The data contained in these data products are based on the American Community Survey (ACS) sample interviewed from January 1, 2013 through December 31, 2013. The ACS sample is selected from all counties and county-equivalents in the United States. In 2006, the ACS began collection of data from sampled persons in group quarters (GQs) – for example, military barracks, college dormitories, nursing homes, and correctional facilities. Persons in group quarters are included with persons in housing units (HUs) in all 2013 ACS estimates that are based on the total population. All ACS population estimates from years prior to 2006 include only persons in housing units. The ACS, like any other statistical activity, is subject to error. The purpose of this documentation is to provide data users with a basic understanding of the ACS sample design, estimation methodology, and accuracy of the ACS data. The ACS is sponsored by the U.S. Census Bureau, and is part of the Decennial Census Program.
Additional information on the design and methodology of the ACS, including data collection and processing, can be found at:: http://www.census.gov/acs/www/methodology/methodology_main/.

The 2013 Accuracy of the Data from the Puerto Rico Community Survey can be found at
http://www.census.gov/acs/www/Downloads/data_documentation/Accuracy/PRCS_Accuracy_of_Data_2013.pdf.

Housing Units

The ACS employs three modes of data collection:

• Internet
• Mailout/Mailback
• Computer Assisted Telephone Interview (CATI)
• Computer Assisted Personal Interview (CAPI)

With the exception of addresses in Remote Alaska, the general timing of data collection is:

Month 1: Addresses in sample that are determined to be mailable are sent an initial mailing package – this package contains information for completing the ACS questionnaire on the internet (on-line). If, after two weeks, a sample address has not responded on-line, then it is sent a second mailing package. This package contains a paper questionnaire. Once the second package is received, sampled addresses then have the option of which mode to use for filling out the questionnaire.

Month 2: All mail non-responding addresses with an available phone number are sent to CATI.

Month 3: A sample of mail non-responses without a phone number, CATI non-responses, and unmailable addresses are selected and sent to CAPI.

Note that mail responses are accepted during all three months of data collection.

All Remote Alaska addresses that are in sample are assigned to one of two data collection periods, January-April, or September-December and are all sent to the CAPI mode of data collection.¹ Data for these addresses are collected using CAPI only and up to four months are given to complete the interviews in Remote Alaska for each data collection period.


¹ Prior to the 2011 sample year, all remote Alaska sample cases were subsampled for CAPI at a rate of 2-in-3.

The Census Bureau has modified or suppressed some data on this site to protect confidentiality. Title 13 United States Code, Section 9, prohibits the Census Bureau from publishing results in which an individual's data can be identified.

The Census Bureau's internal Disclosure Review Board sets the confidentiality rules for all data releases. A checklist approach is used to ensure that all potential risks to the confidentiality of the data are considered and addressed.

• Title 13, United States Code: Title 13 of the United States Code authorizes the Census Bureau to conduct censuses and surveys. Section 9 of the same Title requires that any information collected from the public under the authority of Title 13 be maintained as confidential. Section 214 of Title 13 and Sections 3559 and 3571 of Title 18 of the United States Code provide for the imposition of penalties of up to five years in prison and up to $250,000 in fines for wrongful disclosure of confidential census information.
• Disclosure Avoidance: Disclosure avoidance is the process for protecting the confidentiality of data. A disclosure of data occurs when someone can use published statistical information to identify an individual that has provided information under a pledge of confidentiality. For data tabulations, the Census Bureau uses disclosure avoidance procedures to modify or remove the characteristics that put confidential information at risk for disclosure. Although it may appear that a table shows information about a specific individual, the Census Bureau has taken steps to disguise or suppress the original data while making sure the results are still useful. The techniques used by the Census Bureau to protect confidentiality in tabulations vary, depending on the type of data. All disclosure avoidance procedures are done prior to the whole person imputation into not-in-sample GQ facilities.
• Data Swapping: Data swapping is a method of disclosure avoidance designed to protect confidentiality in tables of frequency data (the number or percent of the population with certain characteristics). Data swapping is done by editing the source data or exchanging records for a sample of cases when creating a table. A sample of households is selected and matched on a set of selected key variables with households in neighboring geographic areas that have similar characteristics (such as the same number of adults and same number of children). Because the swap often occurs within a neighboring area, there is no effect on the marginal totals for the area or for totals that include data from multiple areas. Because of data swapping, users should not assume that tables with cells having a value of one or two reveal information about specific individuals. Data swapping procedures were first used in the 1990 Census, and were used again in Census 2000 and the 2010 Census.
• Synthetic Data: The goals of using synthetic data are the same as the goals of data swapping, namely to protect the confidentiality in tables of frequency data. Persons are identified as being at risk for disclosure based on certain characteristics. The synthetic data technique then models the values for another collection of characteristics to protect the confidentiality of that individual.

• Sampling Error - The data in the ACS products are estimates of the actual figures that would have been obtained by interviewing the entire population using the same methodology. The estimates from the chosen sample also differ from other samples of housing units and persons within those housing units. Sampling error in data arises due to the use of probability sampling, which is necessary to ensure the integrity and representativeness of sample survey results. The implementation of statistical sampling procedures provides the basis for the statistical analysis of sample data. Measures used to estimate the sampling error are provided in the next section.
• Nonsampling Error - In addition to sampling error, data users should realize that other types of errors may be introduced during any of the various complex operations used to collect and process survey data. For example, operations such as data entry from questionnaires and editing may introduce error into the estimates. Another source is through the use of controls in the weighting. The controls are designed to mitigate the effects of systematic undercoverage of certain groups who are difficult to enumerate as well as to reduce the variance. The controls are based on the population estimates extrapolated from the previous census. Errors can be brought into the data if the extrapolation methods do not properly reflect the population. However, the potential risk from using the controls in the weighting process is offset by far greater benefits to the ACS estimates. These benefits include reducing the effects of a larger coverage problem found in most surveys, including the ACS, and the reduction of standard errors of ACS estimates. These and other sources of error contribute to the nonsampling error component of the total error of survey estimates. Nonsampling errors may affect the data in two ways. Errors that are introduced randomly increase the variability of the data. Systematic errors which are consistent in one direction introduce bias into the results of a sample survey. The Census Bureau protects against the effect of systematic errors on survey estimates by conducting extensive research and evaluation programs on sampling techniques, questionnaire design, and data collection and processing procedures. In addition, an important goal of the ACS is to minimize the amount of nonsampling error introduced through nonresponse for sample housing units. One way of accomplishing this is by following up on mail nonrespondents during the CATI and CAPI phases. For more information, please see the section entitled "Control of Nonsampling Error".

