Apportioning Seats in the U.S. House of Representatives Using the 2013 Estimated Citizen Population

Contents

• Introduction and Background
• Constitutional Issue
• Practicalities
• Recent Congressional Interest
• Potential Impact of Using the Citizen Population to Apportion Seats in the House
• Estimating the Total and Citizen Apportionment Populations
• Limitations and Caveats
• Estimation Method Used to Estimate the 2013 Total and Citizen Apportionment Population
• 2013 American Community Survey Citizenship Status
• Apportioning Seats to the House of Representatives Using Citizen Population Estimates
• Taking the Citizen Population into Account in the Apportionment Process: Some Possible Options
• Constitutional Amendment
• Using the Citizen Population in the Redistricting Process Rather than in the Apportionment Process
• Legal Considerations
• Practicalities
• Changing the Apportionment Method

Summary

Congressional apportionment is the process of determining the number of Representatives to which each state is entitled in the U.S. House of Representatives based on the decennial census of population. Congressional redistricting, often confused with apportionment, is the process of revising the geographic boundaries of areas from which voters elect Representatives to the House. The apportionment process is a function of four factors: (1) population size, (2) the number of Representatives or seats to be apportioned, (3) the number of states, and (4) the method of apportionment.

Recently, some commentators and Members of Congress have called for a change in the nature of the population used to apportion seats in the U.S. House of Representatives, advocating a change from using all "persons" to using all "citizens." Section 2 of the 14^th Amendment to the U.S. Constitution states that "Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed." Consequently, such a change would appear to necessitate a constitutional amendment.

This report examines the impact on the apportionment of seats in the House of Representatives if such a change were to occur, using an estimate of the 2013 citizen population in place of the 2010 apportionment population to determine the potential distribution of seats in the House of Representatives for the 114^th Congress. In addition, the apportionment of the House of Representatives is shown using an estimate of the 2013 total apportionment population, as well.

If the apportionment of seats in the House of Representatives for the 114^th Congress were to be based on the 2013 estimated citizen apportionment population rather than the 2010 total apportionment population, as required by the Constitution, it is estimated that seven seats would shift among 11 states. California would lose four seats relative to its actual distribution of seats as a result of the 2010 apportionment. Texas, Florida, and New York would each lose one seat relative to the number of seats received in the 2010 apportionment.

On the other hand, Louisiana, Missouri, Montana, North Carolina, Ohio, Oklahoma, and Virginia would each pick up a single seat, if the 2013 citizen population were used to apportion seats rather than the 2010 total apportionment population. Using citizenship status to apportion the seats in the U.S. House of Representatives tends to benefit states with smaller immigrant populations and cost states with larger immigrant populations.

For those seeking to change the current population standard for apportioning the seats in the House of Representatives, there appears to be at least three possible choices. First, and most obvious, amend the U.S. Constitution. Second, use the citizen population in the redistricting process to geographically define the congressional districts. Or third, change the apportionment law to adopt an apportionment formula that, when used with the total population, mimics the apportionment distribution that occurs when using the citizen population.

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Apportioning Seats in the U.S. House of Representatives Using the 2013 Estimated Citizen Population

Introduction and Background

How seats in the U.S. House of Representatives are apportioned among the states is determined, in part, by the U.S. Constitution and, in part, by federal legislation and legal determinations by the courts. The U.S. Constitution determines the maximum and minimum size of the House of Representatives as well as the nature of the population upon which any apportionment is determined.

Historically, the issue of the nature of the population upon which the apportionment of the House of Representatives is based has been raised periodically. Rather than "persons," as is required in the Constitution, historical proposals have advocated "free Citizens," "legal voters," "male citizens," "the voting population," "citizens," or "exclude aliens" as the basis for the apportionment population.¹

From time to time, commentators and Members of Congress raise the issue, proposing to change the population upon which the apportionment of House seats is based from "persons" to "citizens."² This report examines the impact on the apportionment of seats in the House of Representatives if such a change were to occur, using an estimate of the 2013 citizen population in place of the 2010 apportionment population to determine the distribution of seats in the House of Representatives for the 114^th Congress. In addition, the apportionment of seats in the 114^th Congress is shown using an estimate of the 2013 total apportionment population as well.

