	2.77	Among tracts and counties	2,405	3.02	50	55
2.98	2.42	Among tracts and counties	2,134	2.71	55	60
2.71	2.04	Among tracts and counties	1,859	2.38	60	65
2.22	1.68	Among tracts and counties	1,530	1.97	65	70
1.95	1.36	Among tracts and counties	1,302	1.66	70	75
1.70	1.10	Among tracts and counties	1,095	1.40	75	80
1.32	0.702	Among tracts and counties	753	0.987	80	85
0.764	0.303	Among tracts and counties	402	0.497	85	90
0.215	0.100	Among tracts and counties	116	0.156	90	95
0.023	0.003	Among tracts and counties	8	0.011	95	100

Both distributions peak near zero and are wide; the distribution among residents is centered on zero and the distribution among tracts and counties is centered to the right. A bar is the share of residents whose tract percentile exceeds their county's percentile by an amount in the bin, so positive values mean the tract is more deprived than the county. The first distribution ranks tracts and counties by the residents they hold; the second ranks each tract and each county once.Note: Percentiles come from the index in each box. Among residents, a unit's percentile is the share of residents of its box who live in units that score lower; among tracts and counties, it is the share of units that score lower.Note: Intervals in the tooltip are 95% intervals from a bootstrap over counties (replicates and seed in the methods note). One tract has no county in the county frame and is left out.Source: ACS 2019-2023 five-year estimates (tracts and counties); population-weighted (bins: shares of residents)

A county percentile hides a wide spread of neighborhoods

Los Angeles County is the most populous county. Built from the county's own estimates, its index places it at the 29.1 percentile among residents and at the 8.0 percentile among counties. Its tracts run from percentile 2.0 at the 5th percentile of residents to percentile 94.2 at the 95th, and 53.0% of its residents live in a tract more than 25 points from the county's percentile.

Figure 3 draws the 30 most populous counties in the same way. In each of them the county percentile lies between the 5th and 95th percentile of its residents' tracts, and in 28 it lies farther from the middle of the scale than the average of those tracts. Across these counties the median share of residents more than 25 points from their county's percentile is 47.1%. The counties are chosen by population and ordered by the county percentile, since the spread of a small county rests on few tracts. The line is a spread of tracts and not an interval for the county.

Figure 3

Los Angeles County has a county percentile of 29.1, and its residents' tracts run from 2.0 to 94.2

Percentile among residents of the county index built from the county's own estimates, beside the average and the 5th to 95th percentile range of the percentiles of its tracts, the 30 most populous counties

