Chapter 10.1 · The factory floor

Gradients, slopes and variance

Life expectancy is 1.12 years lower per ten-point step of the ADI within counties and lower in all 267 metros, and 70.3 percent of the variance of tract life expectancy lies between tracts in the same county, of which 26.7 points are estimation error in the modeled tract estimates.

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

Life expectancy at birth is 0.84 (95% CI 0.75 to 0.92) years lower for each ten-point step up the Area Deprivation Index (ADI) national percentile across the 77,936 census tracts that have an ADI rank and a USALEEP estimate for deaths in 2010 to 2015.[1, 2] Within counties the difference is 1.12 (95% CI 1.07 to 1.16) years, and a separate regression in each of 267 metros finds lower life expectancy in more deprived tracts in every one. This chapter shows how those estimates are made and where they stop being informative. It covers the regression and its fixed effects, one regression per metro and per state, a nine-measure index, the change in a correlation with the size of the area, the split of variance between states, counties and tracts, and the suppressed cells of CDC WONDER. The gradient by decile of deprivation is the subject of Chapter 6.1, Place and the length of a life.

The slope is steeper within counties than across all tracts

The regression behind most figures in this book is a population-weighted least-squares line through tracts,

Y_i = \alpha + \beta\,\mathrm{ADI}_i + \varepsilon_i,

where $Y_i$ is the life expectancy of tract $i$ in years, $\mathrm{ADI}_i$ is its national percentile (higher is more deprived), $\alpha$ is the intercept, $\beta$ is the slope and $\varepsilon_i$ is the part of life expectancy the line leaves unexplained. The line minimizes the sum of squared residuals with each tract weighted by its 2019-2023 population, so a tract with few residents counts for less. The book reports the estimated $\beta$ with its sign reversed and scaled to a ten-point step, so a reported slope is the years of life expectancy lower for a ten-point step, and a slope above zero means life expectancy is lower where the ADI is higher. Counting each tract once moves none of the three slopes in Figure 1 by more than 0.015 years, so the weights do not produce the result.

A national slope can come from composition, with the least deprived tracts concentrated in some states and the most deprived in others. The fixed-effects ladder tests for that by giving each state, and then each county, its own intercept,

Y_{ig} = \beta\,\mathrm{ADI}_{ig} + \mu_g + \varepsilon_{ig},

where $g$ indexes states in the second row of the figure and counties in the third, and $\mu_g$ is the constant of group $g$ . The slope $\beta$ then compares only tracts in the same state or county. The fits subtract each group's weighted mean from life expectancy and from the ADI before fitting, which gives the same slope as a dummy variable for every group. Errors cluster on the group that was absorbed, states for the first two rows and counties for the third, and the intervals use the t distribution with one fewer degree of freedom than there are clusters.[3]

Across all tracts, life expectancy is 0.84 years lower per step, within states 0.92 and within counties 1.12, so the within-county slope is 1.3 times the national one. A composition story predicts the opposite order. The county fit uses 77,722 tracts, because a tract that is alone in its county adds no contrast.

Figure 1

Life expectancy is 1.12 years lower per ten-point step of the ADI within counties, against 0.84 years across all tracts

Slope of tract life expectancy at birth on the Area Deprivation Index national percentile, years lower per ten-point step, three specifications, deaths in 2010 to 2015

Population-weighted
Each tract once

Show data

Data for Life expectancy is 1.12 years lower per ten-point step of the ADI within counties, against 0.84 years across all tracts
Specification	Weights	Years lower per ten points	Lower limit of the 95% interval	Upper limit of the 95% interval	Clusters	Tracts
All tracts	Population-weighted	0.84	0.75	0.92	51	77,936
All tracts	Each tract once	0.84	0.75	0.93	51	77,936
Within states	Population-weighted	0.92	0.78	1.05	51	77,936
Within states	Each tract once	0.91	0.77	1.05	51	77,936
Within counties	Population-weighted	1.12	1.07	1.16	2,890	77,722
Within counties	Each tract once	1.13	1.09	1.17	2,890	77,722

The within-county dots lie right of the all-tracts dots, with the within-state dots between them and a wider interval. Each dot is a regression slope with a 95% interval; the two dots in a row weight tracts by population or count each tract once, as the key above the chart says.Note: Intervals use cluster-robust errors, clustered on states for the first two rows and on counties for the third, with t intervals on one fewer degree of freedom than there are clusters. The county fit leaves out tracts that are alone in their county, so it uses 77,722 of 77,936 tracts.Note: Institutional tracts, such as prisons and dormitories, are dropped. USALEEP covers deaths in 2010 to 2015 and the 2020-tract file is area-weighted from 2010 tracts.Source: USALEEP life expectancy, 2010-2015; Area Deprivation Index, 2023; ACS 2019-2023; population-weighted and unweighted regression slopes, modeled estimates

A slope that survives these comparisons shows that rich and poor states at opposite ends of one line do not produce the pattern. It still compares tracts, and families sort themselves among tracts for reasons the regression does not observe, so it does not say what would happen to a family that moved.

Life expectancy is lower in more deprived tracts in every metro

A single slope assumes that the relationship is the same everywhere, and fitting the regression separately in each metro measures how much it differs. A metro here is a core-based statistical area, metropolitan or micropolitan, as the Census Bureau's county file codes it. Every tract takes the area of its county, which keeps Connecticut, whose planning regions stand in for counties. The file has no names, so Figure 2 labels each metro by its most populous county, and Connecticut metros by a planning region. A metro enters if it has at least 40 tracts with a life expectancy and an ADI rank. 267 do, and they hold 82% of the residents in the sample. A floor of 25 tracts gives 403 metros and a floor of 100 gives 134, and life expectancy is lower in more deprived tracts in every metro at each of the three floors.

The model is the first one, fitted within each metro $m$ with the same tract weights,

Y_{im} = \alpha_m + \beta_m\,\mathrm{ADI}_{im} + \varepsilon_{im},

where $\alpha_m$ and $\beta_m$ are the intercept and slope of metro $m$ . Errors cluster on counties in the 64 metros that have at least 5 counties. The rest use HC3 errors, which let the variance differ across tracts but treat tracts as independent, so their intervals may be too narrow where neighboring tracts resemble one another.

All 267 reported slopes are above zero, and the 95% interval of 260 of them lies above zero. The median metro has a life expectancy 1.20 (95% CI 1.14 to 1.23) years lower per ten-point step, with an interval from a bootstrap over metros. At the 5th percentile of metros the difference is 0.70 years and at the 95th it is 1.67, a ratio of 2.4.

Part of that range is estimation error. Let $\hat\beta_m$ be the estimated slope of metro $m$ and $v_m$ its squared standard error, let $s^2$ be the variance of the $\hat\beta_m$ across metros and let $\bar v$ be the mean of the $v_m$ . The variance of the true slopes is estimated by $\tau^2 = s^2 - \bar v$ , and each estimate can be shrunk toward the mean $\bar\beta$ in proportion to its reliability,

\tilde\beta_m = \bar\beta + \frac{\tau^2}{\tau^2 + v_m}\left(\hat\beta_m - \bar\beta\right).

Estimation error accounts for 48% of the variance of the estimated slopes. The standard deviation of the true slopes is 0.22 years against 0.31 for the estimates, and after shrinkage the 5th and 95th percentiles move to 0.88 and 1.46. The second tab of the figure sorts the estimates, which puts the metros with the least precise slopes at both ends, so the order of neighbors carries no information and the chapter names no metro as the steepest or the flattest.

Figure 2

Life expectancy is lower in more deprived tracts in all 267 metros, by a median of 1.20 years per ten-point step

One regression of tract life expectancy on the ADI national percentile in each metro with enough tracts, shown by metro and as a distribution, deaths in 2010 to 2015

After shrinkage the 5th and 95th percentile metro slopes move from 0.70 and 1.67 years to 0.88 and 1.46

Number of metros by slope of life expectancy on the ADI, years lower per ten-point step, estimated and shrunken, in bins of equal width

The shrunken slopes bunch near the median and the estimated slopes spread out on both sides. Each bar counts metros in a bin; shrinkage pulls every slope toward the mean by an amount that grows with its squared standard error.

Show data

Data for Life expectancy is lower in more deprived tracts in all 267 metros, by a median of 1.20 years per ten-point step, Distribution
metros	series	x0	x1
1	Estimated slope	0	0.200
0	Estimated slope	0.200	0.400
3	Estimated slope	0.400	0.600
17	Estimated slope	0.600	0.800
48	Estimated slope	0.800	1
63	Estimated slope	1	1.20
76	Estimated slope	1.20	1.40
38	Estimated slope	1.40	1.60
14	Estimated slope	1.60	1.80
3	Estimated slope	1.80	2
2	Estimated slope	2	2.20
2	Estimated slope	2.20	2.40
0	Estimated slope	2.40	2.60
0	Estimated slope	2.60	2.80
0	Shrunken slope	0	0.200
0	Shrunken slope	0.200	0.400
1	Shrunken slope	0.400	0.600
3	Shrunken slope	0.600	0.800
30	Shrunken slope	0.800	1
104	Shrunken slope	1	1.20
103	Shrunken slope	1.20	1.40
25	Shrunken slope	1.40	1.60
1	Shrunken slope	1.60	1.80
0	Shrunken slope	1.80	2
0	Shrunken slope	2	2.20
0	Shrunken slope	2.20	2.40
0	Shrunken slope	2.40	2.60
0	Shrunken slope	2.60	2.80

The first tab compares the distribution of the estimated slopes with the distribution after shrinkage, and the second lists the metro slopes with their intervals. The median metro has a slope of 1.20 years lower per ten-point step, with a bootstrap interval over metros.Source: USALEEP life expectancy, 2010-2015; Area Deprivation Index, 2023; ACS 2019-2023; population-weighted regression slopes, modeled estimates

Figure 3 plots the metro slope against a metro's median household income, taken as the population-weighted median of its tracts' median incomes. Two further traits are the dispersion of tract ADI in the metro (the population-weighted standard deviation) and the metro's population. Each correlation is computed weighted by metro residents and counting each metro once, with a bootstrap interval over metros, and all six intervals include zero, the one for ADI dispersion counting each metro once only just. The correlation with income is +0.13 (95% CI −0.24 to 0.46) weighted and +0.05 (95% CI −0.11 to 0.19) unweighted, with ADI dispersion −0.21 (95% CI −0.46 to 0.12) and −0.14 (95% CI −0.27 to 0.01), and with population −0.20 (95% CI −0.47 to 0.10) and −0.06 (95% CI −0.18 to 0.08), the slope measured as years lower per step. No line is drawn through the cloud.

This is a failure to detect a relationship and not evidence that none exists. The slopes carry estimation error, 48% of their variance, which pulls every correlation toward zero, and the weighted intervals are wide enough to leave a moderate correlation of either sign for income, dispersion or population. The traits also do not exhaust the candidates, which include health systems and housing, and the chapter tests no others.