Sampling error is the difference between an estimate based on a sample and the corresponding value that would be obtained if the estimate were based on the entire population (as from a census). Note that sample-based estimates will vary depending on the particular sample selected from the population. Measures of the magnitude of sampling error reflect the variation in the estimates over all possible samples that could have been selected from the population using the same sampling methodology.
Estimates of the magnitude of sampling errors - in the form of margins of error - are provided with all published ACS data. The Census Bureau recommends that data users incorporate this information into their analyses, as sampling error in survey estimates could impact the conclusions drawn from the results.

Direct estimates of the margin of error were calculated for all estimates reported in this product. The margin of error is calculated from the variance. The variance, in most cases, is calculated using a replicate-based methodology known as successive difference replication that takes into account the sample design and estimation procedures.
The formula provided below calculates the variance using the ACS estimate (X₀) and the 80 replicate estimates (X_r).



X₀ is the estimate calculated using the production weight and X_r is the estimate calculated using the r^th replicate weight. The standard error is the square root of the variance. The 90^th percent margin of error is 1.645 times the standard error.
For more information on the formation of the replicate weights, see chapter 12 of the Design and Methodology documentation at http://www.census.gov/acs/www/Downloads/survey_methodology/acs_design_methodology_ch12_2014.pdf.

Beginning with the ACS 2011 1-year estimates, a new imputation-based methodology was incorporated into processing (see the description in the Group Quarters Person Weighting Section). An adjustment was made to the production replicate weight variance methodology to account for the non-negligible amount of additional variation being introduced by the new technique.⁵
Excluding the base weights, replicate weights were allowed to be negative in order to avoid underestimating the standard error. Exceptions include:
1. The estimate of the number or proportion of people, households, families, or housing units in a geographic area with a specific characteristic is zero. A special procedure is used to estimate the standard error.
2. There are either no sample observations available to compute an estimate or standard error of a median, an aggregate, a proportion, or some other ratio, or there are too few sample observations to compute a stable estimate of the standard error. The estimate is represented in the tables by "-" and the margin of error by "**" (two asterisks).
3. The estimate of a median falls in the lower open-ended interval or upper open-ended interval of a distribution. If the median occurs in the lowest interval, then a "-" follows the estimate, and if the median occurs in the upper interval, then a "+" follows the estimate. In both cases the margin of error is represented in the tables by "***" (three asterisks).

⁵For more information regarding this issue, see Asiala, M. and Castro, E. 2012. Developing Replicate Weight- Based Methods to Account for Imputation Variance in a Mass Imputation Application. In JSM proceedings, Section on Survey Research Methods, Alexandria, VA: American Statistical Association.

Significant differences - Users may conduct a statistical test to see if the difference between a PRCS estimate and any other chosen estimates is statistically significant at a given confidence level. "Statistically significant" means that the difference is not likely due to random chance alone. With the two estimates (Est¹ and Est²) and their respective standard errors (SE¹ and SE²), calculate a Z statistic:





If Z > 1.645 or Z < -1.645, then the difference can be said to be statistically significant at the 90 percent confidence level. ⁶
Users are also cautioned to not rely on looking at whether confidence intervals for two estimates overlap or not to determine statistical significance, because there are circumstances where that method will not give the correct test result. If two confidence intervals do not overlap, then the estimates will be significantly different (i.e. the significance test will always agree). However, if two confidence intervals do overlap, then the estimates may or may not be significantly different. The Z calculation above is recommended in all cases.

Here is a simple example of why it is not recommended to use the overlapping confidence bounds rule of thumb as a substitute for a statistical test.

Let: X₁ = 6.0 with SE₁ = 0.5 and X₂ = 5.0 with SE₂ = 0.2.

The Lower Bound for X₁ = 6.0 - 0.5 x 1.645 = 5.2 while the Upper Bound for X₂ = 5.0 + 0.2 x 1.645 = 5.3. The confidence bounds overlap, so, the rule of thumb would indicate that the estimates are not significantly different at the 90% level.

However, if we apply the statistical significance test we obtain:



Z = 1.857 > 1.645 which means that the difference is significant (at the 90% level).

All statistical testing in ACS data products is based on the 90 percent confidence level. Users should understand that all testing was done using unrounded estimates and standard errors, and it may not be possible to replicate test results using the rounded estimates and margins of error as published.

⁶The ACS Accuracy of the Data document in 2005 used a Z statistic of +/-1.65. Data users should use +/-1.65 for estimates published in 2005 or earlier.

We will present some examples based on the real data to demonstrate the use of the formulas.

As mentioned earlier, sample data are subject to nonsampling error. This component of error could introduce serious bias into the data, and the total error could increase dramatically over that which would result purely from sampling. While it is impossible to completely eliminate nonsampling error from a survey operation, the Census Bureau attempts to control the sources of such error during the collection and processing operations. Described below are the primary sources of nonsampling error and the programs instituted for control of this error. The success of these programs, however, is contingent upon how well the instructions were carried out during the survey.

• Coverage Error

- It is possible for some sample housing units or persons to be missed entirely by the survey (undercoverage), but it is also possible for some sample housing units and persons to be counted more than once (overcoverage). Both the undercoverage and overcoverage of persons and housing units can introduce biases into the data, increase respondent burden and survey costs.
A major way to avoid coverage error in a survey is to ensure that its sampling frame, for ACS an address list in each state, is as complete and accurate as possible. The source of addresses for the ACS is the MAF. An attempt is made to assign all appropriate geographic codes to each MAF address via an automated procedure using the Census Bureau TIGER (Topologically Integrated Geographic Encoding and Referencing) files. A manual coding operation based in the appropriate regional offices is attempted for addresses which could not be automatically coded. The MAF was used as the source of addresses for selecting sample housing units and mailing questionnaires. TIGER produced the location maps for CAPI assignments. Sometimes the MAF has an address that is the duplicate of another address already on the MAF. This could occur when there is a slight difference in the address such as 123 Main Street versus 123 Maine Street.
In the CATI and CAPI nonresponse follow-up phases, efforts were made to minimize the chances that housing units that were not part of the sample were interviewed in place of units in sample by mistake. If a CATI interviewer called a mail nonresponse case and was not able to reach the exact address, no interview was conducted and the case was eligible for CAPI. During CAPI follow-up, the interviewer had to locate the exact address for each sample housing unit. If the interviewer could not locate the exact sample unit in a multi-unit structure, or found a different number of units than expected, the interviewers were instructed to list the units in the building and follow a specific procedure to select a replacement sample unit. Person overcoverage can occur when an individual is included as a member of a housing unit but does not meet ACS residency rules.
Coverage rates give a measure of undercoverage or overcoverage of persons or housing units in a given geographic area. Rates below 100 percent indicate undercoverage, while rates above 100 percent indicate overcoverage. Coverage rates are released concurrent with the release of estimates on American FactFinder in the B98 series of detailed tables. Further information about ACS coverage rates may be found at http://www.census.gov/acs/www/methodology/methodology_main/.