Constitutional Issue

According to Section 2 of the 14^th Amendment to the U.S. Constitution,

Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed. But when the right to vote at any election for the choice of electors for President and Vice President of the United States, Representatives in Congress, the Executive and Judicial officers of a State, or the members of the Legislature thereof, is denied to any of the male inhabitants of such State, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such State. (Emphasis added.)

As stated, it has been taken to mean that the apportionment population is all persons residing in the United States. As Section 1 of this same amendment defines U.S. citizenship, the use of the term "persons" rather than "citizens" has not been taken to be an oversight by most.³ Thus, changing the meaning of population in the apportionment process is, most likely, going to require a constitutional amendment.⁴

Practicalities

The U.S. Supreme Court has held that, for purposes of apportionment only, actual population counts from the census must be used. Population estimates based on sample surveys cannot be used to apportion the seats in the House of Representatives.⁵

Currently, as will be highlighted below, the only source for information on citizenship status is the U.S. Census Bureau's American Community Survey (ACS), a sample survey.⁶ Even assuming that a constitutional amendment were to be passed and ratified by the required number of states relatively quickly, without the Census Bureau conducting a special census prior to the scheduled 2020 census, the earliest that another apportionment using citizenship status information is likely to occur is 2020. If such an amendment were to be passed, presumably the Census Bureau would ask a question about citizenship status of all persons in the 2020 census.

Recent Congressional Interest⁷

While no legislation has been introduced in the most recent congresses, in the 111^th Congress, Representative Candice Miller introduced H.J.Res. 11, a constitutional amendment that provided for the apportionment of seats in the House of Representatives based on the citizen population rather than total population.⁸ The proposed amendment had 28 cosponsors.

At the same time, Representative Virginia Foxx and Senator Robert F. Bennett introduced The Fairness in Representation Act (H.R. 3797/S. 1688). The proposed legislation would have amended Title 13 to require that the Census Bureau include on the 2010 census questionnaire "a checkbox or other similar option for respondents to indicate citizenship status or lawful presence in the United States." The proposed legislation further required that the Secretary of Commerce adjust the total population figures to assure that only the citizen population was used in apportioning seats to the House of Representatives.

In addition, Senator David Vitter introduced an amendment to the Commerce, Justice, Science, and Related Agencies Appropriations Act, 2010 (S.Amdt. 2635 to H.R. 2847). The amendment stated, in part, that "none of the funds provided in this Act or any other act for any fiscal year may be used for collection of census data that does not include questions regarding United States citizenship and immigration status." The amendment was subsequently ruled non-germane.

Prior to the 2010 Census, in the 111^th Congress, there was also opposition to the idea of restricting the apportionment based on the citizen population. Representative Joe Baca introduced the Every Person Counts Act (H.R. 3855). This bill would have prevented the Census Bureau from collecting information about U.S. citizenship or immigration status in any census.

None of the above legislation came to a vote.

Potential Impact of Using the Citizen Population to Apportion Seats in the House

In the 1990 and 2000 censuses, estimates of citizenship status were derived from the results of such questions on the "long-form" questionnaires. Both censuses included two types of questionnaires, a "short-form" questionnaire, which included a few basic questions on age, sex , race, and Hispanic heritage, and a "long-form" questionnaire, which included all of the questions from the short form and a large number of other demographic questions, including citizenship status. The long-form questionnaire was sent to a probability sample of about one-sixth of the U.S. households. The other five-sixths received only the short form. For the 1990 and 2000 censuses, the information derived from the short form and the long form constituted the results of the census.

Plans for the 2010 census were dramatically different. While the basic set of similar questions from the short form would again be posed on the census questionnaire going to the American public on April 1, 2010, there would be no comparable long form sent out at the same time. Rather, the information originally collected on the long form now would be collected by the American Community Survey (ACS), a cumulative, rolling sample survey that would collect, starting in 2006, the same or similar information collected in the previous long form used in the 1990 and 2000 censuses.⁹ Again, like in 1990 and 2000, the ACS is the only source for geographically detailed information about citizenship status.

Estimating the Total and Citizen Apportionment Populations

Limitations and Caveats

Citizenship Verification

Counts of citizens derived from the ACS are based on how respondents answered a question related to their citizenship status.¹⁰ The Census Bureau does nothing to attempt to verify whether or not the person responding is or is not a citizen by asking for legal documentation that could establish this fact. And, unless such a request was required by law, it is very doubtful that, even if the Census Bureau were to include such a question on the 2020 Census form, they would attempt such legal verification.