Figure 3

Metro slopes are not detectably related to metro median income, a correlation of +0.05 counting each metro once

Slope of life expectancy on the ADI, years lower per ten-point step, against the population-weighted median of tract median household income, one dot per metro, dot area is residents, ACS 2019-2023

Years of life expectancy lower per ten-point step in the ADI

Dot area: Residents1,900,0006,600,00019,000,000

Show data

Data for Metro slopes are not detectably related to metro median income, a correlation of +0.05 counting each metro once
Metro (most populous county)	Median household income (dollars)	Years lower per ten points	Residents
Summit, OH	78,539	1.27	669,646
Dougherty, GA	58,616	1.22	137,062
Albany, NY	90,562	1.24	836,414
Bernalillo, NM	67,143	0.97	893,158
Rapides, LA	55,364	1.40	140,716
Lehigh, PA	84,487	0.96	833,485
Randall, TX	68,494	0.97	237,500
Anchorage, AK	98,834	1.45	380,453
Washtenaw, MI	96,960	1.43	304,946
Outagamie, WI	79,222	1.07	219,811
Buncombe, NC	68,432	0.65	441,184
Clarke, GA	69,709	1.23	199,046
Fulton, GA	87,864	1.07	5,630,116
Atlantic, NJ	82,927	0.86	268,098
Lee, AL	70,429	0.41	164,528
Richmond, GA	69,885	1.09	574,113
Travis, TX	100,981	0.68	2,125,441
Kern, CA	65,661	0.96	825,064
Baltimore, MD	105,865	1.40	2,720,602
Barnstable, MA	95,323	1.92	216,294
East Baton Rouge, LA	72,773	1.33	773,655
Jefferson, TX	69,211	1.23	370,574
Whatcom, WA	86,204	0.81	209,575
Deschutes, OR	87,928	1.42	186,931
Yellowstone, MT	74,303	1.40	180,017
Broome, NY	69,856	1.29	229,131
Jefferson, AL	73,171	1.31	1,073,001
McLean, IL	93,924	1.13	146,591
Ada, ID	82,830	1.00	770,927
Middlesex, MA	115,783	1.30	4,655,005
Boulder, CO	111,280	1.31	269,739
Kitsap, WA	96,978	2.37	254,129
Western Connecticut, CT	119,204	1.13	906,110
Cameron, TX	49,397	1.36	420,423
Erie, NY	74,430	1.33	1,114,712
Chittenden, VT	97,573	1.20	212,127
Stark, OH	67,916	1.58	393,729
Lee, FL	73,765	0.80	706,110
Linn, IA	79,604	1.14	267,683
Champaign, IL	78,227	1.87	189,134
Kanawha, WV	56,842	0.97	240,764
Charleston, SC	84,750	0.88	755,397
Mecklenburg, NC	79,411	1.13	2,441,459
Albemarle, VA	99,461	1.10	205,622
Hamilton, TN	66,386	1.31	550,749
Cook, IL	89,535	1.15	9,078,307
Butte, CA	66,437	1.63	199,170
Hamilton, OH	83,974	1.56	2,187,695
Montgomery, TN	69,185	0.96	216,994
Cuyahoga, OH	75,421	1.32	1,974,832
Brazos, TX	64,066	0.85	215,331
El Paso, CO	90,786	1.45	683,216
Boone, MO	75,882	1.07	177,863
Richland, SC	68,108	1.14	774,726
Muscogee, GA	56,087	1.44	307,364
Franklin, OH	84,228	1.36	1,996,447
Nueces, TX	62,659	0.85	400,651
Okaloosa, FL	81,407	1.04	282,957
Dallas, TX	89,919	0.91	6,987,097
Baldwin, AL	72,143	1.04	233,001
Scott, IA	73,210	1.00	371,800
Montgomery, OH	71,585	1.66	767,209
Volusia, FL	68,729	1.26	654,841
Denver, CO	103,222	1.19	2,715,379
Polk, IA	88,621	1.03	699,409
Wayne, MI	78,215	1.30	4,220,000
St. Louis, MN	73,474	1.09	269,181
Durham, NC	80,667	1.03	577,271
Monroe, PA	82,889	0.87	150,264
Elkhart, IN	74,014	1.77	202,494
El Paso, TX	59,731	0.63	815,804
Erie, PA	68,900	1.50	241,679
Lane, OR	75,900	1.36	356,564
Vanderburgh, IN	70,479	1.80	307,015
Cass, ND	81,328	1.67	245,120
Cumberland, NC	63,983	1.21	481,759
Benton, AR	79,398	0.69	532,009
Genesee, MI	67,173	1.32	386,955
Florence, SC	51,228	1.13	194,799
Lauderdale, AL	62,256	1.34	150,584
Larimer, CO	96,086	1.21	335,193
Sebastian, AR	57,749	1.27	246,136
Allen, IN	74,450	1.58	419,042
Fresno, CA	68,789	1.04	972,223
Alachua, FL	65,453	1.49	274,469
Hall, GA	78,409	0.84	197,646
Warren, NY	73,926	0.70	120,895
Kent, MI	79,418	1.06	1,042,581
Weld, CO	91,034	1.07	303,989
Brown, WI	78,555	1.07	314,505
Guilford, NC	64,720	1.42	734,908
Greenville, SC	67,109	1.18	907,427
Harrison, MS	63,333	0.83	403,294
Washington, MD	81,677	1.56	285,382
Dauphin, PA	80,314	1.27	577,920
Capitol, CT	101,384	1.15	1,084,341
Forrest, MS	57,582	1.13	168,319
Catawba, NC	60,922	0.88	349,670
Hawaii, HI	82,193	0.95	203,684
Beaufort, SC	80,222	0.93	208,704
Citrus, FL	52,582	0.94	158,693
Terrebonne, LA	66,584	0.87	201,316
Harris, TX	82,729	0.82	6,642,463
Cabell, WV	59,798	1.24	342,756
Madison, AL	90,881	1.30	458,766
Marion, IN	82,707	1.33	2,032,367
Jackson, MI	73,094	1.12	153,400
Hinds, MS	63,404	1.25	552,763
Madison, TN	60,270	1.32	173,169
Duval, FL	79,227	1.38	1,564,210
Washington, TN	55,932	1.02	207,033
Jasper, MO	64,575	1.54	183,022
Maui, HI	99,412	1.54	159,226
Kalamazoo, MI	76,432	1.22	245,459
Jackson, MO	84,494	1.27	2,096,382
Benton, WA	84,220	0.93	299,764
Bell, TX	69,611	0.69	405,407
Sullivan, TN	55,583	1.51	300,116
Ulster, NY	84,187	1.10	142,011
Knox, TN	72,138	1.44	809,385
Lafayette, LA	66,671	1.13	448,515
Tippecanoe, IN	66,937	1.44	195,160
Calcasieu, LA	66,533	1.11	202,151
Mohave, AZ	53,143	0.89	184,833
Polk, FL	65,270	1.20	714,860
Lancaster, PA	85,303	1.16	537,447
Ingham, MI	73,858	1.12	491,538
Webb, TX	56,078	0.99	245,692
Doña Ana, NM	52,415	0.48	210,924
Clark, NV	76,382	0.89	2,040,360
Grafton, NH	80,713	1.03	214,011
Fayette, KY	74,213	1.41	469,966
Lancaster, NE	78,349	1.32	309,128
Pulaski, AR	66,246	1.39	705,921
Laurel, KY	48,033	1.20	135,185
Gregg, TX	66,104	0.74	264,952
Los Angeles, CA	93,203	1.30	12,424,893
Jefferson, KY	75,097	1.51	1,237,206
Lubbock, TX	67,469	0.68	281,286
Bedford, VA	68,254	1.40	246,474
Bibb, GA	63,730	1.40	218,037
Dane, WI	95,609	0.78	572,839
Hillsborough, NH	111,157	1.12	406,867
Hidalgo, TX	51,427	0.63	862,862
Jackson, OR	69,562	1.20	219,490
Shelby, TN	66,331	1.29	1,235,221
Merced, CA	62,533	0.84	270,880
Miami-Dade, FL	74,414	0.82	5,791,746
Milwaukee, WI	82,816	1.20	1,378,567
Hennepin, MN	100,713	1.23	3,551,467
Mobile, AL	60,264	1.31	406,513
Stanislaus, CA	79,423	1.02	548,836
Ouachita, LA	53,701	1.49	194,368
Monroe, MI	73,561	1.62	155,001
Montgomery, AL	63,880	1.23	333,773
Skagit, WA	84,454	1.24	130,407
Muskegon, MI	65,723	1.56	172,022
Horry, SC	67,828	0.87	489,212
Collier, FL	86,133	0.90	346,920
Davidson, TN	83,658	1.27	1,838,601
South Central Connecticut, CT	93,307	1.06	534,415
Jefferson, LA	67,691	1.16	1,171,586
Kings, NY	100,747	0.77	18,857,008
Berrien, MI	68,611	1.52	146,726
Sarasota, FL	80,341	0.95	831,108
Southeastern Connecticut, CT	94,811	1.24	260,834
Marion, FL	61,597	0.91	333,673
Davis, UT	100,390	1.64	684,276
Oklahoma, OK	73,307	1.30	1,362,954
Thurston, WA	97,796	1.69	289,042
Douglas, NE	84,841	1.14	906,982
Orange, FL	78,256	0.86	2,563,054
Ventura, CA	104,381	1.04	814,047
Brevard, FL	77,672	1.24	605,284
Bay, FL	74,261	0.80	173,076
Escambia, FL	75,748	1.45	475,092
Peoria, IL	71,097	1.24	389,448
Philadelphia, PA	95,391	1.20	5,987,126
Maricopa, AZ	86,916	0.89	4,383,220
Allegheny, PA	76,103	1.05	2,255,125
Cumberland, ME	90,084	1.06	484,107
Multnomah, OR	96,267	1.36	2,415,437
St. Lucie, FL	73,760	1.33	492,192
Schuylkill, PA	66,594	1.63	134,044
Orange, NY	100,646	0.67	654,415
Yavapai, AZ	65,085	0.74	239,019
Providence, RI	89,419	1.26	1,583,138
Utah, UT	101,864	1.15	622,944
Pueblo, CO	67,283	1.47	165,819
Charlotte, FL	63,346	1.11	166,856
Racine, WI	79,997	0.98	176,535
Wake, NC	94,676	0.89	1,312,735
Berks, PA	84,157	1.18	415,678
Shasta, CA	73,870	1.23	177,622
Washoe, NV	91,819	1.24	436,487
Chesterfield, VA	87,203	1.24	1,220,266
Riverside, CA	86,902	1.02	4,445,399
Roanoke, VA	68,774	1.31	304,511
Olmsted, MN	90,266	0.89	227,252
Monroe, NY	75,298	1.22	1,017,611
Winnebago, IL	72,373	1.46	333,345
Sacramento, CA	95,171	1.44	2,275,221
Saginaw, MI	62,664	1.72	178,008
Stearns, MN	78,277	1.18	191,054
St. Louis, MO	80,401	1.25	2,698,897
Marion, OR	80,970	1.41	420,236
Monterey, CA	88,897	0.95	412,418
Sussex, DE	76,838	0.99	409,522
Salt Lake, UT	98,169	1.20	1,180,115
Bexar, TX	73,970	0.85	2,362,483
San Diego, CA	105,089	1.08	3,038,849
Alameda, CA	139,249	2.35	4,509,425
Santa Clara, CA	161,876	0.62	1,901,120
San Luis Obispo, CA	96,635	0.72	245,057
Santa Cruz, CA	119,621	0.59	237,745
Santa Fe, NM	73,619	0.70	148,272
Santa Barbara, CA	99,372	1.22	412,638
Sonoma, CA	102,512	1.34	464,875
Chatham, GA	80,415	1.04	386,024
Luzerne, PA	64,824	1.36	547,160
King, WA	116,777	1.56	3,901,567
Indian River, FL	69,670	0.91	159,904
Caddo, LA	58,198	1.26	387,561
Minnehaha, SD	81,909	1.29	259,327
St. Joseph, IN	66,265	1.28	306,731
Spartanburg, SC	68,253	1.26	332,585
Spokane, WA	73,703	1.55	571,186
Sangamon, IL	81,653	1.57	206,373
Hampden, MA	78,217	1.47	661,944
Greene, MO	67,133	1.46	460,198
Clark, OH	60,631	2.13	124,716
San Joaquin, CA	93,350	1.46	765,093
Onondaga, NY	78,968	1.15	571,929
Leon, FL	73,029	1.01	313,008
Hillsborough, FL	72,580	0.99	2,915,720
Vigo, IN	62,079	1.84	173,868
Bowie, TX	56,942	0.95	132,963
Lucas, OH	69,543	1.23	618,783
Shawnee, KS	72,654	1.22	230,593
Grand Traverse, MI	80,819	1.10	152,857
Mercer, NJ	99,710	1.34	365,389
Pima, AZ	68,805	1.08	970,791
Tulsa, OK	67,647	1.24	992,751
Lee, MS	60,211	1.20	154,901
Tuscaloosa, AL	66,848	0.92	245,890
Smith, TX	72,525	0.88	229,377
Honolulu, HI	114,427	1.17	920,726
Oneida, NY	73,753	1.62	269,625
Solano, CA	100,671	2.16	438,687
Virginia Beach, VA	82,992	1.36	1,641,154
Tulare, CA	67,494	1.08	471,294
McLennan, TX	64,453	1.34	256,286
Houston, GA	83,283	0.80	189,105
Fairfax, VA	129,801	1.10	5,859,377
Naugatuck Valley, CT	93,202	1.11	434,486
Black Hawk, IA	75,013	1.09	155,456
Marathon, WI	77,127	1.69	163,997
Belmont, OH	60,282	1.61	129,839
Sedgwick, KS	71,185	1.29	639,062
Wichita, TX	65,991	1.49	129,389
New Hanover, NC	74,780	0.98	269,411
Forsyth, NC	66,974	1.24	653,947
Worcester, MA	99,647	1.01	840,052
Yakima, WA	68,633	1.11	253,792
York, PA	84,907	1.43	444,752
Mahoning, OH	58,912	1.70	512,839
Yuma, AZ	59,195	0.14	190,651