• Nonresponse Error

- Survey nonresponse is a well-known source of nonsampling error. There are two types of nonresponse error - unit nonresponse and item nonresponse. Nonresponse errors affect survey estimates to varying levels depending on amount of nonresponse and the extent to which nonrespondents differ from respondents on the characteristics measured by the survey. The exact amount of nonresponse error or bias on an estimate is almost never known. Therefore, survey researchers generally rely on proxy measures, such as the nonresponse rate, to indicate the potential for nonresponse error.

- Unit Nonresponse - Unit nonresponse is the failure to obtain data from housing units in the sample. Unit nonresponse may occur because households are unwilling or unable to participate, or because an interviewer is unable to make contact with a housing unit. Unit nonresponse is problematic when there are systematic or variable differences between interviewed and noninterviewed housing units on the characteristics measured by the survey. Nonresponse bias is introduced into an estimate when differences are systematic, while nonresponse error for an estimate evolves from variable differences between interviewed and noninterviewed households.

The ACS makes every effort to minimize unit nonresponse, and thus, the potential for nonresponse error. First, the ACS used a combination of mail, CATI, and CAPI data collection modes to maximize response. The mail phase included a series of three to four mailings to encourage housing units to return the questionnaire. Subsequently, mail nonrespondents (for which phone numbers are available) were contacted by CATI for an interview. Finally, a subsample of the mail and telephone nonrespondents was contacted by personal visit to attempt an interview. Combined, these three efforts resulted in a very high overall response rate for the ACS.

ACS response rates measure the percent of units with a completed interview. The higher the response rate, and consequently the lower the nonresponse rate, the less chance estimates may be affected by nonresponse bias. Response and nonresponse rates, as well as rates for specific types of nonresponse, are released concurrent with the release of estimates on American FactFinder in the B98 series of detailed tables. Further information about response and nonresponse rates may be found at http://www.census.gov/acs/www/methodology/methodology_main/.

- Item Nonresponse - Nonresponse to particular questions on the survey questionnaire and instrument allows for the introduction of error or bias into the data, since the characteristics of the nonrespondents have not been observed and may differ from those reported by respondents. As a result, any imputation procedure using respondent data may not completely reflect this difference either at the elemental level (individual person or housing unit) or on average.

Some protection against the introduction of large errors or biases is afforded by minimizing nonresponse. In the ACS, item nonresponse for the CATI and CAPI operations was minimized by the requirement that the automated instrument receive a response to each question before the next one could be asked. Questionnaires returned by mail were edited for completeness and acceptability. They were reviewed by computer for content omissions and population coverage. If necessary, a telephone follow-up was made to obtain missing information. Potential coverage errors were included in this follow-up.

Allocation tables provide the weighted estimate of persons or housing units for which a value was imputed, as well as the total estimate of persons or housing units that were eligible to answer the question. The smaller the number of imputed responses, the lower the chance that the item nonresponse is contributing a bias to the estimates. Allocation tables are released concurrent with the release of estimates on American Factfinder in the B99 series of detailed tables with the overall allocation rates across all person and housing unit characteristics in the B98 series of detailed tables. Additional information on item nonresponse and allocations can be found at http://www.census.gov/acs/www/methodology/methodology_main/.

• Measurement and Processing Error

- The person completing the questionnaire or responding to the questions posed by an interviewer could serve as a source of error, although the questions were cognitively tested for phrasing and detailed instructions for completing the questionnaire were provided to each household.
- Interviewer monitoring - The interviewer may misinterpret or otherwise incorrectly enter information given by a respondent; may fail to collect some of the information for a person or household; or may collect data for households that were not designated as part of the sample. To control these problems, the work of interviewers was monitored carefully. Field staff were prepared for their tasks by using specially developed training packages that included hands-on experience in using survey materials. A sample of the households interviewed by CAPI interviewers was reinterviewed to control for the possibility that interviewers may have fabricated data.
- Processing Error - The many phases involved in processing the survey data represent potential sources for the introduction of nonsampling error. The processing of the survey questionnaires includes the keying of data from completed questionnaires, automated clerical review, follow-up by telephone, manual coding of write-in responses, and automated data processing. The various field, coding and computer operations undergo a number of quality control checks to insure their accurate application.

- Content Editing - After data collection was completed, any remaining incomplete or inconsistent information was imputed during the final content edit of the collected data. Imputations, or computer assignments of acceptable codes in place of unacceptable entries or blanks, were needed most often when an entry for a given item was missing or when the information reported for a person or housing unit on that item was inconsistent with other information for that same person or housing unit. As in other surveys and previous censuses, the general procedure for changing unacceptable entries was to allocate an entry for a person or housing unit that was consistent with entries for persons or housing units with similar characteristics. Imputing acceptable values in place of blanks or unacceptable entries enhances the usefulness of the data.

Several examples are provided here to demonstrate how different the approximated standard errors of sums can be compared to those derived and published with ACS microdata.
A. Suppose we wish to estimate the total number of males with income below the poverty level in the past 12 months using both state and PUMA level estimates for the state of Wyoming. Part of the collapsed table C17001 is displayed below with estimates and their margins of error in parentheses.
Table A: 2009 Estimates of Males with Income Below Poverty from table C17001: Poverty Status in the Past 12 Months by Sex by Age

Characteristic	Wyoming	PUMA 00100	PUMA 00200	PUMA 00300	PUMA 00400
Male	23,001 (3,309)	5,264 (1,624)	6,508 (1,395)	4,364 (1,026)	6,865 (1,909)
Under 18 Years Old	8,479 (1,874)	2,041 (920)	2,222 (778)	1,999 (750)	2,217 (1,192)
18 to 64 Years Old	12,976 (2,076)	3,004 (1,049)	3,725 (935)	2,050 (635)	4,197 (1,134)
65 Years and Older	1546 (500)	219 (237)	561 (286)	315 (173)	451 (302)
2009 American FactFinder

The first way is to sum the three age groups for Wyoming:
Estimate(Male) = 8,479 + 12,976 + 1,546 = 23,001.
The first approximation for the standard error in this case gives us:

A second way is to sum the four PUMA estimates for Male to obtain:
Estimate(Male) = 5,264 + 6,508 + 4,364 + 6,865 = 23,001 as before.
The second approximation for the standard error yields:



Finally, we can sum up all three age groups for all four PUMAs to obtain an estimate based on a total of twelve estimates:

And the third approximated standard error is

However, we do know that the standard error using the published MOE is 3,309 /1.645 = 2,011.6. In this instance, all of the approximations under-estimate the published standard error and should be used with caution.