County's own percentile
Average of its tracts' percentiles

Show data

Data for Los Angeles County has a county percentile of 29.1, and its residents' tracts run from 2.0 to 94.2
conf_high	conf_low	county	measure	n	percentile
n/a	n/a	Santa Clara County, CA	County's own percentile	n/a	0.500
59.50	0.100	Santa Clara County, CA	Average of its tracts' percentiles	392	13.50
n/a	n/a	Nassau County, NY	County's own percentile	n/a	2.10
63.50	1.10	Nassau County, NY	Average of its tracts' percentiles	217	16.10
n/a	n/a	Alameda County, CA	County's own percentile	n/a	2.60
80.40	0.300	Alameda County, CA	Average of its tracts' percentiles	357	23.40
n/a	n/a	Middlesex County, MA	County's own percentile	n/a	3.50
68.70	0.900	Middlesex County, MA	Average of its tracts' percentiles	328	20
n/a	n/a	King County, WA	County's own percentile	n/a	4.40
73	0.800	King County, WA	Average of its tracts' percentiles	476	21.40
n/a	n/a	Suffolk County, NY	County's own percentile	n/a	6.40
53.80	2.80	Suffolk County, NY	Average of its tracts' percentiles	311	19.60
n/a	n/a	Orange County, CA	County's own percentile	n/a	8.30
81.90	1.40	Orange County, CA	Average of its tracts' percentiles	587	30.30
n/a	n/a	New York County, NY	County's own percentile	n/a	9.40
93.90	1.70	New York County, NY	Average of its tracts' percentiles	217	31.60
n/a	n/a	San Diego County, CA	County's own percentile	n/a	13.20
86.50	1.10	San Diego County, CA	Average of its tracts' percentiles	684	31.80
n/a	n/a	Los Angeles County, CA	County's own percentile	n/a	29.10
94.20	2	Los Angeles County, CA	Average of its tracts' percentiles	2,226	46.20
n/a	n/a	Queens County, NY	County's own percentile	n/a	32.10
91.70	14.30	Queens County, NY	Average of its tracts' percentiles	612	49.70
n/a	n/a	Sacramento County, CA	County's own percentile	n/a	35.20
92	6	Sacramento County, CA	Average of its tracts' percentiles	341	46.40
n/a	n/a	Palm Beach County, FL	County's own percentile	n/a	36.30
90.90	4.40	Palm Beach County, FL	Average of its tracts' percentiles	321	44.50
n/a	n/a	Riverside County, CA	County's own percentile	n/a	37.20
89.90	6.70	Riverside County, CA	Average of its tracts' percentiles	491	45.20
n/a	n/a	Maricopa County, AZ	County's own percentile	n/a	38.40
93.10	6.60	Maricopa County, AZ	Average of its tracts' percentiles	911	44.70
n/a	n/a	Kings County, NY	County's own percentile	n/a	40.20
93.60	3.40	Kings County, NY	Average of its tracts' percentiles	651	53.30
n/a	n/a	Tarrant County, TX	County's own percentile	n/a	42.60
94.60	5.70	Tarrant County, TX	Average of its tracts' percentiles	406	46.60
n/a	n/a	Broward County, FL	County's own percentile	n/a	44.70
90.40	5	Broward County, FL	Average of its tracts' percentiles	381	47.40
n/a	n/a	Orange County, FL	County's own percentile	n/a	48.80
91.30	10.10	Orange County, FL	Average of its tracts' percentiles	244	49.60
n/a	n/a	Hillsborough County, FL	County's own percentile	n/a	50.60
91.10	8.10	Hillsborough County, FL	Average of its tracts' percentiles	297	47.70
n/a	n/a	San Bernardino County, CA	County's own percentile	n/a	52
94.50	8.10	San Bernardino County, CA	Average of its tracts' percentiles	432	55.10
n/a	n/a	Cook County, IL	County's own percentile	n/a	54
96	5	Cook County, IL	Average of its tracts' percentiles	1,221	51.50
n/a	n/a	Miami-Dade County, FL	County's own percentile	n/a	57.50
94.10	6.70	Miami-Dade County, FL	Average of its tracts' percentiles	606	53.10
n/a	n/a	Dallas County, TX	County's own percentile	n/a	60.40
95.70	4	Dallas County, TX	Average of its tracts' percentiles	548	57.10
n/a	n/a	Clark County, NV	County's own percentile	n/a	63.80
95.70	14.90	Clark County, NV	Average of its tracts' percentiles	502	55.10
n/a	n/a	Bexar County, TX	County's own percentile	n/a	67.20
97.40	11.60	Bexar County, TX	Average of its tracts' percentiles	352	57.80
n/a	n/a	Harris County, TX	County's own percentile	n/a	69.50
97.60	5.90	Harris County, TX	Average of its tracts' percentiles	909	56.10
n/a	n/a	Philadelphia County, PA	County's own percentile	n/a	89.60
99.10	14.90	Philadelphia County, PA	Average of its tracts' percentiles	342	69.30
n/a	n/a	Bronx County, NY	County's own percentile	n/a	92.90
98.50	20.10	Bronx County, NY	Average of its tracts' percentiles	188	72.40
n/a	n/a	Wayne County, MI	County's own percentile	n/a	93.60
99.50	13.80	Wayne County, MI	Average of its tracts' percentiles	488	67.50

In every county the county percentile lies inside the line for its tracts, and in nearly every one it sits farther from the middle than the average of those tracts. The first dot is the percentile of the county index built from the county's own ACS estimates; the second is the population-weighted mean of the percentiles of its tracts, and its line runs from the 5th to the 95th percentile of the tract percentiles of its residents. Counties are the most populous in the county frame, ordered by the county percentile.Note: The line is a spread of the county's tract percentiles, weighted by residents, and not a confidence interval. The county percentile has no interval because the staged county files carry no margins of error for the ACS estimates it rests on.Note: Tract percentiles are among residents of the tract frame. Tracts missing a home value, rent or mortgage median are outside the frame, so for counties where the frame holds less than 90% of residents (Nassau County, NY; Suffolk County, NY; New York County, NY; Kings County, NY; Miami-Dade County, FL; Dallas County, TX; Harris County, TX; Bronx County, NY; Wayne County, MI) the average and the spread describe only the tracts that remain.Note: Counties are chosen by population, and ordered by county percentile, because the spread of a small county rests on few tracts.Source: ACS 2019-2023 five-year estimates (tracts and counties); population-weighted (the line is a spread of tract percentiles, not an interval)