The dots form a cloud with no visible slope, and no fit line is drawn through it. Each dot is a metro with enough tracts for a slope; its area is the metro's residents and the income axis is logarithmic.Note: The income of a metro is the population-weighted median of its tracts' median household incomes, a proxy built from tract values. Slopes are estimates with the intervals shown in the metro figure, which this plot does not draw.Note: The correlations in the text are weighted by metro residents and counting each metro once, with bootstrap intervals over metros; all six intervals include zero.Source: USALEEP life expectancy, 2010-2015; ACS 2019-2023; Area Deprivation Index, 2023; metro slopes, population-weighted within metros, modeled estimates

The coefficient zoo returns coefficients of both signs

The method does not depend on life expectancy. For six behaviors and conditions in CDC PLACES, model-based estimates of the share of adults in each tract (modeled estimates),[4] the regression

P_i = a_s + \gamma_s\,\ln(\mathrm{income}_i) + \boldsymbol{\delta}_s'\,\mathbf{c}_i + \varepsilon_i

is fitted in each state $s$ across the tracts $i$ in it. Here $P_i$ is the share of adults with the condition or behavior, $\mathrm{income}_i$ is the tract's median household income, $\mathbf{c}_i$ holds the shares of residents who are ages 65 and over, Black alone and Hispanic, and the weight is the tract's adult population. The intercept $a_s$ , the income coefficient $\gamma_s$ and the control coefficients $\boldsymbol{\delta}_s$ are specific to state $s$ . The coefficient reported is $\gamma_s \ln 2$ , the change in points of prevalence for a doubling of income. A state enters if it has at least 60 tracts with every variable, and all 51 states, counting the District of Columbia as one, do, which gives 306 coefficients. Chapter 5.1, Health behaviors and the supply of care reads what they say about behavior, and Figure 4 shows the same dots.

The coefficients for smoking, obesity, diabetes, frequent mental distress and physical inactivity are negative in all 51 states, and the median for smoking is −4.7 points per doubling. The coefficient for binge drinking is positive in 50 states, with a median of +1.2 points. The state coefficients can themselves be analyzed. States where smoking is more common have more negative smoking coefficients, a correlation of −0.73 (95% CI −0.84 to −0.60) across states. Most of that is scale, since the same proportional gradient is more points where the level is higher. Dividing each coefficient by the state's smoking level gives a correlation of −0.18 (95% CI −0.42 to 0.08).

Figure 4

The same regression in every state gives coefficients below zero for five measures in all 51 states and above zero for binge drinking in 50

Points of prevalence per doubling of tract median household income, one dot per state and measure, adults, with controls for the age, Black and Hispanic shares of residents, 2022