B. Suppose we wish to estimate the total number of males at the national level using age and citizenship status. The relevant data from table B05003 is displayed in table B below.
Table B: 2009 Estimates of males from B05003: Sex by Age by Citizenship Status

Characteristic	Estimate	MOE
Male	151,375,321	27,279
Under 18 Years	38,146,514	24,365
Native	36,747,407	31,397
Foreign Born	1,399,107	20,177
Naturalized U.S. Citizen	268,445	10,289
Not a U.S. Citizen	1,130,662	20,228
18 Years and Older	113,228,807	23,525
Native	95,384,433	70,210
Foreign Born	17,844,374	59,750
Naturalized U.S. Citizen	7,507,308	39,658
Not a U.S. Citizen	10,337,066	65,533
2009 American FactFinder

The estimate and its MOE are actually published. However, if they were not available in the tables, one way of obtaining them would be to add together the number of males under 18 and over 18 to get:


And the first approximated standard error is



Another way would be to add up the estimates for the three subcategories (Native, and the two subcategories for Foreign Born: Naturalized U.S. Citizen, and Not a U.S. Citizen), for males under and over 18 years of age. From these six estimates we obtain:


With a second approximated standard error of:



We do know that the standard error using the published margin of error is 27,279 / 1.645 = 16,583.0. With a quick glance, we can see that the ratio of the standard error of the first method to the published-based standard error yields 1.24; an over-estimate of roughly 24%, whereas the second method yields a ratio of 4.07 or an over-estimate of 307%. This is an example of what could happen to the approximate SE when the sum involves a controlled estimate. In this case, it is sex by age.
C. Suppose we are interested in the total number of people aged 65 or older and its standard error. Table C shows some of the estimates for the national level from table B01001 (the estimates in gray were derived for the purpose of this example only).

Table C: Some Estimates from AFF Table B01001: Sex by Age for 2009

Age Category	Estimate, Male	MOE, Male	Estimate, Female	MOE, Female	Total	Estimated MOE, Total
65 and 66 years old	2,492,871	20,194	2,803,516	23,327	5,296,387	30,854
67 to 69 years old	3,029,709	18,280	3,483,447	24,287	6,513,225	30,398
70 to 74 years old	4,088,428	21,588	4,927,666	26,867	9,016,094	34,466
75 to 79 years old	3,168,175	19,097	4,204,401	23,024	7,372,576	29,913
80 to 84 years old	2,258,021	17,716	3,538,869	25,423	5,796,890	30,987
85 years and older	1,743,971	17,991	3,767,574	19,294	5,511,545	26,381
Total	16,781,175	NA	22,725,473	NA	39,506,648	74,932
2009 American FactFinder

To begin we find the total number of people aged 65 and over by simply adding the totals for males and females to get 16,781,175 + 22,725,542 = 39,506,717. One way we could use is summing males and female for each age category and then using their MOEs to approximate the standard error for the total number of people over 65.

... etc. ...
Now, we calculate for the number of people aged 65 or older to be 39,506,648 using the six derived estimates and approximate the standard error:

For this example the estimate and its MOE are published in table B09017. The total number of people aged 65 or older is 39,506,648 with a margin of error of 20,689. Therefore the published- based standard error is:


The approximated standard error, using six derived age group estimates, yields an approximated standard error roughly 3.6 times larger than the published-based standard error.

As a note, there are two additional ways to approximate the standard error of people aged 65 and over in addition to the way used above. The first is to find the published MOEs for the males age 65 and older and of females aged 65 and older separately and then combine to find the approximate standard error for the total. The second is to use all twelve of the published estimates together, that is, all estimates from the male age categories and female age categories, to create the SE for people aged 65 and older. However, in this particular example, the results from all three ways are the same. So no matter which way you use, you will obtain the same approximation for the SE. This is different from the results seen in example A.

D. For an alternative to approximating the standard error for people 65 years and older seen in part C, we could find the estimate and its SE by summing all of the estimate for the ages less than 65 years old and subtracting them from the estimate for the total population. Due to the large number of estimates, Table D does not show all of the age groups. In addition, the estimates in part of the table shaded gray were derived for the purposes of this example only and cannot be found in base table B01001.

Table D: Some Estimates from AFF Table B01001: Sex by Age for 2009:

Age Category	Estimate, Male	MOE, Male	Estimate, Female	MOE, Female	Total	Estimated MOE, Total
Total Population	151,375,321	27,279	155,631,235	27,280	307,006,556	38,579
Under 5 years	10,853,263	15,661	10,355,944	14,707	21,209,207	21,484
5 to 9 years old	10,273,948	43,555	9,850,065	42,194	20,124,013	60,641
10 to 14 years old	10,532,166	40,051	9,985,327	39,921	20,517,493	56,549
...	...	...	...	...
62 to 64 years old	4,282,178	25,636	4,669,376	28,769	8,951,554	38,534
Total for Age 0 to 64 years old	134,594,146	117,166	132,905,762	117,637	267,499,908	166,031
Total for Age 65 years and older	16,781,175	120,300	22,725,473	120,758	39,506,648	170,454
2009 American FactFinder

An estimate for the number of people age 65 and older is equal to the total population minus the population between the ages of zero and 64 years old:
Number of people aged 65 and older: 307,006,556 - 267,499,908 = 39,506,648.
The way to approximate the SE is the same as in part C. First we will sum male and female estimates across each age category and then approximate the MOEs. We will use that information to approximate the standard error for our estimate of interest:

... etc. ...
And the SE for the total number of people aged 65 and older is:



Again, as in Example C, the estimate and its MOE are we published in B09017. The total number of people aged 65 or older is 39,506,648 with a margin of error of 20,689. Therefore the standard error is:

The approximated standard error using the thirteen derived age group estimates yields a standard error roughly 8.2 times larger than the actual SE.
Data users can mitigate the problems shown in examples A through D to some extent by utilizing a collapsed version of a detailed table (if it is available) which will reduce the number of estimates used in the approximation. These issues may also be avoided by creating estimates and SEs using the Public Use Microdata Sample (PUMS) or by requesting a custom tabulation, a fee- based service offered under certain conditions by the Census Bureau. More information regarding custom tabulations may be found at http://www.census.gov/acs/www/data_documentation/custom_tabulations/.

