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Technical Document
ACS Overview
The American Community Survey is an integral part of the Census Bureaus revised Decennial Census program. It is intended to replace the Decennial Census long form and provide users with more current estimates on a yearly basis as opposed to once every ten years. Approximately three million households across the United States in every county will be surveyed each year and the topics covered will reflect those covered by the Census 2000 long form. However, the ACS will require five years of data collection to approach the accuracy and size of the data previously collected from the Decennial Census long form which was an approximate 1 in 6 sample of all households.
2005 is the first year of full-implementation of the ACS with data available for geographies with populations of at least 65,000 persons. In 2008, three year estimates (2005-2007) will be available for geographies with populations of at least 20,000. Starting in 2010, five year estimates (2005-2009) will be available for geographies down to the census tract and block-group level. These one-year, three-year, and five-year estimates will be continually updated each subsequent year.
Sampling Error
As is the case with any population sample, the 2005 ACS is subject to both sampling and non-sampling error. This was also the case with the larger 2000 Census long form sample, but no specific measure of accuracy was provided with the long form estimates. However, the Census Bureau is now providing margins of error with each published ACS estimate to help assess the accuracy of estimates. The margin of error defines an interval of values about an estimate in which the true population value may reside with a given amount of certainty. Adding and subtracting the margins of error from the estimate produce a confidence interval which is defined by a specified level of confidence. The Census Bureau has chosen a 90% confidence level. The confidence level refers to the percentage of all confidence intervals that would capture the true population value if all possible samples and their respective estimates could be calculated. All published estimates are accompanied by a +/- margin of error at the 90% confidence level. However, margins of error, which are large relative to their estimate should warrant some caution, as this implies less precision in the estimate itself.
Users of the ACS data should also recognize that non-sampling error may also be present in the estimates. Non-sampling error results from errors committed during the collection and/or processing of the survey data. Although these forms of error can not be quantified, it should be recognized that they may be present in the data and that margins of error might in fact be slightly larger if non-sampling error could be integrated.
2005 ACS PUMS File
In addition to the published 2005 ACS estimates and errors, the Census Bureau provides a person records file and household records file from which custom analyses can be conducted which are not available through the published ACS tables. These two files, known as Public Use Microdata Sample (PUMS) Files, are based on a sub-sample of the complete ACS sample and are representative of about 1% of the Nations households. The person records file consists of 2,913,796 person records while the household file consists of 1,259,653 household records. Each record within these two files is assigned a weight value consistent with the sampling structure of the ACS sample and PUMS sub-sample. Total estimated numbers of persons (or households) possessing a specific characteristic are simply calculated by summing all record weights for all cases possessing the characteristic of interest. The person and household weights must always be used when calculating estimates from these PUMS files.
CONFIDENTIALITY
The Census Bureau has implemented disclosure avoidance methods and confidentiality edits within the PUMS files to protect the identities of individual persons and households. Some of these techniques include limiting geographic detail, data swapping, top-coding, age perturbation, and collapsing of detail within categorical variables.
Geographic detail is limited to the nation, states, and 5% Public Use Microdata Areas (PUMAs). PUMAs are sub-state regions with a population of about 100,000 persons and are the smallest geographic region defined in the 2005 ACS PUMS file. These PUMA regions are consistent with the PUMA regions defined for use with the 2000 Census PUMS files.
Data swapping involves the matching of person records based upon a selected number of primary characteristics and swapping their data in such a way as to preserve the accuracy and usefulness of the data while improving confidentiality.
Top-coding is a technique where a maximum value for a given variable is defined based on the distribution of values within the variable itself. Any values greater than the defined top-code are assigned the top code value itself. This helps eliminate outlier records that might be suspect to identification.
Age perturbation is the modification of person ages within a given household. This is primarily used for larger households where the age break-out of the occupying persons might be unique to the household size itself.
Detailed categorical variables are limited to categorical break-outs where minimum population threshold standards defined by the Census Bureau are met.
2005 ACS PUMS Accuracy and Error Calculations
The ACS PUMS file allows for calculating custom person and household estimates that are not available within the published ACS estimates. However, particular attention must be given to the accuracy of estimates when using these data. Detailed breakouts of chosen variables can result in small numbers of cases and thus non-representative and imprecise estimates. Standard errors must be calculated for all estimates and used to derive appropriate margins of error to help assess statistical accuracy. The Census Bureau provides 2005 ACS PUMS users with two major tools for calculating standard errors. One method incorporates the use of replicate weights while the other requires the use of design factor coefficients. Using replicate weights to approximate standard errors is generally more accurate, and this is the method employed by the Census Bureau to calculate errors for the 2005 ACS published estimates. However, either method can be used to approximate standard errors. It should be noted that there will be some difference in the errors calculated from these two methods and that both techniques become problematic when calculating errors in mass quantities, as in the case of estimates calculated for all 50 states by age, race/ethnicity, and/or education level.