Interval excludes zero
Interval includes zero

Show data

Data for The same regression in every state gives coefficients below zero for five measures in all 51 states and above zero for binge drinking in 50
Measure	State	Points per doubling	Lower limit of the 95% interval	Upper limit of the 95% interval	Tracts
Current smoking	Alabama	−5.29	−6.54	−4.05	1,423
Current smoking	Alaska	−8.13	−10.80	−5.45	173
Current smoking	Arizona	−5.12	−7.05	−3.18	1,725
Current smoking	Arkansas	−6.01	−7.17	−4.85	818
Current smoking	California	−3.66	−4.10	−3.23	9,003
Current smoking	Colorado	−2.88	−3.61	−2.15	1,423
Current smoking	Connecticut	−3.76	−4.87	−2.65	870
Current smoking	Delaware	−3.63	−5.14	−2.13	256
Current smoking	District of Columbia	−2.38	−3.45	−1.32	201
Current smoking	Florida	−4.95	−5.54	−4.36	5,053
Current smoking	Georgia	−5.70	−6.27	−5.14	2,766
Current smoking	Hawaii	−3.96	−4.52	−3.40	419
Current smoking	Idaho	−3.30	−4.00	−2.59	453
Current smoking	Illinois	−4.67	−5.93	−3.42	3,239
Current smoking	Indiana	−5.07	−6.55	−3.60	1,678
Current smoking	Iowa	−4.47	−5.64	−3.31	890
Current smoking	Kansas	−5.16	−6.46	−3.87	811
Current smoking	Kentucky	−7.14	−7.89	−6.38	1,287
Current smoking	Louisiana	−6.01	−6.60	−5.43	1,352
Current smoking	Maine	−5.80	−6.68	−4.91	399
Current smoking	Maryland	−4.84	−5.75	−3.92	1,449
Current smoking	Massachusetts	−3.95	−5.70	−2.20	1,585
Current smoking	Michigan	−5.85	−6.69	−5.01	2,869
Current smoking	Minnesota	−4.56	−5.34	−3.78	1,497
Current smoking	Mississippi	−5.77	−7.25	−4.29	865
Current smoking	Missouri	−6.34	−7.36	−5.31	1,644
Current smoking	Montana	−6.65	−8.29	−5.00	315
Current smoking	Nebraska	−3.80	−4.23	−3.37	550
Current smoking	Nevada	−4.54	−5.64	−3.44	767
Current smoking	New Hampshire	−4.38	−5.14	−3.62	347
Current smoking	New Jersey	−4.31	−4.87	−3.75	2,154
Current smoking	New Mexico	−6.93	−8.55	−5.31	594
Current smoking	New York	−4.70	−5.23	−4.17	5,182
Current smoking	North Carolina	−5.40	−6.02	−4.78	2,628
Current smoking	North Dakota	−4.04	−6.23	−1.86	227
Current smoking	Ohio	−6.77	−7.24	−6.30	3,129
Current smoking	Oklahoma	−6.30	−7.23	−5.36	1,189
Current smoking	Oregon	−4.57	−5.48	−3.66	991
Current smoking	Pennsylvania	−5.51	−5.98	−5.05	3,377
Current smoking	Rhode Island	−4.53	−5.11	−3.94	246
Current smoking	South Carolina	−5.61	−6.44	−4.78	1,301
Current smoking	South Dakota	−7.73	−10.72	−4.74	242
Current smoking	Tennessee	−6.64	−7.92	−5.36	1,675
Current smoking	Texas	−4.35	−4.98	−3.73	6,802
Current smoking	Utah	−1.76	−2.66	−0.86	707
Current smoking	Vermont	−3.95	−5.08	−2.83	192
Current smoking	Virginia	−4.66	−5.25	−4.07	2,152
Current smoking	Washington	−3.93	−4.54	−3.32	1,767
Current smoking	West Virginia	−5.86	−7.73	−3.99	543
Current smoking	Wisconsin	−4.04	−4.66	−3.42	1,523
Current smoking	Wyoming	−2.44	−5.45	0.56	159
Obesity	Alabama	−4.19	−5.38	−3.00	1,423
Obesity	Alaska	−5.44	−6.79	−4.08	173
Obesity	Arizona	−2.94	−4.29	−1.60	1,725
Obesity	Arkansas	−4.27	−5.48	−3.06	818
Obesity	California	−4.02	−5.36	−2.69	9,003
Obesity	Colorado	−1.90	−3.21	−0.58	1,423
Obesity	Connecticut	−5.18	−7.75	−2.61	870
Obesity	Delaware	−3.57	−4.88	−2.26	256
Obesity	District of Columbia	−1.46	−2.58	−0.33	201
Obesity	Florida	−5.09	−5.94	−4.24	5,053
Obesity	Georgia	−6.05	−7.26	−4.83	2,766
Obesity	Hawaii	−3.12	−3.40	−2.84	419
Obesity	Idaho	−3.29	−4.95	−1.62	453
Obesity	Illinois	−4.31	−5.85	−2.77	3,239
Obesity	Indiana	−3.79	−5.61	−1.96	1,678
Obesity	Iowa	−3.37	−4.61	−2.12	890
Obesity	Kansas	−4.54	−5.89	−3.19	811
Obesity	Kentucky	−5.33	−6.31	−4.34	1,287
Obesity	Louisiana	−5.19	−6.09	−4.30	1,352
Obesity	Maine	−6.92	−8.25	−5.60	399
Obesity	Maryland	−5.11	−7.78	−2.45	1,449
Obesity	Massachusetts	−3.57	−5.94	−1.20	1,585
Obesity	Michigan	−5.40	−6.53	−4.27	2,869
Obesity	Minnesota	−5.36	−6.53	−4.18	1,497
Obesity	Mississippi	−4.27	−5.67	−2.86	865
Obesity	Missouri	−4.95	−6.98	−2.93	1,644
Obesity	Montana	−5.67	−8.49	−2.85	315
Obesity	Nebraska	−3.15	−4.74	−1.56	550
Obesity	Nevada	−3.67	−4.87	−2.48	767
Obesity	New Hampshire	−2.80	−4.04	−1.56	347
Obesity	New Jersey	−5.19	−6.17	−4.22	2,154
Obesity	New Mexico	−5.71	−6.82	−4.61	594
Obesity	New York	−5.19	−6.80	−3.59	5,182
Obesity	North Carolina	−4.68	−5.96	−3.40	2,628
Obesity	North Dakota	−2.65	−4.32	−0.98	227
Obesity	Ohio	−5.73	−6.28	−5.18	3,129
Obesity	Oklahoma	−4.94	−6.09	−3.79	1,189
Obesity	Oregon	−3.21	−4.36	−2.07	991
Obesity	Pennsylvania	−4.76	−5.47	−4.05	3,377
Obesity	Rhode Island	−3.64	−5.39	−1.90	246
Obesity	South Carolina	−5.64	−6.83	−4.46	1,301
Obesity	South Dakota	−4.30	−5.52	−3.08	242
Obesity	Tennessee	−5.61	−7.06	−4.16	1,675
Obesity	Texas	−3.87	−4.48	−3.25	6,802
Obesity	Utah	−1.56	−2.61	−0.51	707
Obesity	Vermont	−3.52	−4.60	−2.43	192
Obesity	Virginia	−4.49	−5.82	−3.17	2,152
Obesity	Washington	−5.22	−7.57	−2.88	1,767
Obesity	West Virginia	−3.40	−4.67	−2.14	543
Obesity	Wisconsin	−3.44	−4.32	−2.57	1,523
Obesity	Wyoming	−3.13	−7.58	1.33	159
Diagnosed diabetes	Alabama	−2.33	−3.32	−1.34	1,423
Diagnosed diabetes	Alaska	−2.87	−3.89	−1.84	173
Diagnosed diabetes	Arizona	−2.22	−3.76	−0.69	1,725
Diagnosed diabetes	Arkansas	−2.85	−3.87	−1.84	818
Diagnosed diabetes	California	−1.35	−1.71	−0.98	9,003
Diagnosed diabetes	Colorado	−0.76	−1.28	−0.25	1,423
Diagnosed diabetes	Connecticut	−1.76	−2.78	−0.74	870
Diagnosed diabetes	Delaware	−0.86	−2.34	0.62	256
Diagnosed diabetes	District of Columbia	−0.39	−0.92	0.13	201
Diagnosed diabetes	Florida	−2.46	−3.01	−1.90	5,053
Diagnosed diabetes	Georgia	−2.57	−3.04	−2.09	2,766
Diagnosed diabetes	Hawaii	−1.82	−2.94	−0.70	419
Diagnosed diabetes	Idaho	−1.23	−2.01	−0.46	453
Diagnosed diabetes	Illinois	−1.71	−2.59	−0.83	3,239
Diagnosed diabetes	Indiana	−1.57	−2.43	−0.72	1,678
Diagnosed diabetes	Iowa	−1.28	−2.25	−0.31	890
Diagnosed diabetes	Kansas	−1.75	−2.43	−1.07	811
Diagnosed diabetes	Kentucky	−3.07	−3.50	−2.63	1,287
Diagnosed diabetes	Louisiana	−3.08	−3.65	−2.51	1,352
Diagnosed diabetes	Maine	−2.38	−2.91	−1.86	399
Diagnosed diabetes	Maryland	−1.72	−2.41	−1.03	1,449
Diagnosed diabetes	Massachusetts	−1.43	−2.19	−0.66	1,585
Diagnosed diabetes	Michigan	−2.11	−2.63	−1.60	2,869
Diagnosed diabetes	Minnesota	−1.59	−1.96	−1.22	1,497
Diagnosed diabetes	Mississippi	−3.08	−4.13	−2.04	865
Diagnosed diabetes	Missouri	−2.30	−2.85	−1.76	1,644
Diagnosed diabetes	Montana	−2.87	−3.85	−1.90	315
Diagnosed diabetes	Nebraska	−0.99	−1.47	−0.52	550
Diagnosed diabetes	Nevada	−2.04	−2.93	−1.14	767
Diagnosed diabetes	New Hampshire	−1.35	−1.94	−0.75	347
Diagnosed diabetes	New Jersey	−1.46	−1.94	−0.99	2,154
Diagnosed diabetes	New Mexico	−3.61	−4.53	−2.69	594
Diagnosed diabetes	New York	−2.24	−2.87	−1.61	5,182
Diagnosed diabetes	North Carolina	−2.41	−2.95	−1.87	2,628
Diagnosed diabetes	North Dakota	−1.70	−3.17	−0.23	227
Diagnosed diabetes	Ohio	−2.58	−2.99	−2.18	3,129
Diagnosed diabetes	Oklahoma	−2.95	−3.68	−2.23	1,189
Diagnosed diabetes	Oregon	−1.38	−2.13	−0.62	991
Diagnosed diabetes	Pennsylvania	−1.91	−2.22	−1.59	3,377
Diagnosed diabetes	Rhode Island	−2.01	−2.55	−1.47	246
Diagnosed diabetes	South Carolina	−2.82	−3.47	−2.18	1,301
Diagnosed diabetes	South Dakota	−3.14	−4.61	−1.67	242
Diagnosed diabetes	Tennessee	−2.84	−3.76	−1.91	1,675
Diagnosed diabetes	Texas	−1.86	−2.42	−1.29	6,802
Diagnosed diabetes	Utah	−0.38	−1.20	0.45	707
Diagnosed diabetes	Vermont	−1.09	−1.61	−0.57	192
Diagnosed diabetes	Virginia	−1.49	−1.94	−1.05	2,152
Diagnosed diabetes	Washington	−1.41	−1.93	−0.89	1,767
Diagnosed diabetes	West Virginia	−2.40	−3.84	−0.95	543
Diagnosed diabetes	Wisconsin	−1.03	−1.50	−0.55	1,523
Diagnosed diabetes	Wyoming	−1.02	−2.99	0.94	159
Frequent mental distress	Alabama	−4.47	−4.82	−4.12	1,423
Frequent mental distress	Alaska	−4.04	−5.03	−3.04	173
Frequent mental distress	Arizona	−4.21	−5.30	−3.11	1,725
Frequent mental distress	Arkansas	−4.24	−4.78	−3.70	818
Frequent mental distress	California	−3.34	−3.76	−2.93	9,003
Frequent mental distress	Colorado	−3.44	−4.15	−2.73	1,423
Frequent mental distress	Connecticut	−3.41	−3.88	−2.93	870
Frequent mental distress	Delaware	−3.95	−5.59	−2.31	256
Frequent mental distress	District of Columbia	−3.02	−4.58	−1.45	201
Frequent mental distress	Florida	−3.51	−3.82	−3.20	5,053
Frequent mental distress	Georgia	−4.03	−4.25	−3.80	2,766
Frequent mental distress	Hawaii	−2.41	−2.82	−2.00	419
Frequent mental distress	Idaho	−4.19	−5.20	−3.17	453
Frequent mental distress	Illinois	−3.42	−3.79	−3.05	3,239
Frequent mental distress	Indiana	−4.33	−4.68	−3.98	1,678
Frequent mental distress	Iowa	−4.31	−5.00	−3.62	890
Frequent mental distress	Kansas	−3.96	−4.35	−3.57	811
Frequent mental distress	Kentucky	−4.11	−4.41	−3.80	1,287
Frequent mental distress	Louisiana	−3.71	−4.17	−3.25	1,352
Frequent mental distress	Maine	−3.60	−4.13	−3.07	399
Frequent mental distress	Maryland	−3.93	−4.17	−3.69	1,449
Frequent mental distress	Massachusetts	−3.54	−3.83	−3.26	1,585
Frequent mental distress	Michigan	−4.30	−4.59	−4.00	2,869
Frequent mental distress	Minnesota	−3.95	−4.32	−3.58	1,497
Frequent mental distress	Mississippi	−3.82	−4.30	−3.34	865
Frequent mental distress	Missouri	−4.22	−4.65	−3.79	1,644
Frequent mental distress	Montana	−4.06	−4.83	−3.29	315
Frequent mental distress	Nebraska	−3.52	−3.99	−3.06	550
Frequent mental distress	Nevada	−2.82	−3.21	−2.42	767
Frequent mental distress	New Hampshire	−3.46	−4.09	−2.83	347
Frequent mental distress	New Jersey	−3.18	−3.63	−2.73	2,154
Frequent mental distress	New Mexico	−4.02	−4.70	−3.34	594
Frequent mental distress	New York	−2.93	−3.35	−2.50	5,182
Frequent mental distress	North Carolina	−3.89	−4.14	−3.64	2,628
Frequent mental distress	North Dakota	−3.91	−4.69	−3.13	227
Frequent mental distress	Ohio	−4.71	−4.99	−4.43	3,129
Frequent mental distress	Oklahoma	−4.33	−4.60	−4.06	1,189
Frequent mental distress	Oregon	−4.19	−4.87	−3.50	991
Frequent mental distress	Pennsylvania	−3.60	−3.82	−3.38	3,377
Frequent mental distress	Rhode Island	−2.93	−3.65	−2.22	246
Frequent mental distress	South Carolina	−3.80	−4.32	−3.28	1,301
Frequent mental distress	South Dakota	−4.69	−5.57	−3.81	242
Frequent mental distress	Tennessee	−4.32	−4.50	−4.14	1,675
Frequent mental distress	Texas	−3.83	−4.11	−3.55	6,802
Frequent mental distress	Utah	−3.80	−5.22	−2.38	707
Frequent mental distress	Vermont	−4.37	−5.55	−3.19	192
Frequent mental distress	Virginia	−3.86	−4.08	−3.63	2,152
Frequent mental distress	Washington	−4.30	−4.64	−3.96	1,767
Frequent mental distress	West Virginia	−4.42	−5.08	−3.77	543
Frequent mental distress	Wisconsin	−4.26	−4.76	−3.76	1,523
Frequent mental distress	Wyoming	−3.49	−4.43	−2.55	159
No leisure-time physical activity	Alabama	−8.26	−9.49	−7.02	1,423
No leisure-time physical activity	Alaska	−7.43	−9.28	−5.57	173
No leisure-time physical activity	Arizona	−6.01	−7.81	−4.22	1,725
No leisure-time physical activity	Arkansas	−9.36	−10.76	−7.97	818
No leisure-time physical activity	California	−5.16	−5.83	−4.48	9,003
No leisure-time physical activity	Colorado	−3.81	−4.54	−3.07	1,423
No leisure-time physical activity	Connecticut	−5.60	−6.98	−4.22	870
No leisure-time physical activity	Delaware	−6.14	−7.34	−4.95	256
No leisure-time physical activity	District of Columbia	−3.05	−3.82	−2.27	201
No leisure-time physical activity	Florida	−7.40	−8.10	−6.70	5,053
No leisure-time physical activity	Georgia	−8.61	−9.48	−7.73	2,766
No leisure-time physical activity	Hawaii	−4.83	−7.09	−2.57	419
No leisure-time physical activity	Idaho	−6.49	−7.48	−5.50	453
No leisure-time physical activity	Illinois	−6.54	−7.55	−5.53	3,239
No leisure-time physical activity	Indiana	−7.30	−8.70	−5.91	1,678
No leisure-time physical activity	Iowa	−7.56	−8.65	−6.46	890
No leisure-time physical activity	Kansas	−6.53	−7.42	−5.63	811
No leisure-time physical activity	Kentucky	−9.02	−9.63	−8.41	1,287
No leisure-time physical activity	Louisiana	−8.32	−9.14	−7.50	1,352
No leisure-time physical activity	Maine	−8.03	−9.35	−6.70	399
No leisure-time physical activity	Maryland	−6.69	−7.77	−5.62	1,449
No leisure-time physical activity	Massachusetts	−5.93	−7.56	−4.29	1,585
No leisure-time physical activity	Michigan	−7.22	−8.06	−6.37	2,869
No leisure-time physical activity	Minnesota	−6.25	−6.85	−5.65	1,497
No leisure-time physical activity	Mississippi	−8.38	−10.04	−6.72	865
No leisure-time physical activity	Missouri	−8.13	−8.97	−7.29	1,644
No leisure-time physical activity	Montana	−8.17	−9.75	−6.58	315
No leisure-time physical activity	Nebraska	−5.56	−6.21	−4.91	550
No leisure-time physical activity	Nevada	−5.65	−7.08	−4.22	767
No leisure-time physical activity	New Hampshire	−5.29	−6.12	−4.46	347
No leisure-time physical activity	New Jersey	−5.76	−6.59	−4.92	2,154
No leisure-time physical activity	New Mexico	−7.85	−9.10	−6.59	594
No leisure-time physical activity	New York	−6.95	−8.08	−5.82	5,182
No leisure-time physical activity	North Carolina	−7.53	−8.25	−6.82	2,628
No leisure-time physical activity	North Dakota	−6.37	−8.10	−4.63	227
No leisure-time physical activity	Ohio	−8.44	−8.88	−8.00	3,129
No leisure-time physical activity	Oklahoma	−9.23	−10.46	−7.99	1,189
No leisure-time physical activity	Oregon	−5.06	−5.98	−4.14	991
No leisure-time physical activity	Pennsylvania	−6.93	−7.46	−6.40	3,377
No leisure-time physical activity	Rhode Island	−5.88	−6.26	−5.50	246
No leisure-time physical activity	South Carolina	−8.46	−9.27	−7.64	1,301
No leisure-time physical activity	South Dakota	−7.28	−9.25	−5.30	242
No leisure-time physical activity	Tennessee	−8.52	−9.83	−7.21	1,675
No leisure-time physical activity	Texas	−6.93	−7.78	−6.07	6,802
No leisure-time physical activity	Utah	−3.44	−4.31	−2.56	707
No leisure-time physical activity	Vermont	−5.43	−6.39	−4.47	192
No leisure-time physical activity	Virginia	−5.79	−6.42	−5.16	2,152
No leisure-time physical activity	Washington	−5.31	−6.22	−4.40	1,767
No leisure-time physical activity	West Virginia	−8.03	−9.68	−6.37	543
No leisure-time physical activity	Wisconsin	−6.16	−6.64	−5.68	1,523
No leisure-time physical activity	Wyoming	−4.84	−8.10	−1.57	159
Binge drinking	Alabama	1.26	0.97	1.54	1,423
Binge drinking	Alaska	1.02	0.43	1.61	173
Binge drinking	Arizona	0.91	0.37	1.44	1,725
Binge drinking	Arkansas	1.97	1.23	2.71	818
Binge drinking	California	0.66	−0.07	1.40	9,003
Binge drinking	Colorado	0.65	−0.18	1.47	1,423
Binge drinking	Connecticut	0.15	−0.40	0.70	870
Binge drinking	Delaware	0.95	0.63	1.28	256
Binge drinking	District of Columbia	0.92	0.13	1.70	201
Binge drinking	Florida	1.18	0.86	1.49	5,053
Binge drinking	Georgia	1.35	0.96	1.75	2,766
Binge drinking	Hawaii	0.97	0.41	1.53	419
Binge drinking	Idaho	1.16	0.71	1.61	453
Binge drinking	Illinois	1.54	0.70	2.38	3,239
Binge drinking	Indiana	1.20	0.61	1.79	1,678
Binge drinking	Iowa	1.49	1.23	1.76	890
Binge drinking	Kansas	0.65	0.22	1.07	811
Binge drinking	Kentucky	1.99	1.73	2.24	1,287
Binge drinking	Louisiana	2.33	1.81	2.84	1,352
Binge drinking	Maine	1.74	0.89	2.59	399
Binge drinking	Maryland	−0.77	−1.71	0.17	1,449
Binge drinking	Massachusetts	0.51	−0.26	1.27	1,585
Binge drinking	Michigan	1.12	0.41	1.84	2,869
Binge drinking	Minnesota	0.63	−0.05	1.32	1,497
Binge drinking	Mississippi	1.41	0.90	1.92	865
Binge drinking	Missouri	1.88	1.42	2.34	1,644
Binge drinking	Montana	2.18	1.44	2.93	315
Binge drinking	Nebraska	0.91	0.58	1.23	550
Binge drinking	Nevada	0.89	0.19	1.59	767
Binge drinking	New Hampshire	1.12	0.05	2.20	347
Binge drinking	New Jersey	0.36	−0.19	0.90	2,154
Binge drinking	New Mexico	1.59	1.17	2.02	594
Binge drinking	New York	1.37	0.26	2.48	5,182
Binge drinking	North Carolina	1.57	0.96	2.18	2,628
Binge drinking	North Dakota	1.94	1.42	2.46	227
Binge drinking	Ohio	1.67	1.25	2.09	3,129
Binge drinking	Oklahoma	1.68	0.95	2.41	1,189
Binge drinking	Oregon	1.01	0.59	1.43	991
Binge drinking	Pennsylvania	1.16	0.68	1.63	3,377
Binge drinking	Rhode Island	1.13	0.64	1.62	246
Binge drinking	South Carolina	2.25	1.24	3.26	1,301
Binge drinking	South Dakota	1.32	0.46	2.18	242
Binge drinking	Tennessee	1.99	1.39	2.60	1,675
Binge drinking	Texas	0.89	0.49	1.28	6,802
Binge drinking	Utah	1.44	0.99	1.89	707
Binge drinking	Vermont	1.21	0.28	2.15	192
Binge drinking	Virginia	0.04	−0.72	0.79	2,152
Binge drinking	Washington	0.37	−0.17	0.92	1,767
Binge drinking	West Virginia	1.62	1.11	2.14	543
Binge drinking	Wisconsin	1.43	0.91	1.95	1,523
Binge drinking	Wyoming	0.82	−0.66	2.30	159