The data contained in these data products are based on the Puerto Rico Community Survey (PRCS) sample interviewed from January 1, 2013 through December 31, 2013. The PRCS sample is selected from all municipios in Puerto Rico (PR). Data for Puerto Rico was first released in 2005. In 2006, the PRCS began collection of data from sampled persons in group quarters (GQs) – for example, military barracks, college dormitories, nursing homes, and correctional facilities. Persons in group quarters are included with persons in housing units (HUs) in all 2013 PRCS estimates that are based on the total population. All PRCS population estimates from years prior to 2006 include only persons in housing units. The PRCS, like any other statistical activity, is subject to error. The purpose of this documentation is to provide data users with a basic understanding of the PRCS sample design, estimation methodology, and accuracy of the PRCS data. The PRCS is sponsored by the U.S. Census Bureau, and is part of the Decennial Census Program.

Additional information on the design and methodology of the PRCS, including data collection and processing, can be found at:
http://www.census.gov/acs/www/methodology/methodology_main/.
The 2013 Accuracy of the Data for the United States can be found at:
http://www.census.gov/acs/www/Downloads/data_documentation/Accuracy/PRCS_Accuracy_of_Data_2013.pdf.

The estimates that appear in this product are obtained from a raking ratio estimation procedure that results in the assignment of two sets of weights: a weight to each sample person record and a weight to each sample housing unit record. Estimates of person characteristics are based on the person weight. Estimates of family, household, and housing unit characteristics are based on the housing unit weight. For any given tabulation area, a characteristic total is estimated by summing the weights assigned to the persons, households, families or housing units possessing the characteristic in the tabulation area. Each sample person or housing unit record is assigned exactly one weight to be used to produce estimates of all characteristics. For example, if the weight given to a sample person or housing unit has a value 40, all characteristics of that person or housing unit are tabulated with the weight of 40.
The weighting is conducted in two main operations: a group quarters person weighting operation which assigns weights to persons in group quarters, and a household person weighting operation which assigns weights both to housing units and to persons within housing units. The group quarters person weighting is conducted first and the household person weighting second. The household person weighting is dependent on the group quarters person weighting because estimates for total population, which include both group quarters and household population, are controlled to the Census Bureau's official 2012 total resident population estimates.

The Census Bureau has modified or suppressed some data on this site to protect confidentiality. Title 13 United States Code, Section 9, prohibits the Census Bureau from publishing results in which an individual's data can be identified.
The Census Bureau's internal Disclosure Review Board sets the confidentiality rules for all data releases. A checklist approach is used to ensure that all potential risks to the confidentiality of the data are considered and addressed.

• Title 13, United States Code: Title 13 of the United States Code authorizes the Census Bureau to conduct censuses and surveys. Section 9 of the same Title requires that any information collected from the public under the authority of Title 13 be maintained as confidential. Section 214 of Title 13 and Sections 3559 and 3571 of Title 18 of the United States Code provide for the imposition of penalties of up to five years in prison and up to $250,000 in fines for wrongful disclosure of confidential census information.
• Disclosure Avoidance: Disclosure avoidance is the process for protecting the confidentiality of data. A disclosure of data occurs when someone can use published statistical information to identify an individual that has provided information under a pledge of confidentiality. For data tabulations, the Census Bureau uses disclosure avoidance procedures to modify or remove the characteristics that put confidential information at risk for disclosure. Although it may appear that a table shows information about a specific individual, the Census Bureau has taken steps to disguise or suppress the original data while making sure the results are still useful. The techniques used by the Census Bureau to protect confidentiality in tabulations vary, depending on the type of data. All disclosure avoidance procedures are done prior to the whole person imputation into not-in-sample GQ facilities.
• Data Swapping: Data swapping is a method of disclosure avoidance designed to protect confidentiality in tables of frequency data (the number or percent of the population with certain characteristics). Data swapping is done by editing the source data or exchanging records for a sample of cases when creating a table. A sample of households is selected and matched on a set of selected key variables with households in neighboring geographic areas that have similar characteristics (such as the same number of adults and same number of children). Because the swap often occurs within a neighboring area, there is no effect on the marginal totals for the area or for totals that include data from multiple areas. Because of data swapping, users should not assume that tables with cells having a value of one or two reveal information about specific individuals. Data swapping procedures were first used in the 1990 Census, and were used again in Census 2000 and the 2010 Census.
• Synthetic Data: The goals of using synthetic data are the same as the goals of data swapping, namely to protect the confidentiality in tables of frequency data. Persons are identified as being at risk for disclosure based on certain characteristics. The synthetic data technique then models the values for another collection of characteristics to protect the confidentiality of that individual.

• Sampling Error - The data in the PRCS products are estimates of the actual figures that would have been obtained by interviewing the entire population using the same methodology. The estimates from the chosen sample also differ from other samples of housing units and persons within those housing units. Sampling error in data arises due to the use of probability sampling, which is necessary to ensure the integrity and representativeness of sample survey results. The implementation of statistical sampling procedures provides the basis for the statistical analysis of sample data. Measures used to estimate the sampling error are provided in the next section.
• Nonsampling Error - In addition to sampling error, data users should realize that other types of errors may be introduced during any of the various complex operations used to collect and process survey data. For example, operations such as data entry from questionnaires and editing may introduce error into the estimates. Another source is through the use of controls in the weighting. The controls are designed to mitigate the effects of systematic undercoverage of certain groups who are difficult to enumerate and to reduce the variance. The controls are based on the population estimates extrapolated from the previous census. Errors can be brought into the data if the extrapolation methods do not properly reflect the population. However, the potential risk from using the controls in the weighting process is offset by far greater benefits to the PRCS estimates. These benefits include reducing the effects of a larger coverage problem found in most surveys, including the PRCS, and the reduction of standard errors of PRCS estimates. These and other sources of error contribute to the nonsampling error component of the total error of survey estimates. Nonsampling errors may affect the data in two ways. Errors that are introduced randomly increase the variability of the data. Systematic errors which are consistent in one direction introduce bias into the results of a sample survey. The Census Bureau protects against the effect of systematic errors on survey estimates by conducting extensive research and evaluation programs on sampling techniques, questionnaire design, and data collection and processing procedures. In addition, an important goal of the PRCS is to minimize the amount of nonsampling error introduced through nonresponse for sample housing units. One way of accomplishing this is by following up on mail nonrespondents during the CATI and CAPI phases. For more information, see the section entitled "Control of Nonsampling Error".

Sampling error is the difference between an estimate based on a sample and the corresponding value that would be obtained if the estimate were based on the entire population (as from a census). Note that sample-based estimates will vary depending on the particular sample selected from the population. Measures of the magnitude of sampling error reflect the variation in the estimates over all possible samples that could have been selected from the population using the same sampling methodology.
Estimates of the magnitude of sampling errors - in the form of margins of error - are provided with all published PRCS data. The Census Bureau recommends that data users incorporate this information into their analyses, as sampling error in survey estimates could impact the conclusions drawn from the results.