Across the country, 64.6% (95% CI 60.5% to 68.7%) of the variance of the tract percentile lies between tracts of the same county, which a county percentile cannot see. Among the 728 counties with at least 20 tracts in the tract frame, which hold 81.8% of residents, the median range from the 5th to the 95th percentile of a county's tracts is 79.0 (95% CI 75.5 to 80.8) points when counties are weighted by residents and 67.4 (95% CI 66.0 to 68.6) points when each county counts once. The median grows with the floor on the number of tracts. Weighted by residents it goes from 76.5 at a floor of 10 to 81.0 at a floor of 50, and counting each county once it goes from 58.5 to 76.7. The within-county share depends on the index: Chapter 10.1, Gradients, slopes and variance splits the published ADI and a nine-measure index the same way and gets different shares.

A county value that keeps some of this structure is the share of its residents who live in tracts at or above the 80th percentile, the most deprived fifth of the tract ranking. That share correlates 0.75 (95% CI 0.73 to 0.77) with the county's own percentile across counties. Counties in the middle fifth of the county ranking, with an own percentile from 40th to 60th and at least 20 tracts in the frame, number 159 and hold 17.7% of residents. In those counties, weighted by residents, the share of residents in the most deprived tracts is 4.3% (95% CI 2.3% to 5.8%) at the 5th percentile of counties, 16.6% (95% CI 14.5% to 20.4%) at the median and 25.3% (95% CI 23.9% to 27.1%) at the 95th. Counting each county once, the three values are 0.0% (95% CI 0.0% to 2.1%), 11.6% (95% CI 9.9% to 13.2%) and 23.9% (95% CI 21.9% to 25.5%). A single county percentile does not record that spread.

Correlations change with the box

Figure 4 correlates the index percentile with four tract measures, first across tracts and then across counties. A county's value of a measure is the mean of its tracts' values weighted by residents, so that only the unit changes.

Life expectancy at birth, from USALEEP for deaths in 2010 to 2015, correlates −0.62 (95% CI −0.64 to −0.60) with the index across tracts and −0.76 (95% CI −0.79 to −0.72) across counties weighted by residents, a stronger relationship at the larger unit. Counting each county once gives −0.56 (95% CI −0.59 to −0.54), weaker than across tracts, so the strengthening depends on how counties are weighted. Upward mobility, the Opportunity Atlas rank of children from low-income families, correlates −0.58 (95% CI −0.60 to −0.56) across tracts, −0.59 (95% CI −0.64 to −0.54) across weighted counties and −0.36 (95% CI −0.38 to −0.33) across counties counted once, and the tract and weighted-county intervals overlap. The poverty rate follows the same pattern, with +0.78 (95% CI 0.78 to 0.79), +0.75 (95% CI 0.72 to 0.78) and +0.65 (95% CI 0.63 to 0.66).

Poverty is one of the measures the index is built from, so that correlation is partly built in at any unit. Homeownership is another, and its correlation with the index is −0.43 (95% CI −0.46 to −0.40) across tracts, +0.06 (95% CI −0.06 to 0.17) across weighted counties, an interval that includes zero, and −0.07 (95% CI −0.11 to −0.03) across counties counted once. The loss matches the loss of weight in Figure 1.

Figure 4

The index correlates −0.62 with life expectancy across tracts and −0.76 across counties, and −0.43 with homeownership across tracts and +0.06 across counties

Correlation of the index percentile among residents with four tract measures, across tracts and across counties, ACS 2019 to 2023, USALEEP 2010 to 2015 and Opportunity Atlas 1978 to 1983 cohorts