The strips for the five other measures lie left of zero and the binge drinking strip lies right of zero in all but one state. Each dot is one state's coefficient from a population-weighted regression across its tracts, and the key marks the dots whose 95% interval excludes zero.Note: Each dot is a regression across the tracts of one state, and every state has at least 60 tracts with all the variables. The intervals use counties as clusters; Delaware and the District of Columbia use HC3 errors because they have too few counties for cluster-robust errors.Note: PLACES values are modeled from BRFSS responses with census and ACS inputs, and median household income comes from the ACS, so part of each coefficient reflects shared inputs. These are differences between tracts within a state and do not describe what any person does.Note: The highlighted dot is Maryland, the one state with a negative binge drinking coefficient; its interval includes zero.Source: CDC PLACES 2024 release (BRFSS 2022) and ACS 2019-2023; modeled estimates, population-weighted (adults in each tract)

PLACES draws on the same census inputs as the income measure, and within a county it separates tracts only through their demographic mix, so the coefficients describe how the model maps composition into prevalence as well as how prevalence varies with income. A positive tract-level coefficient for binge drinking does not say who drinks.

A nine-measure index keeps one component and discards a second

The ADI is the deprivation measure behind this book's gradients, and Chapter 10.2, The anatomy of a deprivation index examines how it is built. To study how an index of this kind behaves, this chapter builds a second one from nine tract measures in the American Community Survey for 2019-2023: the poverty rate, the share of households on cash assistance or SNAP, the unemployment rate, the share of adults with a high school diploma or less, the share of households headed by a single parent, the log of median household income, the share of adults with a bachelor's degree or more, labor-force participation and homeownership. A tract needs all nine and an ADI rank, which leaves 82,545 tracts, and 1,066 tracts with residents are dropped for lacking a measure or a rank. Each measure is standardized to mean zero and standard deviation one across tracts, each tract counted once as the ADI counts tracts, and the principal components are the eigenvectors of the correlation matrix,[5]

z_{ik} = \frac{x_{ik}-\bar x_k}{s_k}, \qquad R\,\ell_j = \lambda_j\,\ell_j, \qquad \mathrm{index}_i = \text{percentile rank of } \sum_{k}\ell_{1k}\,z_{ik},

where $x_{ik}$ is measure $k$ in tract $i$ , $\bar x_k$ and $s_k$ are its mean and standard deviation across tracts, $R$ is the correlation matrix, $\ell_j$ is the loading vector of component $j$ and $\lambda_j$ is its eigenvalue, the variance of the component in units of one standardized measure.