Direct estimates of the margin of error were calculated for all estimates reported in this product. The standard errors, in most cases, are calculated using a replicate-based methodology known as successive difference replication that takes into account the sample design and estimation procedures.
The formula provided below calculates the variance using the PRCS estimate (X₀) and the 80 replicate estimates (X_r).

X₀ is the estimate calculated using the production weight and X_r is the estimate calculated using the r^th replicate weight. The standard error is the square root of the variance. The 90^th percent margin of error is 1.645 times the standard error.
For more information on the formation of the replicate weights, see chapter 12 of the Design and Methodology documentation at http://www.census.gov/acs/www/Downloads/survey_methodology/acs_design_methodology_ch12_2014.pdf.
Beginning with the PRCS 2011 1-year estimates, a new imputation-based methodology was incorporated into processing (see the description in the Group Quarters Person Weighting Section). An adjustment was made to the production replicate weight variance methodology to account for the non-negligible amount of additional variation being introduced by the new technique. ¹

Excluding the base weights, replicate weights were allowed to be negative in order to avoid underestimating the standard error. Exceptions include:

1. The estimate of the number or proportion of people, households, families, or housing units in a geographic area with a specific characteristic is zero. A special procedure is used to estimate the standard error.
2. There are either no sample observations available to compute an estimate or standard error of a median, an aggregate, a proportion, or some other ratio, or there are too few sample observations to compute a stable estimate of the standard error. The estimate is represented in the tables by "-" and the margin of error by "**" (two asterisks).
3. The estimate of a median falls in the lower open-ended interval or upper open-ended interval of a distribution. If the median occurs in the lowest interval, then a "-" follows the estimate, and if the median occurs in the upper interval, then a "+" follows the estimate. In both cases the margin of error is represented in the tables by "***" (three asterisks).
¹ For more information regarding this issue, see Asiala, M. and Castro, E. 2012. Developing Replicate Weight- Based Methods to Account for Imputation Variance in a Mass Imputation Application. In JSM proceedings, Section on Survey Research Methods, Alexandria, VA: American Statistical Association.

Significant differences - Users may conduct a statistical test to see if the difference between a PRCS estimate and any other chosen estimates is statistically significant at a given confidence level. "Statistically significant" means that the difference is not likely due to random chance alone. With the two estimates (Est₁ and Est₂) and their respective standard errors (SE₁ and SE₂), calculate a Z statistic:



If Z > 1.645 or Z < -1.645, then the difference can be said to be statistically significant at the 90 percent confidence level. Any estimate can be compared to a PRCS estimate using this method, including other PRCS estimates from the current year, the PRCS estimate for the same characteristic and geographic area but from a previous year, ACS estimates, 2010 Census counts, estimates from other Census Bureau surveys, and estimates from other sources. Not all estimates have sampling error - 2010 Census counts do not - but they should be used if they exist to give the most accurate result of the test.

Users are also cautioned to not rely on looking at whether confidence intervals for two estimates overlap or not to determine statistical significance, because there are circumstances where that method will not give the correct test result. If two confidence intervals do not overlap, then the estimates will be significantly different (i.e. the significance test will always agree). However, if two confidence intervals do overlap, then the estimates may or may not be significantly different. The Z calculation above is recommended in all cases.

Here is a simple example of why it is not recommended to use the overlapping confidence bounds rule of thumb as a substitute for a statistical test.

Let: X₁ = 6.0 with SE₁ = 0.5 and X₂ = 5.0 with SE₂ = 0.2.

The Lower Bound for X₁ = 6.0 - 0.5 x 1.645 = 5.2 while the Upper Bound for X₂ = 5.0 + 0.2 x 1.645 = 5.3. The confidence bounds overlap, so, the rule of thumb would indicate that the estimates are not significantly different at the 90% level.

However, if we apply the statistical significance test we obtain:



Z = 1.857 > 1.645 which means that the difference is significant (at the 90% level).

All statistical testing in PRCS data products is based on the 90 percent confidence level. Users should understand that all testing was done using unrounded estimates and standard errors, and it may not be possible to replicate test results using the rounded estimates and margins of error as published.

As mentioned earlier, sample data are subject to nonsampling error. This component of error could introduce serious bias into the data, and the total error could increase dramatically over that which would result purely from sampling. While it is impossible to completely eliminate nonsampling error from a survey operation, the Census Bureau attempts to control the sources of such error during the collection and processing operations. Described below are the primary sources of nonsampling error and the programs instituted for control of this error. The success of these programs, however, is contingent upon how well the instructions were carried out during the survey.

• Coverage Error

- It is possible for some sample housing units or persons to be missed entirely by the survey (undercoverage), but it is also possible for some sample housing units and persons to be counted more than once (overcoverage). Both the undercoverage and overcoverage of persons and housing units can introduce biases into the data, increase respondent burden and survey costs.
A major way to avoid coverage error in a survey is to ensure that its sampling frame, for Puerto Rico an address list in each municipio, is as complete and accurate as possible. The source of addresses for the PRCS is the MAF, which was created using the address list for Census 2000. An attempt is made to assign all appropriate geographic codes to each MAF address via an automated procedure using the Census Bureau TIGER (Topologically Integrated Geographic Encoding and Referencing) files. A manual coding operation based in the appropriate regional offices is attempted for addresses, which could not be automatically coded. The MAF was used as the source of addresses for selecting sample housing units and mailing questionnaires. TIGER produced the location maps for CAPI assignments. Sometimes the MAF has an address that is the duplicate of another address already on the MAF. This could occur when there is a slight difference in the address such as 123 Calle 1, Bayamon versus URB Hermosillo, 123 Calle 1, Bayamon.
In the CATI and CAPI nonresponse follow-up phases, efforts were made to minimize the chances that housing units that were not part of the sample were interviewed in place of units in sample by mistake. If a CATI interviewer called a mail nonresponse case and was not able to reach the exact address, no interview was conducted and the case was eligible for CAPI. During CAPI follow-up, the interviewer had to locate the exact address for each sample housing unit. If the interviewer could not locate the exact sample unit in a multi-unit structure, or found a different number of units than expected, the interviewers were instructed to list the units in the building and follow a specific procedure to select a replacement sample unit. Person overcoverage can occur when an individual is included as a member of a housing unit but does not meet PRCS residency rules.
Coverage rates give a measure of undercoverage or overcoverage of persons or housing units in a given geographic area. Rates below 100 percent indicate undercoverage, while rates above 100 percent indicate overcoverage. Coverage rates are released concurrent with the release of estimates on American FactFinder in the B98 series of detailed tables. Further information about PRCS coverage rates may be found at http://www.census.gov/acs/www/methodology/sample_size_and_data_quality/