Tracts
Counties, weighted by residents
Counties, each counted once

Show data

Data for The index correlates −0.62 with life expectancy across tracts and −0.76 across counties, and −0.43 with homeownership across tracts and +0.06 across counties
conf_high	conf_low	n	outcome	r	zoom
−0.600	−0.640	71,874	Life expectancy at birth (deaths 2010 to 2015)	−0.621	Tracts
−0.717	−0.792	3,101	Life expectancy at birth (deaths 2010 to 2015)	−0.758	Counties, weighted by residents
−0.537	−0.587	3,101	Life expectancy at birth (deaths 2010 to 2015)	−0.562	Counties, each counted once
−0.555	−0.598	75,731	Upward mobility (children born 1978 to 1983)	−0.577	Tracts
−0.542	−0.640	3,155	Upward mobility (children born 1978 to 1983)	−0.593	Counties, weighted by residents
−0.331	−0.383	3,155	Upward mobility (children born 1978 to 1983)	−0.356	Counties, each counted once
0.788	0.775	76,496	Poverty rate (ACS 2019 to 2023)	0.782	Tracts
0.782	0.724	3,203	Poverty rate (ACS 2019 to 2023)	0.752	Counties, weighted by residents
0.665	0.634	3,203	Poverty rate (ACS 2019 to 2023)	0.649	Counties, each counted once
−0.401	−0.463	76,496	Homeownership rate (ACS 2019 to 2023)	−0.432	Tracts
0.175	−0.059	3,203	Homeownership rate (ACS 2019 to 2023)	0.065	Counties, weighted by residents
−0.032	−0.111	3,203	Homeownership rate (ACS 2019 to 2023)	−0.071	Counties, each counted once

The tract dots and the weighted county dots part for life expectancy and homeownership and sit together for upward mobility and poverty, and counting each county once moves the dots for life expectancy, mobility and poverty toward zero. A dot is a correlation of the index percentile with a tract measure, or with the population-weighted mean of that measure over a county's tracts, with a 95% interval from a bootstrap over counties. The county index is built from the county's own estimates.Note: A county's value of a measure is the population-weighted mean of its tracts' values, so only the unit changes between the tract dots and the county dots. Poverty and homeownership are ingredients of the index, so their correlations are partly built in; life expectancy and upward mobility are not.Note: Life expectancy is a modeled estimate for deaths in 2010 to 2015 on 2020 tracts, interpolated from 2010 tracts, with institutional tracts dropped; upward mobility is the Opportunity Atlas rank of children from low-income families, interpolated to 2020 tracts.Source: ACS 2019-2023; NCHS USALEEP 2010-2015; Opportunity Atlas 1978-1983 birth cohorts; population-weighted unless the row says each county is counted once

Gehlke and Biehl reported in 1934 that the size of a correlation computed from census tract data depended on how the tracts were grouped,[4] and Openshaw and Taylor regrouped one data set into many zonings and obtained a wide range of correlations from it.[5, 6] The pattern is the modifiable areal unit problem, which reaches multivariate analysis as well,[7] and Chapter 10.1, Gradients, slopes and variance measures it for correlations among ACS measures. The results here come from one set of boundaries and show no general direction. Under weights, the correlation with life expectancy rises with the unit, those with mobility and poverty hold, and the one with homeownership disappears. A correlation across counties describes counties. Robinson showed that a correlation across areas can differ from the correlation across the people inside them,[8, 9] and nothing in this chapter measures individuals.

What these data cannot show

The data describe places. A county percentile and a tract percentile are properties of places, and neither says how deprived any resident is: a poor household in a comfortable tract takes the tract's percentile, which is the problem of ecological inference. The correlations in the last section are across places and say nothing about the people inside them.

The ACS files carry no margins of error, and the medians of small tracts rest on few households, so part of the spread of tract percentiles within a county is sampling error, and the data cannot say how much. The tract box leaves out tracts with a missing measure, mostly a missing median home value, rent or mortgage cost, as Chapter 10.2, The anatomy of a deprivation index finds, and tracts without a published ADI rank. The frame holds 92.4% of all residents and 92.9% of the residents of ranked tracts, and 1,691 tracts with 2.1 million residents have no rank. The tracts outside the frame are poorer, with a poverty rate of 17.8% against 12.5% inside. The missing tracts are concentrated in some counties: the frame holds 52.5% of the residents of Bronx County and 74.2% of New York County, so for those counties and others with low coverage the average and the spread of tracts describe only the tracts that remain.

The percentile convention is a choice. This chapter ranks by residents, county files usually rank counties, and the second distribution in Figure 2 shows how far the choice moves a statement about residents. The analysis uses one recipe and one set of measures. The ADI formula would rank counties by home value, as the correlations above show, and the state ADI, which ranks units within a state, is not tested. The county index is not compared with published county indexes.