The first component holds 51.3% (95% CI 50.4% to 52.1%) of the variance and the second 16.0% (95% CI 15.5% to 16.4%), together 67.2% (95% CI 66.5% to 68.0%) because the shares are rounded separately. Weighting tracts by population gives 51.4% for the first. The Kaiser rule keeps components with an eigenvalue above one, and 2 clear it.[6] The rule is a convention with no statistical test behind it. The measures overlap. The share of adults with a bachelor's degree and the share with a high school diploma or less correlate at −0.90 (95% CI −0.91 to −0.90), and Cronbach's alpha for the nine, signed so that higher means more deprived, is 0.87 (95% CI 0.86 to 0.87).[7]

Figure 5

The first of nine components holds 51.3% of the variance in nine census measures and the second holds 16.0%

Principal components of poverty, cash assistance, unemployment, education, single-parent households, income, labor-force participation and homeownership across tracts, 2019-2023

Two of nine components have an eigenvalue above one, and the first holds 51.3% of the variance

Eigenvalue of each principal component of the correlation matrix of nine standardized tract measures, with the Kaiser line at one

Eigenvalue (variance in units of one standardized measure)

Principal component

The first bar is the tallest by a wide margin, and the second is the only other bar above the line. Each bar is a component's eigenvalue, which is its variance in units of one standardized measure, with a 95% interval from a bootstrap over counties.

Show data

Data for The first of nine components holds 51.3% of the variance in nine census measures and the second holds 16.0%, Scree
component	conf_high	conf_low	eigenvalue
PC1	4.69	4.54	4.61
PC2	1.48	1.40	1.44
PC3	0.907	0.854	0.880
PC4	0.743	0.699	0.720
PC5	0.543	0.520	0.532
PC6	0.303	0.274	0.286
PC7	0.283	0.263	0.276
PC8	0.186	0.167	0.177
PC9	0.082	0.073	0.077

The first tab is the scree, the eigenvalue of each component. The second gives the weights of the nine measures in the first component, which is the index, and the third gives the weights in the second component, which the index drops.Source: ACS 2019-2023, census tracts; principal components of nine standardized measures, unweighted (each tract counted once)

The weights matter little. The index correlates with the score of a one-factor factor analysis at +0.994 (95% CI 0.993 to 0.994) and with an equal-weight average of the nine signed measures at +0.997 (95% CI 0.996 to 0.997), both rank correlations. Dropping any one measure and refitting moves the median tract by at most 2.3 percentile points, and the largest absolute loading on the first component is 0.41, so no measure dominates the score. The choice of measures matters more, since the ADI correlates with the index at +0.68 (95% CI 0.61 to 0.74).

The second component is orthogonal to the first by construction, so an index built on the first discards it. It contrasts homeownership (loading −0.59) with labor-force participation (+0.56) and the college share (+0.35), and tracts with the same index value can differ on it. That the nine measures cohere statistically does not show that the index measures what a family in the tract would call deprivation. Chapter 10.3, A deprivation index at two zooms rebuilds a deprivation index for counties and Chapter 10.4, Families of places groups tracts instead of ranking them.

A correlation depends on the size of the area

The same data can give different correlations at different grains, a case of the modifiable areal unit problem.[8] Robinson showed in 1950 that a correlation across states can differ in size and sign from the correlation across the people inside them.[9, 10] Figure 6 computes six pairs of tract measures across tracts, across counties and across states, all on the same 77,775 tracts, which lie in 3,112 counties and Connecticut planning regions. A county or state value is the population-weighted mean of its tracts' values. Each correlation is computed both weighted by the population of its unit and counting each unit once, with a bootstrap interval that draws counties for the tract correlations and states for the others. The state correlations rest on 51 states, so their intervals are wide.

Weighted by population, 4 of the 6 pairs are larger in absolute value across states than across tracts, and counting each unit once 4 are, but not the same pairs. College share and income go from +0.73 (95% CI 0.71 to 0.74) across tracts to +0.83 (95% CI 0.73 to 0.94) across states when weighted. Homeownership and poverty fall toward zero under both weightings. Weighted, they go from −0.53 (95% CI −0.55 to −0.51) across tracts through −0.40 (95% CI −0.53 to −0.26) across counties to −0.05 (95% CI −0.30 to 0.17) across states, and counting each unit once from −0.52 (95% CI −0.54 to −0.50) to −0.11 (95% CI −0.32 to 0.11), so both state intervals include zero.

The weights decide the result for 2 of the 6 pairs. Unemployment and poverty rise from +0.43 (95% CI 0.41 to 0.46) across tracts to +0.59 (95% CI 0.52 to 0.66) across counties and fall to +0.33 (95% CI 0.08 to 0.59) across states when weighted. Counting each unit once they are +0.45 (95% CI 0.42 to 0.47), +0.53 (95% CI 0.44 to 0.61) and +0.50 (95% CI 0.32 to 0.65). College share and life expectancy rise from +0.56 (95% CI 0.54 to 0.58) across tracts to +0.71 (95% CI 0.55 to 0.83) across states when weighted and fall from +0.55 (95% CI 0.53 to 0.57) to +0.48 (95% CI 0.13 to 0.81) counting each unit once. A weighted correlation across states gives populous states most of the weight, so the two weightings answer different questions. Averaging within an area removes the variation inside it, so a correlation of averages describes how the areas differ and says nothing about how the tracts or people inside them do.

Figure 6

Weighted by population, the same pair of measures has a different correlation at each grain, and homeownership and poverty go from −0.53 across tracts to −0.05 across states

Correlation of six pairs of tract measures across tracts, across counties and across states, weighted by population or counting each unit once, with 95% intervals from a bootstrap over counties or states, 2019-2023

Census measures only
Includes life expectancy

Show data

Data for Weighted by population, the same pair of measures has a different correlation at each grain, and homeownership and poverty go from −0.53 across tracts to −0.05 across states
Pair of measures	Tracts, weighted	Counties, weighted	States, weighted	Tracts, each once	Counties, each once	States, each once	States, weighted, lower limit	States, weighted, upper limit	States, each once, lower limit	States, each once, upper limit
College share and income	+0.73	+0.79	+0.83	+0.72	+0.71	+0.81	+0.73	+0.94	+0.73	+0.91
Poverty rate and college share	−0.50	−0.56	−0.69	−0.49	−0.50	−0.52	−0.84	−0.50	−0.81	−0.20
Homeownership and poverty rate	−0.53	−0.40	−0.05	−0.52	−0.36	−0.11	−0.30	+0.17	−0.32	+0.12
Unemployment and poverty rate	+0.43	+0.58	+0.33	+0.45	+0.53	+0.50	+0.08	+0.58	+0.32	+0.65
College share and life expectancy	+0.56	+0.64	+0.70	+0.55	+0.51	+0.48	+0.55	+0.83	+0.13	+0.81
Poverty rate and life expectancy	−0.50	−0.60	−0.66	−0.52	−0.57	−0.78	−0.88	−0.45	−0.89	−0.65

Weighted by population, 4 of 6 correlations are larger in absolute value across states than across tracts, and counting each unit once 4 are, but not the same pairs. Homeownership with poverty falls toward zero under both weightings. Each view joins two grains, tracts to counties or counties to states, weighted first and then counting each unit once; hover a line for its interval and the number of units.Note: Every correlation uses the same 77,775 tracts. County and state values are population-weighted means of the tract values; the weighted views weight each correlation by the population of its unit and the others count each unit once. The county correlations rest on 3,112 counties and the state correlations on 51 states, so the state intervals are wide.Note: The correlation with life expectancy is between tract life expectancy, a modeled estimate, and census measures.Note: ACS tract values are survey estimates with sampling error, and the staged file has no margins of error, so they are treated as exact.Source: ACS 2019-2023 tracts and USALEEP life expectancy, 2010-2015; correlations of tract values and of population-weighted county and state means, population-weighted and unweighted

Most variation in life expectancy lies between tracts in the same county

Split the total variance of a tract measure $y$ , with population weights $w_i$ , into a part between states, a part between counties within states and a part between tracts within counties,

\underbrace{\sum_i w_i (y_i-\bar y)^2}_{\text{total}} = \underbrace{\sum_i w_i (\bar y_{s(i)}-\bar y)^2}_{\text{between states}} + \underbrace{\sum_i w_i (\bar y_{c(i)}-\bar y_{s(i)})^2}_{\text{between counties}} + \underbrace{\sum_i w_i (y_i-\bar y_{c(i)})^2}_{\text{between tracts}},

where $\bar y$ is the weighted mean of all tracts and $\bar y_{s(i)}$ and $\bar y_{c(i)}$ are the weighted means of the state and the county that contain tract $i$ . Each part over the total is a share of the variance, and the three shares sum to the whole.

For life expectancy at birth in the 78,008 tracts of 3,112 counties and Connecticut planning regions, the shares are 13.7% between states, 15.9% between counties in the same state and 70.3% between tracts in the same county. The split covers every tract in the sample and has no sampling interval, but it needs a caveat. The tract estimates are modeled, and their mean squared standard error equals 26.7% of the total variance, which sits inside the within-county share. Taking the published errors at face value, 60% of the variance that is not estimation error lies within counties. The errors of the 2020-tract file are mapping grade and understate the noise, so the share of the true differences that lies within counties is lower than that.

Figure 7

70.3 percent of the variance of tract life expectancy lies between tracts in the same county, 26.7 points of it estimation error, against 34% percent for the ADI

Share of the population-weighted variance of three tract measures between states, between counties in a state and between tracts in a county, percent

Between states
Between counties in a state
Between tracts in a county

Show data

Data for 70.3 percent of the variance of tract life expectancy lies between tracts in the same county, 26.7 points of it estimation error, against 34% percent for the ADI
level	measure	share
Between states	Tract life expectancy	13.75
Between counties in a state	Tract life expectancy	15.92
Between tracts in a county	Tract life expectancy	70.33
Between states	ADI national percentile	36.64
Between counties in a state	ADI national percentile	29.38
Between tracts in a county	ADI national percentile	33.98
Between states	Nine-measure index percentile	5.13
Between counties in a state	Nine-measure index percentile	23.29
Between tracts in a county	Nine-measure index percentile	71.59

The life expectancy bar and the index bar are mostly the right-hand segment, between tracts in the same county, and the ADI bar is mostly the other two. Each bar sums to the whole variance of its measure; the shares come from every tract in the sample and have no sampling interval.Note: Tract life expectancy is modeled. The mean squared standard error of the tract estimates equals 26.7 percent of the total variance and sits inside the between-tract segment; the 2020-tract standard errors are mapping grade and understate the noise, so the share of the true differences that lies between tracts is lower than the net share in the text.Note: The life expectancy bar uses 78,008 tracts in 3,112 counties and Connecticut planning regions; the ADI and index bars use the 82,545 tracts of the index. Connecticut's planning regions stand in for its counties.Source: USALEEP life expectancy, 2010-2015; ACS 2019-2023; Area Deprivation Index, 2023; population-weighted decomposition of the variance, full counts of tracts

The ADI is the exception among the measures in the figure. Only 34% of its variance lies within counties and 37% lies between states, against 72% within counties for the nine-measure index. The two deprivation measures put their variation at different levels, and Chapter 10.2, The anatomy of a deprivation index examines what the ADI is made of. A county map of life expectancy paints the county average and hides the largest share of its variance.