Each person and household case in the PUMS file is assigned 80 replicate weights consistent with the ACS and PUMS sample design in addition to the primary weight used to calculate the actual estimates from the file. These replicate weights are used to calculate 80 replicate estimates which are combined in a single formula with the primary estimate to calculate the standard error. The advantage here is that one formula is used to calculate the standard error. The disadvantage is the enormous amount of computer time needed to calculate 80 replicate estimates in addition to the primary estimate from a file with nearly 3,000,000 person cases. This becomes even more time consuming when calculating multi-layered estimates (by race/ethnicity, education levels, age, etc) for all 50 states, the District of Columbia, and the United States. Custom templates must be generated to help facilitate the calculation of standard errors from the 80 replicate estimates. Once the standard errors are obtained, their respective margins of error can be calculated at the chosen confidence level. If we assign the standard error itself as the margin of error, this results in a confidence level of 68% (approximately 68% of all intervals calculated from all possible PUMS samples spanning one standard error below the estimate to one standard error above the estimate would contain the average estimate calculated from all possible samples). However, this is generally not an acceptable level of confidence. To obtain margins of error at the 90% confidence level, we must multiply the standard errors in all cases by 1.65 (approximately 90% of all intervals calculated from all possible PUMS samples spanning 1.65 times the standard error below the estimate to 1.65 times the standard error above the estimate would contain the average estimate calculated from all possible samples). Calculating margins of error with lower confidence levels results in tighter intervals about the estimate, but the odds of the calculated interval actually capturing the average value of all possible samples are not as good. Calculating margins of error above the 90% level increases the chances of the calculated interval capturing the average value of all possible samples, but the intervals can become so large as to lose their usefulness. The 90% confidence level is a nice compromise.
The second option available to calculate standard errors is the use of design factors. Design Factors are coefficients published by the Census Bureau which reflect the characteristics and estimation procedures of the actual PUMS and ACS sample design. These data are published for each state, the nation, and Puerto Rico for all subjects covered in the PUMS file. Design Factors can be used to estimate standard errors for most estimates calculated from the PUMS file. This method is generally not as accurate as the replicate weights method, but the computer time needed to run the necessary data is not so large. However, there are multiple formulas and steps that must be applied to calculate the standard errors. The computer time saved is offset by the awkward process that must be employed. Depending upon the estimate being calculated, one must select the proper formula(s) to employ, the appropriate design factors published for each state and the nation, and calculate the sum of the respective person weights from the PUMS file. Again, a template must be set up to help speed the calculation process, but the appropriate published design factors must still be keyed manually (as they vary for each state and subject) and a custom template set up for each different variable.
Whenever possible, we will use the replicate weights method to calculate standard errors for estimates calculated from the PUMS file. It should be noted that in some cases, it is more appropriate to use the design factor method to generate standard errors. In the case of median earnings by state and education level, some standard errors calculate to zero (all replicate estimates are identical to the primary estimate resulting in no variance among the replicate estimates and primary estimate). This can happen when calculating median earnings from the PUMS file due to the rounding of earnings that the Census Bureau employs and the very small errors that would result anyway using exact earnings figures and more precise calculation methods. Using design factors for these cases will result in non-zero estimates of the standard errors.