• Nonresponse Error

- Survey nonresponse is a well-known source of nonsampling error. There are two types of nonresponse error - unit nonresponse and item nonresponse. Nonresponse errors affect survey estimates to varying levels depending on amount of nonresponse and the extent to which nonrespondents differ from respondents on the characteristics measured by the survey. The exact amount of nonresponse error or bias on an estimate is almost never known. Therefore, survey researchers generally rely on proxy measures, such as the nonresponse rate, to indicate the potential for nonresponse error.
- Unit Nonresponse - Unit nonresponse is the failure to obtain data from housing units in the sample. Unit nonresponse may occur because households are unwilling or unable to participate, or because an interviewer is unable to make contact with a housing unit. Unit nonresponse is problematic when there are systematic or variable differences between interviewed and noninterviewed housing units on the characteristics measured by the survey. Nonresponse bias is introduced into an estimate when differences are systematic, while nonresponse error for an estimate evolves from variable differences between interviewed and noninterviewed households.
The PRCS made every effort to minimize unit nonresponse, and thus, the potential for nonresponse error. First, the PRCS used a combination of mail, CATI, and CAPI data collection modes to maximize response. The mail phase included a series of three to four mailings to encourage housing units to return the questionnaire. Subsequently, mail nonrespondents (for which phone numbers are available) were contacted by CATI for an interview. Finally, a subsample of the mail and telephone nonrespondents was contacted for by personal visit to attempt an interview
PRCS response rates measure the percent of units with a completed interview. The higher the response rate, and consequently the lower the nonresponse rate, the less chance estimates may be affected by nonresponse bias. Response and nonresponse rates, as well as rates for specific types of nonresponse, are released concurrent with the release of estimates on American Factfinder in the B98 series of detailed tables. Further information about response and nonresponse rates may be found at http://www.census.gov/acs/www/methodology/sample_size_and_data_quality/.

- Item Nonresponse - Nonresponse to particular questions on the survey questionnaire and instrument allows for the introduction of error or bias into the data, since the characteristics of the nonrespondents have not been observed and may differ from those reported by respondents. As a result, any imputation procedure using respondent data may not completely reflect this difference either at the elemental level (individual person or housing unit) or on average.

Some protection against the introduction of large errors or biases is afforded by minimizing nonresponse. In the PRCS, item nonresponse for the CATI and CAPI operations was minimized by the requirement that the automated instrument receive a response to each question before the next one could be asked. Questionnaires returned by mail were edited for completeness and acceptability. They were reviewed by computer for content omissions and population coverage. If necessary, a telephone follow-up was made to obtain missing information. Potential coverage errors were included in this follow-up.
Allocation tables provide the weighted estimate of persons or housing units for which a value was imputed, as well as the total estimate of persons or housing units that were eligible to answer the question. The smaller the number of imputed responses, the lower the chance that the item nonresponse is contributing a bias to the estimates. Allocation tables are released concurrent with the release of estimates on American Factfinder in the B99 series of detailed tables with the overall allocation rates across all person and housing unit characteristics in the B98 series of detailed tables. Additional information on item nonresponse and allocations can be found at http://www.census.gov/acs/www/methodology/sample_size_and_data_quality/.

• Measurement and Processing Error

- The person completing the questionnaire or responding to the questions posed by an interviewer could serve as a source of error, although the questions were cognitively tested for phrasing, and detailed instructions for completing the questionnaire were provided to each household.
- Interviewer monitoring - The interviewer may misinterpret or otherwise incorrectly enter information given by a respondent; may fail to collect some of the information for a person or household; or may collect data for households that were not designated as part of the sample. To control these problems, the work of interviewers was monitored carefully. Field staff were prepared for their tasks by using specially developed training packages that included hands-on experience in using survey materials. A sample of the households interviewed by CAPI interviewers was reinterviewed to control for the possibility that interviewers may have fabricated data.
- Processing Error - The many phases involved in processing the survey data represent potential sources for the introduction of nonsampling error. The processing of the survey questionnaires includes the keying of data from completed questionnaires, automated clerical review, follow-up by telephone, manual coding of write-in responses, and automated data processing. The various field, coding and computer operations undergo a number of quality control checks to insure their accurate application.

- Content Editing - After data collection was completed, any remaining incomplete or inconsistent information was imputed during the final content edit of the collected data. Imputations, or computer assignments of acceptable codes in place of unacceptable entries or blanks, were needed most often when an entry for a given item was missing or when the information reported for a person or housing unit on that item was inconsistent with other information for that same person or housing unit. As in other surveys and previous censuses, the general procedure for changing unacceptable entries was to allocate an entry for a person or housing unit that was consistent with entries for persons or housing units with similar characteristics. Imputing acceptable values in place of blanks or unacceptable entries enhances the usefulness of the data.

Several examples are provided here to demonstrate how different the approximated standard errors of sums can be compared to those derived and published with PRCS microdata. ACS data is used in the examples. However they are applicable to PRCS data as well.
A. Suppose we wish to estimate the total number of males with income below the poverty level in the past 12 months using both state and PUMA level estimates for the state of Wyoming. Part of the collapsed table C17001 is displayed below with estimates and their margins of error in parentheses.
Table A: 2009 Estimates of Males with Income Below Poverty from table C17001: Poverty Status in the Past 12 Months by Sex by Age

Characteristic	Wyoming	PUMA 00100	PUMA 00200	PUMA 00300	PUMA 00400
Male	23,001 (3,309)	5,264 (1,624)	6,508 (1,395)	4,364 (1,026)	6,865 (1,909)
Under 18 Years Old	8,479 (1,874)	2,041 (920)	2,222 (778)	1,999 (750)	2,217 (1,192)
18 to 64 Years Old	12,976 (2,076)	3,004 (1,049)	3,725 (935)	2,050 (635)	4,197 (1,134)
65 Years and Older	1546 (500)	219 (237)	561 (286)	315 (173)	451 (302)
2009 American FactFinder

The first way is to sum the three age groups for Wyoming:
Estimate(Male) = 8,479 + 12,976 + 1,546 = 23,001.
The first approximation for the standard error in this case gives us:

A second way is to sum the four PUMA estimates for Male to obtain:
Estimate(Male) = 5,264 + 6,508 + 4,364 + 6,865 = 23,001 as before.
The second approximation for the standard error yields:


Finally, we can sum up all three age groups for all four PUMAs to obtain an estimate based on a total of twelve estimates:
Estimate(Male) = 2,041 + 2,222 + ... + 451 = 23,001
And the third approximated standard error is

