census 2000 -- scientifically or politically correct?

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Census 2000 -- Scientifically or Politically Correct?

Stephen E. FienbergDepartment of Statistics

Notes for Stat 36-149October, 2001

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October Census Bureau October Census Bureau DecisionDecision

• March 1, 2001 not to use adjusted data for redistricting.

• New October 17 decision against adjustment for intercensal estimates

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How Many People Were There How Many People Were There in the U.S. on April 1, 2000?in the U.S. on April 1, 2000?

• At march 1 decision here were the numbers:Raw Census Count: 281.4 millionDemographic Analysis: 279.6 millionACE: 284.7 million

• Which number should we trust and use?• Should we count or should we estimate?

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Demographic AnalysisDemographic Analysis

• Population = births - deaths + immigration - emigration

• only available at national level, and for blacks and whites

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Net Census Undercount-Mother Net Census Undercount-Mother RuleRule

UndercountYear Black White Differential Net 1940 10.3% 5.1% 5.2% 5.6%1950 9.6% 3.8% 5.8% 4.4%1960 8.3% 2.7% 5.6% 3.3%1970 8.0% 2.2% 5.8% 2.9%1980* 5.9% 0.7% 5.2% 1.4%1990** 7.4% 1.0% 6.4% 1.9%

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Net Census Undercount-Father Net Census Undercount-Father Rule*Rule*

UndercountYear Black White Differential Net 1940 8.4% 5.0% 3.4% 5.4%1950 7.5% 3.8% 3.8% 4.1%1960 6.6% 2.7% 3.9% 3.1%1970 6.5% 2.2% 4.3% 2.7%1980 4.5% 0.8% 3.7% 1.2%1990 5.7% 1.3% 4.4% 1.8%2000 -0.65%

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2000 DA Census Undercount 2000 DA Census Undercount Estimates (Rev. October 2001)Estimates (Rev. October 2001)

Source Count %Undercount Census 281.4 mil.DA(original) 279.6 mil. -0.65%DA(Alt.March) 282.3 mil. 0.32%DA(Rev. Oct.)* 281.8 mil. 0.12%ACE 284.7 mil. 1.3%

*Changes to births and immigration components

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Demographic AnalysisDemographic Analysis

• No reliable measures of uncertainty (variability).

• Incompatibilities with new Census race measures.

• Major biases for immigration and Hispanics.• Otherwise DA and ACE were much closer

than the Bureau admitted! (Passel, 2001)

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Census AccuracyCensus Accuracy

Myth 3. The ‘actual enumeration’ has been highly successful at counting the population: ‘‘The 1990 census accurately counted 98.4% of the population . . . .”

• What is error in the census?– Omissions AND Erroneous Enumerations

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From A Survey!From A Survey!

• Our information about omissions and erroneous enumerations comes from a survey, taken after the census and matched to census records -- the post enumeration survey(PES in 1990 or ACE in 2000).

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1990 PES Net Undercount 1990 PES Net Undercount EstimatesEstimates

Group Undercount DifferentialNon-Black 1.7Black 4.8 3.1Hispanic 5.2 3.4Asian 3.1 1.0American Indian 5.0 2.9

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2000 ACE Net Undercount 2000 ACE Net Undercount EstimatesEstimates

Group Undercount DifferentialNon-Black 1.0Black 2.1 1.1Hispanic TBA TBAAsian TBA TBAAmerican Indian TBA TBA

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Gross vs. Net ErrorGross vs. Net Error

• Omissions• Erroneous Enumerations

Gross Error = Omissions + Err. Enumerations Net Error = Omissions - Err. Enumerations

• 1990 Gross error (~8-12%) vs. Net error (1.6%)

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Gross v. Net ErrorGross v. Net Error

(in millions) 1980 1990___ 2000* erroneous enumerations 6.0 10.3 5.9omissions 9.2 15.6 9.2net undercount 3.2 5.3 3.3gross errors 15.2 25.9 15.1gross as % of population 7 % 10.4% 5.4%

*(based on March, 2001 reports; excludes imputations, suspected duplicates, and group quarter errors)

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October 17, 2001 DecisionOctober 17, 2001 Decision

• No adjustment for intercensal purposes because of suspected 3 mil. EEs missed by ACE.

• Need revised information on gross error but some estimates now put it at 1990 levels, i.e., in neighborhood of 25 million.

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Sampling and Census 2000Sampling and Census 2000

• The Census enumeration Process:– Short Form and Long Form.– Mail-out and mail-back (trying to count all).– Non-response Follow-up.– Institutions and the Homeless.

• Accuracy and Coverage Evaluation – Post-Enumeration Survey (314,000 HHs)

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ACE & Dual Systems ACE & Dual Systems EstimationEstimation

• Survey approximately 314,000 HH in 11,000 blocks.

• Correct raw census counts using “capture-recapture” or dual systems methodology.

• Corrects for omissions AND erroneous enumerations.

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Political Bias & ManipulationPolitical Bias & Manipulation

Myth 6. Census Sampling Would Favor Democrats. “ Statistical errors in the count, accidental or

deliberate, could result in as many as 24 GOP seats being lost.”

“The ability to ‘create’ or ‘eliminate’ millions of strategically placed citizens with the stroke of a pen introduces a potent and disturbing new political weapon.”

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Winners and Losers in 1990 Winners and Losers in 1990 and 2000and 2000

• 1990 Adjustment winners:– California– Arizona

• 1990 Adjustment losers:– Wisconsin– Pennsylvania

• In 2000, had adjusted data been used for apportionment, Texas would have gained seat.

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Perfection of the SamplePerfection of the Sample

Myth 11. Persons found in the census but not in the sample are inferred to have been counted erroneously by the census.

• ‘Rehnquist-Stark’ fallacy, or “What is dual systems estimation all about?”

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Dual Systems ComponentsDual Systems Components

Census

Sample In Out TotalIn Matches PES

Non-MatchesPESTotal

Out CensusNon-Matches

Missed inBoth

Total CensusTotal

PopulationTotal

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Dual Systems EstimationDual Systems Estimation

CensusSample In Out Total

In a c npesOut b d N-npes

Total ncen N-ncen N

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Dual Systems ExampleDual Systems Example

• Counting people in a census block.• 150 people 1st time -- the census; and 200

2nd time -- the sample.• Of 200 people in sample, 125 were among

150 people in the census • Total no. people seen = 200 + (150 - 125)

= 225.

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Example (cont.)Example (cont.)

• In sample, proportion of people also in census is 125/200, or 5/8.

• Generalizing from sample to entire population, we conclude that only 5/8 of people in the block were captured in census:

150 = (5/8) Ñ

Ñ = (8/5) (1500) = 240.

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More Formal Version More Formal Version

Ñ = ncen npes/a

125 75 200

25 ?

150

Ñ = 150 200/125 = 240

CensusSample In Out Total

In a c npesOut b d N-npes

Total ncen N-ncen N

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Dual Systems For Census 2000Dual Systems For Census 2000

• To apply method in the context of ACE, we need to correct census count for EEs by subtracting them.

• Practical issues regarding implementation.

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Dual Systems AssumptionsDual Systems Assumptions

• Perfect matching• Homogeneity• Dependence between sample and census

– correlation bias?• Errorless assessment of erroneous

enumerations– big issue for 2000 census