Residence Measurement

Partly because the census collects information on the population for purposes of apportionment, the concept of "usual residence," as measured by the census is meant to measure the legal address of the respondent as of census day (i.e., a de jure measure). On the other hand, the concept of residence as used by the ACS is better described as "where the respondent is residing when he or she completes the questionnaire" (i.e., a de facto measure).¹¹ Using the result of a survey that defines residence in one way to estimate a number for the census, which defines residence in a different way, may not prove meaningful. If one were to ask the citizenship status question on the census questionnaire, it is possible that there would be differences in the results (specifically where geographically the counts were to apply) and estimates based on the ACS might be due to differences in the definition of residence used by each survey. The possible impact of this difference on estimating the total 2013 citizen population from the ACS, is difficult, if not impossible, to gauge.

Sampling Error

The results of the decennial census are based on an attempt to count every person residing in the United States. The ACS, unlike this 100 percent count, is based on a sample survey, albeit a large sample survey. Sample surveys are, unlike censuses, subject to sampling error. Therefore, any estimate of the 2013 citizen population based on the ACS is also subject to sampling error. These sampling errors have been calculated and are shown in the tables below.

Different Time Frames between the Census and the ACS

While the decennial census figures are mythically based on the concept of collecting the information on a single day, April 1, 2010, in fact, the information for the census is collected over many months. However, this information, whether collected on April 1, or on September 9, 2010, refers back to the single date of April 1, 2010. This is the reference date for census data.¹²

The ACS, on the other hand, is designed very differently.¹³ Each month, a new, large sample of households (about 250,000) is mailed the ACS questionnaire. Over the course of a full year, about 3 million households receive the ACS questionnaires. Yearly estimates (ACS-1Yr)—the most frequently published figures—are based on the accumulated results from samples over the whole year—accurate for geographical areas containing populations of 65,000 persons or more. Thus, the time frame for the ACS-1Yr is not a single day, but a year of monthly household samples. Rather than a specific time reference as with the census, ACS results are analogous to a yearly average. Consequently, the time reference for the information collected differs between the 2010 census and the ACS. Like the difference with respect to residency, the possible impact of the difference in time references between the two sets of information on any estimated figures is difficult to gauge.

Estimation Method Used to Estimate the 2013 Total and Citizen Apportionment Population

Since 1970, with one exception, the apportionment population for each state has consisted of two components: (1) the state's resident population; and (2) the overseas military and civilian federal employee population and their dependents living with them.¹⁴

2010 Apportionment Population and Its Components

Table 1 shows this information for each state for the 2010 apportionment population. In addition, the ratio of the overseas population to the residential population in 2010 is calculated for each state. This ratio subsequently will be used to estimate the size of the overseas military and civilian federal employee population for 2013, under the assumption that the actual ratio calculated on the basis of the 2010 Census is the same as the ratio would be if one were to use the actual 2013 resident population and the actual 2013 overseas military and civilian federal employee population.

The values in columns 2-4 in Table 1 were the population values used in determining the allocation of seats in the U.S. House of Representatives to the states for the 2012 apportionment process, which produced the seat distribution in the U.S. House of Representatives for the 113^th Congress. Column 5, labelled "Ratio of Overseas to Resident Pop.," subsequently will be used to estimate the 2013 overseas population by multiplying this ratio by the 2013 estimated resident population.

Estimating the 2013 Apportionment Population

Table 2 shows the process of estimating the 2013 apportionment population for each of the states. The U.S. Census Bureau, using a demographic methodology referred to as a "cohort components method,"¹⁵ estimates the resident population of the United States, the states, the counties, and Puerto Rico every year between censuses.¹⁶

Column 3, labelled "Resident Population Estimate (as of July 1, 2013)," shows the U.S. Census Bureau's state population estimates as of July 1, 2013.¹⁷ Column 4 displays the "2010 Ratio of Overseas to Resident Pop.," computed in Table 1. Multiplying this ratio by the estimated 2013 resident population produces estimates of the 2013 overseas population for each state, shown in column 5. Adding the 2013 estimated resident population to the 2013 estimated overseas population produces the 2013 estimated apportionment population, shown in column 2.