However, we do know that the standard error using the published MOE is 3,309 /1.645 = 2,011.6. In this instance, all of the approximations under-estimate the published standard error and should be used with caution.
B. Suppose we wish to estimate the total number of males at the national level using age and citizenship status. The relevant data from table B05003 is displayed in table B below.
Table B: 2009 Estimates of males from B05003: Sex by Age by Citizenship Status

Characteristic	Estimate	MOE
Male	151,375,321	27,279
Under 18 Years	38,146,514	24,365
Native	36,747,407	31,397
Foreign Born	1,399,107	20,177
Naturalized U.S. Citizen	268,445	10,289
Not a U.S. Citizen	1,130,662	20,228
18 Years and Older	113,228,807	23,525
Native	95,384,433	70,210
Foreign Born	17,844,374	59,750
Naturalized U.S. Citizen	7,507,308	39,658
Not a U.S. Citizen	10,337,066	65,533
2009 American FactFinder

The estimate and its MOE are actually published. However, if they were not available in the tables, one way of obtaining them would be to add together the number of males under 18 and over 18 to get:
Estimate (Male) = 38,146,514+ 113,223,807 = 151,375,321
And the first approximated standard error is



Another way would be to add up the estimates for the three subcategories (Native, and the two subcategories for Foreign Born: Naturalized U.S. Citizen, and Not a U.S. Citizen), for males under and over 18 years of age. From these six estimates we obtain:



With a second approximated standard error of:



We do know that the standard error using the published margin of error is 27,279 / 1.645 = 16,583.0. With a quick glance, we can see that the ratio of the standard error of the first method to the published-based standard error yields 1.24; an over-estimate of roughly 24%, whereas the second method yields a ratio of 4.07 or an over-estimate of 307%. This is an example of what could happen to the approximate SE when the sum involves a controlled estimate. In this case, it is sex by age.
C. Suppose we are interested in the total number of people aged 65 or older and its standard error. Table C shows some of the estimates for the national level from table B01001 (the estimates in gray were derived for the purpose of this example only).

Table C: Some Estimates from AFF Table B01001: Sex by Age for 2009

Age Category	Estimate, Male	MOE, Male	Estimate, Female	MOE, Female	Total	Estimated MOE, Total
65 and 66 years old	2,492,871	20,194	2,803,516	23,327	5,296,387	30,854
67 to 69 years old	3,029,709	18,280	3,483,447	24,287	6,513,225	30,398
70 to 74 years old	4,088,428	21,588	4,927,666	26,867	9,016,094	34,466
75 to 79 years old	3,168,175	19,097	4,204,401	23,024	7,372,576	29,913
80 to 84 years old	2,258,021	17,716	3,538,869	25,423	5,796,890	30,987
85 years and older	1,743,971	17,991	3,767,574	19,294	5,511,545	26,381
Total	16,781,175	NA	22,725,473	NA	39,506,648	74,932
2009 American FactFinder

To begin we find the total number of people aged 65 and over by simply adding the totals for males and females to get 16,781,175 + 22,725,542 = 39,506,717. One way we could use is summing males and female for each age category and then using their MOEs to approximate the standard error for the total number of people over 65.

... etc. ...

Now, we calculate for the number of people aged 65 or older to be 39,506,648 using the six derived estimates and approximate the standard error:

For this example the estimate and its MOE are published in table B09017. The total number of people aged 65 or older is 39,506,648 with a margin of error of 20,689. Therefore the published- based standard error is:

SE(39,506,643) = 20,689/1.645 = 12,577.
The approximated standard error, using six derived age group estimates, yields an approximated standard error roughly 3.6 times larger than the published-based standard error.
As a note, there are two additional ways to approximate the standard error of people aged 65 and over in addition to the way used above. The first is to find the published MOEs for the males age 65 and older and of females aged 65 and older separately and then combine to find the approximate standard error for the total. The second is to use all twelve of the published estimates together, that is, all estimates from the male age categories and female age categories, to create the SE for people aged 65 and older. However, in this particular example, the results from all three ways are the same. So no matter which way you use, you will obtain the same approximation for the SE. This is different from the results seen in example A.
D. For an alternative to approximating the standard error for people 65 years and older seen in part C, we could find the estimate and its SE by summing all of the estimate for the ages less than 65 years old and subtracting them from the estimate for the total population. Due to the large number of estimates, Table D does not show all of the age groups. In addition, the estimates in part of the table shaded gray were derived for the purposes of this example only and cannot be found in base table B01001.

Table D: Some Estimates from AFF Table B01001: Sex by Age for 2009:

Age Category	Estimate, Male	MOE, Male	Estimate, Female	MOE, Female	Total	Estimated MOE, Total
Total Population	151,375,321	27,279	155,631,235	27,280	307,006,556	38,579
Under 5 years	10,853,263	15,661	10,355,944	14,707	21,209,207	21,484
5 to 9 years old	10,273,948	43,555	9,850,065	42,194	20,124,013	60,641
10 to 14 years old	10,532,166	40,051	9,985,327	39,921	20,517,493	56,549
...	...	...	...	...
62 to 64 years old	4,282,178	25,636	4,669,376	28,769	8,951,554	38,534
Total for Age 0 to 64 years old	134,594,146	117,166	132,905,762	117,637	267,499,908	166,031
Total for Age 65 years and older	16,781,175	120,300	22,725,473	120,758	39,506,648	170,454
2009 American FactFinder

An estimate for the number of people age 65 and older is equal to the total population minus the population between the ages of zero and 64 years old:
Number of people aged 65 and older: 307,006,556 - 267,499,908 = 39,506,648.
The way to approximate the SE is the same as in part C. First we will sum male and female estimates across each age category and then approximate the MOEs. We will use that information to approximate the standard error for our estimate of interest:

... etc. ...
And the SE for the total number of people aged 65 and older is:



Again, as in Example C, the estimate and its MOE are we published in B09017. The total number of people aged 65 or older is 39,506,648 with a margin of error of 20,689. Therefore the standard error is:
SE(39,506,648) = 20,689 / 1.645 = 12,577.
The approximated standard error using the thirteen derived age group estimates yields a standard error roughly 8.2 times larger than the actual SE.
Data users can mitigate the problems shown in examples A through D to some extent by utilizing a collapsed version of a detailed table (if it is available) which will reduce the number of estimates used in the approximation. These issues may also be avoided by creating estimates and SEs using the Public Use Microdata Sample (PUMS) or by requesting a custom tabulation, a fee- based service offered under certain conditions by the Census Bureau. More information regarding custom tabulations may be found at http://www.census.gov/acs/www/data_documentation/custom_tabulations/.