Life expectancy is a modeled estimate for deaths in 2010 to 2015 and upward mobility concerns children born in 1978 to 1983, so both are older than the ACS measures. They show how an index built from recent measures lines up with older outcomes at two units and do not show which unit is correct. That depends on the question. For a program run by counties the county box is the right one, and a finding in it is a finding about counties.

Data sources

American Community SurveyACS 2019-2023 five-year estimates: the staged tract file, a Census API pull of housing, occupation, income-distribution and schooling tables for tracts, and the same pull for counties, Connecticut planning regions and Puerto Rico municipiosYears: 2019-2023 (5-year) · Weights: ACS 2019-2023 population of the tract or county · License: Public domain (U.S. Census Bureau)
Area Deprivation IndexNeighborhood Atlas ADI, 2023 release (version 4.0.1): a published rank is required for a tract to enter the tract frame, and the ADI is the comparison for the tract indexYears: 2023 release (version 4.0.1; built on ACS 2019-2023) · Weights: none (index); tract values are unweighted means of block-group ranks · License: Free for non-commercial use; cite the Neighborhood Atlas and Kind and Buckingham
USALEEP life expectancyNCHS small-area life expectancy at birth, deaths 2010 to 2015, 2020 tracts (interpolated), institutional tracts droppedYears: 2010-2015 · Weights: ACS 2019-2023 tract population · License: Public domain (NCHS, CDC)
Opportunity AtlasMean adult household income rank of children from low-income families, 1978 to 1983 birth cohorts, 2020 tracts (interpolated)Years: 1978-1983 birth cohorts (2018 release) · Weights: ACS 2019-2023 tract population · License: Public use (Opportunity Insights and the U.S. Census Bureau)

All data sources

Methods

This chapter builds one deprivation index with one recipe in two boxes, 76,496 census tracts and 3,205 counties (with Connecticut's planning regions and Puerto Rico's municipios), and ranks each unit among the residents of its box. The index is the first principal component of 14 census measures from ACS 2019-2023 and is not the Neighborhood Atlas ADI, which ranks block groups. Tracts need a published ADI rank to enter the tract box, and the single-parent measure is left out of both boxes because the tract and county files define it differently. Life expectancy (deaths in 2010 to 2015) and upward mobility (children born 1978 to 1983) describe earlier periods than the ACS measures, and the ACS files carry no margins of error, so the only intervals come from resampling whole counties.

Which tracts and counties are in each box

The comparison uses two boxes. The tract box holds the 76,496 2020 census tracts with a published ADI rank, an ACS 2019-2023 population above zero and all 14 measures (the 15 that chapter 10.2 rebuilds without the share of single-parent households), out of 85,396 tracts in the staged ADI file; they hold 92.9 percent of the residents of tracts with a rank. The county box holds the 3,205 of the 3,222 rows of the county ACS pull (counties, Connecticut's nine planning regions and Puerto Rico's municipios) that have a population above zero and all 14 measures; 17 rows lack a measure.

Tracts outside the tract frame are those without a published ADI rank or with a missing measure (mostly a missing median home value, rent or mortgage cost); Puerto Rico's tracts and municipios are inside both boxes.

Measures and the single-parent measure

The single-parent measure is left out of both boxes because the staged tract file and the county core file define it differently (a share of households and a share of families with own children), so its county value is about 1.52 times the resident-weighted mean of its tracts' values outside Utah and Puerto Rico; with the staged tract value added as a fifteenth measure the tract index ranks tracts with a rank correlation of 0.996 with the 14-measure index.

Tract measures come from the staged ACS tract file and a Census API pull archived under data/raw/acs/deprivation_components_2019_2023; county measures come from the same pull and from the county core file, so a county's median is its own estimate and not an average of tract medians. b2.load has no loader for the pull, so the chapter registers its three files and reads them through load_staged. The measures, their substitutions and Singh's income disparity are those of chapter 10.2.

The published formula is applied with Singh's coefficients (Singh 2003, as printed in Petterson 2023, Table 1) to the 14 measures in their own units; adding the single-parent term from the county core file changes the county ranking by less than a rank correlation of 0.9999.

How the index and percentiles are computed

In each box the measures are standardized with the box's population-weighted means and standard deviations, the first principal component is the leading eigenvector of the population-weighted correlation matrix (the weights are the residents of each tract or each county), signed so that the poverty rate has a positive weight, and a unit's percentile is the share of residents of its box who live in units that score lower, counting half of any tied units.