2013 American Community Survey Citizenship Status

Table 3 below displays the results from the "citizenship" question posed in the 2013 American Community Survey (ACS) for each state. In addition, as the results are based on a sample survey, each estimate is associated with a measurement of error (MoE).¹⁸ By adding or subtracting the value of the associated MoE to the estimate, one calculates the upper and lower bounds for that estimated value at the 90% confidence level.

According to the documentation for the 2013 ACS, citizenship status/U.S. citizenship status was defined in the following way:

The data on citizenship status were derived from answers to Question 8 in the 2013 American Community Survey (ACS). This question was asked about Persons 1 through 5 in the ACS.

Respondents were asked to select one of five categories: (1) born in the United States, (2) born in Puerto Rico, Guam, the U.S. Virgin Islands, or Northern Marianas, (3) born abroad of U.S. citizen parent or parents, (4) U.S. citizen by naturalization, or (5) not a U.S citizen. Respondents indicating they are a U.S. citizen by naturalization also are asked to print their year of naturalization. People born in American Samoa, although not explicitly listed, are included in the second response category.

For the Puerto Rico Community Survey, respondents were asked to select one of five categories: (1) born in Puerto Rico, (2) born in a U.S. state, District of Columbia, Guam, the U.S. Virgin Islands, or Northern Marianas, (3) born abroad of U.S. citizen parent or parents, (4) U.S. citizen by naturalization, or (5) not a U.S. citizen. Respondents indicating they are a U.S. citizen by naturalization also are asked to print their year of naturalization. People born in American Samoa, although not explicitly listed, are included in the second response category.

When no information on citizenship status was reported for a person, information for other household members, if available, was used to assign a citizenship status to the respondent.¹⁹

Summing the estimated values in columns 4, 6, 8, and 10 from Table 3, one arrives at the 2013 estimated total resident citizen population based on the 2013 ACS survey. This sum is displayed in column 6 in Table 4, below. The calculation of the associated Margin of Error at the 95% confidence level (MoE₉₅) for this calculated sum, and consequently, the upper and lower bound population estimates is discussed in the Appendix, and the MoE₉₅ for the resident citizen population is shown in Table A-2.

Estimating the ACS 2013 Citizen Apportionment Population

Table 4 displays the 2013 ACS resident citizen population estimate and the upper and lower bound populations of that estimate for each state (columns 6, 7, and 8). In addition, column 5 displays the estimated 2013 overseas population initially calculated in Table 2 for each state. The apportionment population is the resident population plus the overseas population as defined by the U.S. Census Bureau. Consequently, summing the estimated 2013 overseas population with each of the resident citizen population values shown in columns 6, 7 and 8 above produces the matching apportionment population estimates as shown in columns 2, 3 and 4 in Table 4 below. The value in column 2, the 2013 citizen apportionment population estimate, is the state values used in this report to calculate the apportionment of seats for the U.S. House of Representatives.²⁰

Apportioning Seats to the House of Representatives Using Citizen Population Estimates

If the citizen population had been the basis of apportioning the seats in the House of Representatives after the 2000 census, it was estimated that nine seats would have shifted among 13 states relative to the actual apportionment.²¹ California would have received six fewer Representatives than it actually did. Florida and Texas, scheduled to receive two additional seats, each would have lost one of those two seats. New York, scheduled to lose two seats in the 2000 apportionment, would lose an additional seat if the 2000 citizen population had been used to apportion the seats in the House. And nine states would have gained one more Representatives than they actually received in the 2000 apportionment.

Columns 2 and 3 in Table 5 display the actual 2010 apportionment population, as well as the 2012 apportionment of seats in the U.S. House of Representatives (i.e., the current apportionment of seats).

Column 4 shows the 2013 total apportionment population estimate based upon the 2013 total state resident populations calculated in Table 2. Based on this estimated population, if an apportionment of the seats in the U.S. House of Representatives were to be conducted today, the distribution of seats among the states would be that shown in column 5 of Table 5. As can be seen in column 6, to the extent the estimated 2013 population reflects population changes among the states, then it would appear that Minnesota would lose a seat and North Carolina would gain a seat in an apportionment today, relative to the actual apportionment based on the 2010 population.

Column 7 displays the estimated state citizen population for 2013 as derived in Table 3. If the apportionment of the seats of the U.S. House of Representatives was to be conducted today, and, was based on the estimated 2013 population of U.S. citizens in each state, then the distribution of House seats among the states would be that shown in column 8 of Table 5. As can be seen in column 9, to the extent the 2013 citizen population estimate is an accurate representation of the citizen population in the states, the distribution of seats in the House based on that population would create a 7 seat change affecting 11 states, relative to the actual 2010 seat distribution among the states.