Statistical Significance
Margins of error are useful when assessing the precision of an estimate, but they can also be useful when comparing one estimate to another. Of particular importance here are comparisons of estimates between states. A 50 state picture on a specific measure ranking states from high to low can show us the relative positions of states with respect to their estimates. However, caution should be taken when sizeable errors are present in combination with small dispersion among estimates. In these cases, the picture might look considerably different if we could plot the true (but unknown) population values for each state against each other. Thus, it becomes important to consider the possibility that two or more estimates with differing estimates might not be statistically different at a given confidence level. A conservative way of checking whether two estimates are statistically different is to calculate the difference between the two estimates and compare this with the sum of their respective margins of error. If the difference in the estimates is greater than the sum of the two margins of error, then we conclude that that two estimates are statistically different at the given confidence level (see example 1 below). However, if the difference in the estimates is less than the sum of their respective margins of error, then we might conclude that the estimates are not statistically different when in fact they are. A more precise method of determining statistical significance is to compare the calculated difference in the two estimates with the calculated margin of error of the difference (see example 2 below). To do this, the standard errors for the two estimates must first be calculated. For 90% margins of error, the standard errors are obtained by dividing each margin of error by 1.65. Assuming the two estimates are not highly correlated, the standard error of the difference in the two estimates would be determined by calculating the square root of the sum of the squares of the two standard errors. In the case where the two estimates are correlated, a covariance term for the two estimates would have to be added to the sum of the squares of the two standard errors. The resulting standard error for the difference is then multiplied by 1.65 to obtain the 90% margin of error for the difference. The difference in the estimates is then compared with the margin of error of the difference. If the difference is less than the margin of error, then the two estimates are not statistically different at the 90% confidence level. If the difference is greater than the margin of error, then the two estimates are statistically different at the 90% confidence level.
Example 1: Consider median family income for states from the 2005 ACS published tables. Nevada has a median family income estimate of $57,079 with a 90% margin of error of +/- $1,062. Utah has median family income estimate of $54,595 with a 90% margin of error of +/- $1,039. The difference in Nevadas and Utahs median family income estimates is $57,079 - $54,595 = $2,484. The sum of their two respective 90% margins of error are $1,062 + $1,039 = $2,101. The difference in Nevadas and Utahs median family income estimate ($2,484) is greater than the sum of their 90% margins of error ($2,101). Thus, we can conclude that the median family income estimates for Nevada and Utah are statistically different at the 90% confidence level.
Example 2: Consider median family income for states from the 2005 ACS published tables. Michigan has a median family income estimate of $57,277 with a 90% margin of error of +/- $519. Wyoming has median family income estimate of $55,343 with a 90% margin of error of +/- $1,549. The difference in Michigans and Wyomings median family income estimates is $57,277 - $55,343 = $1,934. The sum of their two respective 90% margins of error are $519 + $1,549 = $2,068. The difference in Michigans and Wyomings median family income estimate ($1,934) is less than the sum of their 90% margins of error ($2,068). We might conclude here that there is no statistical difference in the median family income estimates for Michigan and Wyoming. However, we must use a more precise method to be sure. We will compare the difference in the two estimates with the calculated margin of error of the difference. From the previous calculations, we know the difference in the median family income estimates for Michigan and Wyoming is $1,934. To obtain the margin of error for this difference, we must first calculate the standard errors for Michigan and Wyoming. The standard error for Michigan = 90% margin of error divided by 1.65 = $519/1.65 = $315, and the standard error for Wyoming = 90% margin of error divided by 1.65 = $1,549/1.65 = $939. Thus, the standard error for the difference in median family income = square root of ((Michigan standard error squared) + (Wyoming standard error squared)) = square root of (($315 squared) + ($939 squared)) = square root of ($980946) = $990. The 90% margin of error for the difference = $990 multiplied by 1.65 = $1,634. Since the difference in the median family income estimates for Michigan and Wyoming ($1,934) is larger than the calculated 90% margin of error of the difference ($1,634), we conclude that the median family incomes for Michigan and Wyoming are statistically different at the 90% confidence level. If the difference in the estimates had been less than the calculated margin of error for the difference, then we would conclude that there is no statistical difference in the two estimates.
Data Limitations and Decision Rule
It should be noted that there are limitations to the estimates that can accurately be generated from the 2005 ACS PUMS file. Complex variable breakouts (like migration by age and/or education attainment) can result in very small case numbers and thus very large standard errors. These errors can be so large that their corresponding estimates will not be statistically different from zero at the 90% confidence level. In these cases, the margin of error will be at least as large as the estimate itself. This break point is used by the Census Bureau as the basis for their primary ACS data release rule. They do not publish estimates for any given table and/or geography when more than half of the estimates are not statistically different from 0 at the 90% confidence level. We will use this same convention when posting estimates generated from the ACS PUMS file. In addition, we will omit any individual estimates which are not statistically different from 0. However, users of these data should exercise caution in cases where the margin of error is large relative to the estimate.
Sources
1. U.S. Census Bureau, PUMS Accuracy of the Data (2005)
2. U.S. Census Bureau, Using Data from the 2005 American Community Survey
3. U.S. Census Bureau, ACS 2005 User Notes
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