Large counties differ in how much of the ADI scale their tracts cover

Across the 757 counties and Connecticut planning regions with at least 20 tracts that have an ADI rank, the median distance between the tract at the 10th percentile of ADI and the tract at the 90th, weighted by population, is 39 percentile points. The floor is a choice. With a floor of 10 tracts there are 1,319 counties and the median is 34 points, and with a floor of 40 there are 421 and the median is 43. Among the 30 most populous counties (Figure 8), the range runs from 9 points in Santa Clara County, California, to 69 in Philadelphia County, Pennsylvania, and 11 of the 30 have a range of 25 points or less. The median range in life expectancy between tracts at the 10th and 90th percentiles in those counties is 8.0 years. The counties are chosen by population and not by range, and tract life expectancy is modeled, so part of that spread in years is estimation error.

A county's mean ADI and its range are related, and how closely depends on the floor. Counting each county once, the correlation is −0.08 (95% CI −0.25 to 0.08) at a floor of 10 tracts, +0.27 (95% CI 0.06 to 0.44) at 20 and +0.62 (95% CI 0.45 to 0.74) at 40. Weighted by county population it is +0.47 (95% CI 0.16 to 0.63), +0.63 (95% CI 0.37 to 0.75) and +0.77 (95% CI 0.58 to 0.85). Counting each county once, a county's mean says little about its range when small counties are included and more among large counties. The figure shows the county averages as dots, and a county map shows only those and none of the whiskers.

Figure 8

In each of the 30 most populous counties, tracts at the 10th and 90th percentile of the ADI are between 9 and 69 percentile points apart

Population-weighted mean ADI national percentile of each county (dot) and the 10th to 90th percentile range of its tracts' ADI (whisker), the most populous counties sorted by range, ACS 2019-2023 population

ADI national percentile (dot: county mean; whisker: 10th to 90th percentile of tracts)

Show data

Data for In each of the 30 most populous counties, tracts at the 10th and 90th percentile of the ADI are between 9 and 69 percentile points apart
County	Mean ADI	10th percentile of tracts	90th percentile of tracts	Range	Tracts	Residents
Philadelphia, PA	62.4	25.0	93.8	68.8	386	1,578,494
Wayne, MI	72.8	35.3	99.0	63.7	579	1,772,852
Bexar, TX	59.2	26.9	89.0	62.1	369	2,023,627
Dallas, TX	51.8	17.4	78.6	61.1	641	2,597,456
Cook, IL	47.1	17.0	77.0	60.0	1,322	5,158,123
Harris, TX	55.6	24.5	84.3	59.8	1,106	4,739,169
Palm Beach, FL	38.8	12.0	69.7	57.7	363	1,503,596
Tarrant, TX	48.9	22.1	77.6	55.4	445	2,123,556
Broward, FL	41.0	14.2	69.0	54.8	415	1,946,125
Hillsborough, FL	46.0	20.3	71.8	51.6	322	1,476,792
Orange, FL	44.1	20.0	70.4	50.4	262	1,413,087
Maricopa, AZ	36.1	13.0	60.7	47.7	985	4,468,217
Bronx, NY	31.1	15.2	61.0	45.7	340	1,411,947
Miami-Dade, FL	37.2	15.7	61.2	45.5	691	2,663,978
San Bernardino, CA	31.9	11.9	54.2	42.3	461	2,166,515
Clark, NV	39.2	20.0	62.2	42.2	534	2,293,278
Riverside, CA	28.4	11.0	51.3	40.3	514	2,435,341
Sacramento, CA	27.9	11.3	47.4	36.1	361	1,577,120
Queens, NY	16.4	6.0	31.1	25.1	677	2,325,406
Middlesex, MA	14.5	3.7	27.8	24.0	353	1,619,270
Suffolk, NY	19.7	7.8	31.5	23.7	368	1,437,246
King, WA	12.9	3.0	25.5	22.5	491	2,252,223
San Diego, CA	14.0	3.3	25.5	22.2	723	3,203,557
Los Angeles, CA	14.2	3.0	25.0	22.0	2,447	9,781,315
New York, NY	8.9	1.0	20.5	19.5	294	1,614,981
Nassau, NY	13.8	4.7	22.3	17.6	277	1,384,110
Orange, CA	11.2	3.0	20.0	17.0	611	3,164,006
Kings, NY	10.0	2.0	19.0	17.0	773	2,642,467
Alameda, CA	7.8	2.0	18.0	16.0	373	1,649,334
Santa Clara, CA	5.0	1.0	10.0	9.0	407	1,900,063

Counties with a low mean ADI have short whiskers and counties with a higher mean have long ones. The dot is the county mean and the whisker is the spread of its tracts between the 10th and 90th percentiles, which describes the tracts and is not an interval for the mean.Note: Tract ADI is a national percentile, so a county whose tracts are all among the least deprived has a narrow range by construction. Counties are chosen by population, not by range.Note: Connecticut's planning regions stand in for its counties. Puerto Rico is not included.Source: Area Deprivation Index, 2023; ACS 2019-2023 population; population-weighted percentiles of tract values, full counts of tracts

Suppressed cells are not zeros

CDC WONDER withholds any cell with fewer than 10 events, so a suppressed cell holds at most 9 births, and a published zero is a real zero. The natality file by county and birthweight class for 2018 to 2024 has 11,250 withheld cells of 48,552, or 23.2%, in the 578 counties that WONDER names in every year, which are counties of at least 100,000 residents. The share depends sharply on the class (Figure 9). It is 71.3% for births of 499 grams or less, 77.6% for births of 5,000 grams or more and 65.1% for births whose weight is not stated, and the five middle classes, where counts are large, have 0 withheld cells.

Figure 9

WONDER withholds 71.3% of county-year cells in the lightest birthweight class and 77.6% in the heaviest, against 0.0% in the five middle classes

Share of county-year cells that are withheld, published as zero or published with at least 10 births, by birthweight class, 578 counties named in every year, 2018 to 2024, percent

Birthweight class

Withheld (1 to 9 births)
Published zero
Published, 10 or more births

Show data

Data for WONDER withholds 71.3% of county-year cells in the lightest birthweight class and 77.6% in the heaviest, against 0.0% in the five middle classes
Birthweight class	Cell status	Share of cells (%)	Cells	Cells in the class	Births in published cells of the class	Largest share of the class's births in withheld cells (%)
499 g or less	Withheld (1 to 9 births)	71.3	2,885	4,046	17,300	60.0
499 g or less	Published zero	8.7	350	4,046	17,300	60.0
499 g or less	Published, 10 or more births	20.0	811	4,046	17,300	60.0
500 to 999 g	Withheld (1 to 9 births)	36.4	1,474	4,046	93,575	12.4
500 to 999 g	Published zero	0.4	16	4,046	93,575	12.4
500 to 999 g	Published, 10 or more births	63.2	2,556	4,046	93,575	12.4
1,000 to 1,499 g	Withheld (1 to 9 births)	18.3	741	4,046	144,348	4.4
1,000 to 1,499 g	Published zero	0.0	0	4,046	144,348	4.4
1,000 to 1,499 g	Published, 10 or more births	81.7	3,305	4,046	144,348	4.4
1,500 to 1,999 g	Withheld (1 to 9 births)	1.1	43	4,046	334,713	0.1
1,500 to 1,999 g	Published zero	0.0	0	4,046	334,713	0.1
1,500 to 1,999 g	Published, 10 or more births	98.9	4,003	4,046	334,713	0.1
2,000 to 2,499 g	Withheld (1 to 9 births)	0.0	0	4,046	1,107,825	0.0
2,000 to 2,499 g	Published zero	0.0	0	4,046	1,107,825	0.0
2,000 to 2,499 g	Published, 10 or more births	100.0	4,046	4,046	1,107,825	0.0
2,500 to 2,999 g	Withheld (1 to 9 births)	0.0	0	4,046	3,979,246	0.0
2,500 to 2,999 g	Published zero	0.0	0	4,046	3,979,246	0.0
2,500 to 2,999 g	Published, 10 or more births	100.0	4,046	4,046	3,979,246	0.0
3,000 to 3,499 g	Withheld (1 to 9 births)	0.0	0	4,046	7,991,060	0.0
3,000 to 3,499 g	Published zero	0.0	0	4,046	7,991,060	0.0
3,000 to 3,499 g	Published, 10 or more births	100.0	4,046	4,046	7,991,060	0.0
3,500 to 3,999 g	Withheld (1 to 9 births)	0.0	0	4,046	5,263,258	0.0
3,500 to 3,999 g	Published zero	0.0	0	4,046	5,263,258	0.0
3,500 to 3,999 g	Published, 10 or more births	100.0	4,046	4,046	5,263,258	0.0
4,000 to 4,499 g	Withheld (1 to 9 births)	0.0	0	4,046	1,289,498	0.0
4,000 to 4,499 g	Published zero	0.0	0	4,046	1,289,498	0.0
4,000 to 4,499 g	Published, 10 or more births	100.0	4,046	4,046	1,289,498	0.0
4,500 to 4,999 g	Withheld (1 to 9 births)	8.3	334	4,046	167,374	1.8
4,500 to 4,999 g	Published zero	0.0	0	4,046	167,374	1.8
4,500 to 4,999 g	Published, 10 or more births	91.7	3,712	4,046	167,374	1.8
5,000 g or more	Withheld (1 to 9 births)	77.6	3,141	4,046	8,863	76.1
5,000 g or more	Published zero	10.9	441	4,046	8,863	76.1
5,000 g or more	Published, 10 or more births	11.5	464	4,046	8,863	76.1
Weight not stated	Withheld (1 to 9 births)	65.0	2,632	4,046	9,365	71.7
Weight not stated	Published zero	27.2	1,100	4,046	9,365	71.7
Weight not stated	Published, 10 or more births	7.8	314	4,046	9,365	71.7

The withheld segment is long at the top and bottom of the ladder and absent in the middle. Each bar is the cells of one class, summing to the whole; a withheld cell holds fewer than 10 births and is not a zero, and the figure counts cells and reconstructs none.Note: WONDER withholds a cell with fewer than 10 births, so a withheld cell holds at most 9. The counts here are of cells only; nothing is derived for a withheld cell, and the county totals are not used.Note: The bound in the table is the births in the published cells of a class plus 9 for each withheld cell, which is the largest share of the class's births that the withheld cells could hold.Note: Cells are for the 578 counties that WONDER names in every year, which have at least 100,000 residents; pooled rows for other counties are not cells of a county.Source: CDC WONDER natality, county by birthweight class, 2018-2024; full counts of cells

In the lightest class 2,885 cells are withheld and 350 are published as zero. A withheld cell is never a zero, so reading the blanks as zeros would misstate each of those withheld cells, and in this class they outnumber the real zeros. If every withheld cell held 9 births, the withheld cells of the lightest class would hold 60% of its births and those of the heaviest class 76%. That limit comes from the public threshold and the births in published cells, and it says nothing about any one cell. A count of births in a rare class summed over published cells covers only the county-years where the class is large enough to publish. The book counts withheld cells, leaves them out of both numerator and denominator and derives no value for them. Gradients use no suppression floor, and a map of WONDER deaths needs at least 20 pooled deaths and says so. Chapter 1.1, Birthweight and preterm birth uses this file, and Chapter 10.5, Suppressed counties in death data takes up the same problem in death counts.