California would lose 4 seats, and Florida, New York, and Texas would each lose 1 seat. On the other hand, Louisiana, Missouri, Montana, North Carolina, Ohio, Oklahoma, and Virginia would each pick up a single seat, if the estimated 2013 citizen population were used to apportion seats today rather than the 2010 census population.²²

Taking the Citizen Population into Account in the Apportionment Process: Some Possible Options

As is shown above, using the citizen population to apportion the seats in the House of Representatives, as some have advocated, would have an impact on the distribution of seats among the states. For those who favor the current method and outcome, no change in policy is necessary. However, for those who wish, for whatever reason, to make sure only the citizen population has an impact on the apportionment process, there are several options.

Constitutional Amendment

First, and most obviously, proponents of such a policy can propose and attempt to pass and ratify a constitutional amendment changing the term "persons" to "citizens" in the 14^th Amendment. This strategy was apparent, for example, in the proposed legislation introduced by Representative Candice Miller in the 111^th Congress (H.J.Res. 11). Short of this action, however, it would appear that apportioning the seats in the House of Representatives by using the citizen population is not likely to occur, as it most likely would be unconstitutional.²³

Using the Citizen Population in the Redistricting Process Rather than in the Apportionment Process

The apportionment process determines the number of House seats that are allocated to each state (and, subsequently, the number of electoral votes). Once that process is completed, currently the next step, usually carried out by the state legislatures or state redistricting commissions, is to determine, within the state, what geographic area is to be represented by each seat. That is, the redistricting process draws the boundary lines for each of the congressional seats within each multi-member state. While the Constitution appears clear that the apportionment of seats is to be based on "persons," it is silent with respect to how congressional district boundaries are drawn and on what basis.

Legal Considerations

The federal courts have established criteria for the drawing of congressional districts (as well as state and local political jurisdictions), and it would appear that redistricting, currently, does not necessarily have to use total population, but could, if allowed by the state, use some other well-defined population—like the state's citizen population.²⁴

Practicalities

Currently, the U.S. Census Bureau is required to deliver census information to be used in the redistricting process by one year following census day (i.e., most recently, by April 1, 2011). The information includes block level information on age, sex, race, and Hispanic-origin of all persons living in the states. It does not include citizenship status on all persons living in the states. Such information, if collected on the decennial census form, could be used to draw boundaries for congressional districts rather than total population. The Fairness in Representation Act (H.R. 3797/S. 1688), or something similar, proposed by Representative Foxx and Senator Bennett in the 111^th Congress would require the Census Bureau to collect this information on the 100% census form.

However, the states do have information for very small areas like blocks and precincts. Most states have voter registration information at the address level. As one must be a citizen to vote in most elections, this information could serve as a surrogate for the citizen population.²⁵ The major drawback would be that not every citizen is registered. However, it is very likely that many congressional and state legislative district boundaries already are based on much of this information. To the extent that boundaries are drawn to enhance the power positions of political parties, it is almost certain that voter registration information has been used by the map makers.²⁶

Of course, Congress could pass legislation with respect to congressional redistricting requiring that the citizen population be used in the redistricting of seats for the U.S. House of Representatives in all states. Whether the states choose to follow this path or Congress chooses to, such a procedure could determine the population to be "represented" in the Congress, even if the number of seats for each state is determined by the total population.

Changing the Apportionment Method

The apportionment of the seats in the U.S. House of Representatives is determined by four factors: the population size within the states, the number of seats to be allocated, the method or formula used, and the number of states in which seats are apportioned. Currently, the method of equal proportions is used to apportion the seats. The method is defined by law and, consequently, can be changed by Congress.²⁷

In a 1941 journal article, Walter F. Willcox, the leading proponent of the major fractions method of apportionment at the time, and a noted mathematician from Cornell University, proposed using the method of smallest divisors on the total population as a method that came closest to simulating the impact of using the citizen population with either the method of major fractions or the method of equal proportions.²⁸ In his words,

Let me now explain why I have come to prefer the method of smallest divisors to any of the others, even that of major fractions which I advocated for many years.

My reasons are:

1. It secures the smallest average population per district and the narrowest range between the largest and the smallest average district.