The first edition and the Neighborhood Atlas rank units instead; that convention is reported as 'among tracts and counties'.

Figure explained here: Figure 1

How counties and tracts are compared

Counties in both frames are compared with the population-weighted mean and the 5th and 95th percentiles of the percentiles of their tracts (weighted by residents). A county enters the restricted comparison when tracts of the tract frame hold at least 90 percent of its residents, and the spread summary needs at least 20 tracts in the frame; floors of 10 and 50 are reported beside it.

The median absolute gap is read from bins of 0.1 percentile points. The variance split is the population-weighted variance of the tract percentile within counties over its total.

Figures explained here: Figure 2 and Figure 3

Outcomes and correlations

Life expectancy is USALEEP for deaths in 2010 to 2015 on 2020 tracts (institutional tracts dropped), upward mobility is the Opportunity Atlas rank of children of parents at the 25th income percentile, and poverty and homeownership are the ACS tract rates; a county's value of each is the mean of its tracts' values weighted by residents.

Correlations are Pearson correlations of the index percentile and the measure, weighted by residents of the tract or county, or counting each county once.

Figure explained here: Figure 4

Uncertainty

Intervals are 95% percentile intervals from 2,000 draws of whole counties with replacement (seed 12345; Connecticut's planning regions stand in for counties; in the county box each county is a draw), with percentiles held at their full-box values.

The ACS files carry no margins of error.

References

Kind, Amy J. H.; Buckingham, William R. (2018). Making Neighborhood-Disadvantage Metrics Accessible: The Neighborhood Atlas. New England Journal of Medicine 378(26): 2456-2458. doi:10.1056/NEJMp1802313
Singh, Gopal K. (2003). Area Deprivation and Widening Inequalities in US Mortality, 1969-1998. American Journal of Public Health 93(7): 1137-1143. doi:10.2105/AJPH.93.7.1137
Petterson, Stephen (2023). Deciphering the Neighborhood Atlas Area Deprivation Index: the consequences of not standardizing. Health Affairs Scholar 1(5): qxad063. doi:10.1093/haschl/qxad063
Gehlke, C. E.; Biehl, Katherine (1934). Certain Effects of Grouping upon the Size of the Correlation Coefficient in Census Tract Material. Journal of the American Statistical Association 29(185A): 169-170. doi:10.1080/01621459.1934.10506247
Openshaw, Stan; Taylor, Peter J. (1979). A million or so correlation coefficients: three experiments on the modifiable areal unit problem. In N. Wrigley (ed.), Statistical Applications in the Spatial Sciences, London: Pion, 127-144.
Openshaw, Stan (1984). The Modifiable Areal Unit Problem. CATMOG 38, Norwich: Geo Books.
Fotheringham, A. Stewart; Wong, David W. S. (1991). The modifiable areal unit problem in multivariate statistical analysis. Environment and Planning A 23(7): 1025-1044. doi:10.1068/a231025
Robinson, W. S. (1950). Ecological Correlations and the Behavior of Individuals. American Sociological Review 15(3): 351-357. doi:10.2307/2087176
Subramanian, S. V.; Jones, Kelvyn; Kaddour, Afamia; Krieger, Nancy (2009). Revisiting Robinson: the perils of individualistic and ecologic fallacy. International Journal of Epidemiology 38(2): 342-360. doi:10.1093/ije/dyn359

How to cite

@misc{singh2026deprivationattwozooms,
  author = {Singh, Vishal},
  title = {A deprivation index at two zooms},
  year = {2026},
  url = {https://vishalsingh.org/zipcode/deprivation-at-two-zooms},
  note = {In ZIP Code Destiny. Published 9 October 2026.}
}

Same question at another grain

These chapters take up the same axis with a different unit of analysis.

Deprivation index
- Chapter 10.2, The anatomy of a deprivation index Neighborhoods

One recipe in two boxes

The county ranking follows the average of its neighborhoods

Residents sit far from their county's percentile

A county percentile hides a wide spread of neighborhoods

Correlations change with the box

What these data cannot show

Data sources

Methods

Which tracts and counties are in each box

Measures and the single-parent measure

How the index and percentiles are computed

How counties and tracts are compared

Outcomes and correlations

Uncertainty

References

How to cite

Same question at another grain

Reading paths