What these data cannot show

Every estimate in this chapter describes how an outcome is arranged across places. The slopes, the metro regressions, the index and the variance split compare tracts, counties and states, and none says what would happen to a person who moved or to a place that changed. A gradient of tract life expectancy on the ADI says nothing about individuals, which is the ecological inference problem, and the steeper slope within counties is compatible with more than one explanation that the data cannot separate. Life expectancy is a modeled estimate for deaths in 2010 to 2015 that has not been updated, and the 2020-tract file is area-weighted from 2010 tracts, so the estimate for a single tract is not reliable.

The metro slopes cover the residents of metros with enough tracts and say nothing about the rest. Their intervals use HC3 errors in most metros and may be too narrow, which would make the share of the spread that is estimation error larger. The ADI is a national percentile and understates deprivation in high-cost cities (Chapter 10.2, The anatomy of a deprivation index), which bears on the metro slopes. Puerto Rico is not covered, and Connecticut's planning regions stand in for its counties in the metros, the variance split and the county ranges.

The index is internally coherent, and the data hold no independent measure of what residents would call deprivation, so they cannot show that it is valid. The ACS values behind the index, the ADI and the area-size correlations are survey estimates with sampling error that is largest in small tracts, and the staged file carries no margins of error, so every analysis here treats them as exact. The ADI and the PLACES estimates draw on the same census inputs as the measures they are compared with, so part of each association is built in, and the data cannot say how much.

Weights can decide a result. The correlations across states for unemployment and poverty, and for the college share and life expectancy, change direction between the two weightings in the area-size section, and neither weighting is the correct one. The suppression figure counts withheld cells and cannot show what they hold. Counties below 100,000 residents are pooled by WONDER and do not appear as cells, and the bound on the share held in withheld cells is the largest value the threshold allows.

Data sources

USALEEP life expectancyUSALEEP life expectancy at birth, 2010-2015, on 2020 tracts (area-weighted from 2010 tracts), institutional tracts droppedYears: 2010-2015 · Weights: ACS 2019-2023 tract population · License: Public domain (NCHS, CDC)
Area Deprivation IndexNeighborhood Atlas Area Deprivation Index 2023, national percentile, tractsYears: 2023 release (version 4.0.1; built on ACS 2019-2023) · Weights: ACS 2019-2023 tract population (each tract once for the index split by county) · License: Free for non-commercial use; cite the Neighborhood Atlas and Kind and Buckingham
American Community SurveyACS 2019-2023 tracts: population, the nine measures of the index and the measures of the correlationsYears: 2019-2023 (5-year) · Weights: tract population; each tract once in the index · License: Public domain (U.S. Census Bureau)
Census TIGER/Line tractsCensus 2020 county file: the core-based statistical area code of each county (CBSAFP)Years: 2020 · Weights: none (assignment of counties to metros) · License: Public domain (U.S. Census Bureau)
CDC PLACESCDC PLACES 2024 release, tracts: six measures of the coefficient zooYears: 2024 release (tracts); 2025 release (ZCTAs, 2023 data year) · Weights: adult population of each tract (PLACES) · License: Public domain (CDC, U.S. Department of Health and Human Services)
CDC WONDER natalityCDC WONDER natality 2018-2024, county by birthweight class: counts of withheld cellsYears: 2018-2024 · Weights: none (full counts of cells) · License: Public domain (NCHS, CDC); WONDER data-use restrictions apply

All data sources

Methods

Life expectancy at birth for deaths in 2010 to 2015 is regressed on the 2023 Area Deprivation Index (ADI) across tracts, within counties and within metros, so the outcome and the deprivation measure come from different periods. Tract life expectancy is a modeled estimate area-weighted from 2010 onto 2020 tracts, and the sample is the 77,936 tracts with an ADI rank in the 50 states and DC after institutional tracts are dropped. The variance split has no sampling interval, and the coefficient zoo and the count of withheld birth cells use other sources, described under their own headings.

Which tracts and which years

Tract life expectancy at birth is the USALEEP estimate for deaths in 2010 to 2015, area-weighted from 2010 tracts onto 2020 tracts. Institutional tracts (at least 25 percent of residents in group quarters, or a known case) are dropped, and a tract needs an ACS 2019-2023 population above zero and a county, which leaves 77,936 tracts with an ADI rank (78,008 counting those without one) in the 50 states and DC. Puerto Rico has no USALEEP estimates.

Figure explained here: Figure 1

Measures and weights

Weights are the ACS 2019-2023 tract population. The ADI is the 2023 national percentile (1 least, 100 most deprived).

The nine measures of the index are the poverty rate, the share of households on cash assistance or SNAP, the unemployment rate, the share of adults with a high school diploma or less, the share of households headed by a single parent, the log of median household income, the share of adults with a bachelor's degree or more, labor-force participation and homeownership, from ACS 2019-2023 tracts. Each is standardized across the 82,545 tracts, each counted once; components are the eigenvectors of the correlation matrix.

Figure explained here: Figure 5

Metros, counties and grains of geography

A metro is a core-based statistical area (metropolitan or micropolitan) coded on the Census 2020 county file; each tract takes the area of its county, so Connecticut's planning regions work as counties. A metro needs at least 40 tracts with a life expectancy and an ADI rank.

The six pairs of measures use one sample; county and state values are population-weighted means of tract values, and each correlation is computed weighted by its unit's population and counting each unit once, with bootstrap intervals over counties (tracts) or states (counties and states).

The variance split is the population-weighted sum-of-squares split of b2.canon.variance_split(), computed in the same way for the ADI and the index; it has no sampling interval.

County ranges are population-weighted 10th and 90th percentiles of tract ADI for counties with at least 20 tracts that have an ADI rank; the count of counties, the median range and the correlation of mean ADI with the range are also given at floors of 10 and 40 tracts.

Figures explained here: Figure 2, Figure 8, Figure 6 and Figure 7

The coefficient zoo and withheld birth cells

The coefficient zoo is b2.canon.coefficient_zoo(), the same function chapter 5.1 calls: for each state with at least 60 tracts that have every variable, a weighted regression of PLACES prevalence on the log of ACS median household income with the shares of residents ages 65 and over, Black alone and Hispanic as controls, weighted by adults, with county-clustered errors (HC3 where a state has fewer than five counties), times the natural log of 2.

The suppression count uses WONDER natality, county by birthweight class, for the 578 counties named in every year 2018 to 2024; the file lists a withheld cell as missing, and a published 0 is a real zero. Withheld cells are counted and left out; the bound uses only the published threshold of 10 births and the births in published cells.

Figures explained here: Figure 4 and Figure 9

How the slopes and their errors are estimated

Every slope is a weighted least-squares slope of life expectancy on the ADI, times ten. The ladder uses pyfixest with absorbed fixed effects and CRV1 errors, clustered on states for the first two rows and counties for the third, with t intervals on one fewer degree of freedom than there are clusters; the first two are checked against b2.stats.wls with state dummies and the county fit against weighted demeaning.

Each metro slope comes from b2.stats.wls, clustered on counties when the metro has at least five counties and with HC3 errors otherwise.

The variance of the true metro slopes is the variance of the estimated slopes minus their mean squared standard error, and each slope is shrunk toward the mean by that variance over itself plus its squared standard error.

Figures explained here: Figure 1, Figure 2 and Figure 3

Bootstrap intervals, draws and seeds

Metro correlations carry bootstrap intervals over metros (2,000 draws, seed 12345).

Intervals for eigenvalues, loadings, alpha and the correlation come from a bootstrap over counties (2,000 draws, seed 12345) that recomputes the correlation matrix. Rank correlations hold ranks fixed in the bootstrap.

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
Arias, Elizabeth; Escobedo, Luis A.; Kennedy, Jiaquan; Fu, Chenxi; Cisewski, Jodi (2018). U.S. Small-area Life Expectancy Estimates Project: Methodology and Results Summary. Vital and Health Statistics, Series 2, Number 181, National Center for Health Statistics. www.cdc.gov/nchs/data/series/sr_02/sr02_181.pdf
Cameron, A. Colin; Miller, Douglas L. (2015). A Practitioner's Guide to Cluster-Robust Inference. Journal of Human Resources 50(2): 317-372. doi:10.3368/jhr.50.2.317
Greenlund, Kurt J.; Lu, Hua; Wang, Yan; Matthews, Kevin A.; LeClercq, Jennifer M.; Lee, Benjamin; Carlson, Susan A. (2022). PLACES: Local Data for Better Health. Preventing Chronic Disease 19: 210459. doi:10.5888/pcd19.210459
Messer, Lynne C.; Laraia, Barbara A.; Kaufman, Jay S.; Eyster, Janet; Holzman, Claudia; Culhane, Jennifer; Elo, Irma; Burke, Jessica G.; O'Campo, Patricia (2006). The Development of a Standardized Neighborhood Deprivation Index. Journal of Urban Health 83(6): 1041-1062. doi:10.1007/s11524-006-9094-x
Kaiser, Henry F. (1960). The Application of Electronic Computers to Factor Analysis. Educational and Psychological Measurement 20(1): 141-151. doi:10.1177/001316446002000116
Cronbach, Lee J. (1951). Coefficient Alpha and the Internal Structure of Tests. Psychometrika 16(3): 297-334. doi:10.1007/BF02310555
Openshaw, Stan (1984). The Modifiable Areal Unit Problem. CATMOG 38, Concepts and Techniques in Modern Geography, Geo Books, Norwich.
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{singh2026gradientsslopesandvariance,
  author = {Singh, Vishal},
  title = {Gradients, slopes and variance},
  year = {2026},
  url = {https://vishalsingh.org/zipcode/gradients-slopes-and-variance},
  note = {In ZIP Code Destiny. Published 9 October 2026.}
}

The slope is steeper within counties than across all tracts

Life expectancy is lower in more deprived tracts in every metro

Metro traits are not detectably related to the spread

The coefficient zoo returns coefficients of both signs

A nine-measure index keeps one component and discards a second

A correlation depends on the size of the area

Most variation in life expectancy lies between tracts in the same county

Large counties differ in how much of the ADI scale their tracts cover

Suppressed cells are not zeros

What these data cannot show

Data sources

Methods

Which tracts and which years

Measures and weights

Metros, counties and grains of geography

The coefficient zoo and withheld birth cells

How the slopes and their errors are estimated

Bootstrap intervals, draws and seeds

References

How to cite

Reading paths