2. It is the easiest method for the average citizen to understand and judge.

3. The theory underlying it is persuasive to the non-mathematical mind.

4. Its results based on the whole population come close to those of the method of major fractions or the method of equal proportions based on the citizen population.²⁹

The method of smallest divisors (also referred to as the Adams method, after John Quincy Adams, a proponent) rounds up to the next seat for any fractional remainder. The rounding point between 1 and 2, for example, would be any fraction exceeding 1 with similar rounding points for all other integers. The method of smallest divisors (which has never been used in practice to apportion seats in the U.S. House of Representatives) may be defined in the following manner for a 435-seat House:

Find a number so that when it is divided into each state's population and resulting quotients that include fractions are rounded up, the total number of seats will sum to 435. (In all cases where a state would be entitled to less than one seat, it receives one anyway because of the constitutional entitlement.)³⁰

The method of smallest divisors tends to favor states that are less populated. In general, with respect to the non-citizen population, the smallest divisors method tends to favor geographic areas where non-citizens are less likely to be located—less populated areas with fewer jobs or less-urban states. As a consequence, it could be argued that such a method is less representative than the current method.

Table 6, below, shows a comparison for 2013 between the apportionment of seats using the equal proportion method (the current method) for both the 2013 total population estimate and the 2013 citizen population estimate as compared to the smallest divisor method using the total 2013 total population estimate.

As can be seen in columns 7 and 8, while the distribution of seats based solely on the citizen population using the method of equal proportions is not exactly the same as that based on the total population using the method of smallest divisors, the impact of using the method of smallest divisors appears to fall somewhere between the distributions using the method of equal proportions on the 2013 total and citizen apportionment population estimates.

This is only one example. It is possible that other methods of apportioning the total population could be developed that would mimic the results one would get using the equal proportion methods with the citizen population more closely. The point is that an alternative to pursuing a constitutional amendment to replace the total population with the citizen population for apportionment purposes could be to change the apportionment method.

Calculating the Sampling Errors

The 2013 ACS total population, with respect to citizenship status is composed of five parts: (a) native born citizens (NB), (b) native born citizens born in Puerto Rico, Guam, the Virgin Islands, or the Northern Marianas (PR), (c) citizens born abroad of American parents (BA), (d) naturalized citizens (NAT), and (e) non-citizens (NON). The citizen population is made up of the first four parts of the total population (parts a-d). These values are presented in Table 3, along with the associated measurement of error (MoE), as the values are estimates derived from a sample survey.

As the ACS is a sample survey, estimates derived from the survey results are subject to sampling error. When constructing tables from the ACS, the American Factfinder application produces the margin of error (MOE) for all appropriate estimates at a 90 percent confidence level. For purposes of this paper, all MoEs for population estimates have been converted to MoEs at the 95 percent confidence level using the formula described in the U.S. Census Bureau's description of how to use ACS data.³¹ To create MoEs at the 95 percent confidence level, one multiplies each of the MoE values provided by the Census Bureau by the ratio (1.960/1.645). These values (MoE95), along with the values provided by the U.S. Census Bureau (the estimates and the matching MoE90) are displayed in Table A-1.

Calculating the Measurement Errors for the Citizen Population Estimate

As noted above, the citizen population estimate is composed of the sum of the persons responding to the four categories in the citizenship status question (native born; native born in Puerto Rico, Guam, the Virgin Islands, and the Northern Marianas; born abroad to American parents; and naturalized). Consequently, the estimate of the citizen population merely consists of the sum of the values in these four categories. However, estimates of the sampling error for this sum are somewhat more complicated. The first step in calculating the MOEs for the aggregated counts for each state consists of using the following general formula,

the MOE_CIT for the citizen population is

MOE_CIT = ± √ (MOE_NB² + MOE_PR² + MOE_BA² +MOE_NAT²)

for each state.³²

These calculations for the MoE₉₀ and MoE₉₅ for the sum are shown in the last two columns of Table A-2, below. Estimating the upper and lower bound for any estimate consists of adding and subtracting the value of the MoE to the estimate. Thus, the 95% upper and lower bound for the 2013 ACS resident citizen population estimate for each state shown in Table 4 in the text above consists of adding (upper bound) and subtracting (lower bound) the matching state value for the MoE₉₅ shown in column 11 of Table A-2 to the 2013 ACS resident citizen population estimated value for each state in Table 4.