| Methodology Report #18: Updates to the Medical Expenditure Panel Survey Insurance Component List Sample Design, 2004 John P. Sommers, PhD, Agency for Healthcare Research and Quality. Abstract This report describes changes to the sample design for the Insurance Component of the Medical Expenditure Panel Survey. The paper provides the background of the original sample design and the conditions that now exist that allow for change in this design. The report then describes the new strata and sample allocation scheme for the private sector portion of the sample and how these changes were developed, the changes made in a method used to restrict sample for private sector employers to contain the burden for large employers, and the changes made in the allocation of the survey’s government sample. The estimates in this report are based on the most recent data available at the time the report was written. However, selected elements of MEPS data may be revised on the basis of additional analyses, which could result in slightly different estimates from those shown here. Please check the MEPS Web site for the most current file releases.
Center for Financing, Access, and Cost Trends The Medical Expenditure Panel Survey (MEPS) Background The Medical Expenditure Panel Survey (MEPS) is conducted to provide nationally representative estimates of health care use, expenditures, sources of payment, and insurance coverage for the U.S. civilian noninstitutionalized population. MEPS is cosponsored by the Agency for Healthcare Research and Quality (AHRQ), formerly the Agency for Health Care Policy and Research, and the National Center for Health Statistics (NCHS). MEPS comprises three component surveys: the Household Component (HC), the Medical Provider Component (MPC), and the Insurance Component (IC). The HC is the core survey, and it forms the basis for the MPC sample and part of the IC sample. Together these surveys yield comprehensive data that provide national estimates of the level and distribution of health care use and expenditures, support health services research, and can be used to assess health care policy implications. MEPS is the third in a series of national probability surveys conducted by AHRQ on the financing and use of medical care in the United States. The National Medical Care Expenditure Survey (NMCES) was conducted in 1977, the National Medical Expenditure Survey (NMES) in 1987. Beginning in 1996, MEPS continues this series with design enhancements and efficiencies that provide a more current data resource to capture the changing dynamics of the health care delivery and insurance system. The design efficiencies incorporated into MEPS are in accordance with the Department of Health and Human Services (DHHS) Survey Integration Plan of June 1995, which focused on consolidating DHHS surveys, achieving cost efficiencies, reducing respondent burden, and enhancing analytical capacities. To accommodate these goals, new MEPS design features include linkage with the National Health Interview Survey (NHIS), from which the sample for the MEPS-HC is drawn, and enhanced longitudinal data collection for core survey components. The MEPS-HC augments NHIS by selecting a sample of NHIS respondents, collecting additional data on their health care expenditures, and linking these data with additional information collected from the respondents’ medical providers, employers, and insurance providers. Household Component The MEPS-HC, a nationally representative survey of the U.S. civilian noninstitutionalized population, collects medical expenditure data at both the person and household levels. The HC collects detailed data on demographic characteristics, health conditions, health status, use of medical care services, charges and payments, access to care, satisfaction with care, health insurance coverage, income, and employment. The HC uses an overlapping panel design in which data are collected through a preliminary contact followed by a series of five rounds of interviews over a two and a half year period. Using computer-assisted personal interviewing (CAPI) technology, data on medical expenditures and use for two calendar years are collected from each household. This series of data collection rounds is launched each subsequent year on a new sample of households to provide overlapping panels of survey data and, when combined with other ongoing panels, will provide continuous and current estimates of health care expenditures. The sampling frame for the MEPS-HC is drawn from respondents to NHIS, conducted by NCHS. NHIS provides a nationally representative sample of the U.S. civilian noninstitutionalized population, with oversampling of Hispanics and blacks. Medical Provider Component The MEPS-MPC supplements and validates information on medical care events reported in the MEPS-HC by contacting medical providers and pharmacies identified by household respondents. The MPC sample includes all hospitals, hospital physicians, home health agencies, and pharmacies reported in the HC. Also included in the MPC are all office-based physicians:
The MPC is conducted through telephone interviews and mailed survey materials. Insurance Component The MEPS-IC collects data on health insurance plans obtained through private and public sector employers. Data obtained in the IC include the number and types of private insurance plans offered, benefits associated with these plans, premiums, contributions by employers and employees, and employer characteristics. Establishments participating in the MEPS-IC are selected through three sampling frames:
To provide an integrated picture of health insurance, data collected from the first sampling frame (employers and other insurance providers) are linked back to data provided by the MEPS-HC respondents. Data from the other three sampling frames are collected to provide annual national and State estimates of the supply of private health insurance available to American workers and to evaluate policy issues pertaining to health insurance. Since 2000, the Bureau of Economic Analysis has used national estimates of employer contributions to group health insurance from the MEPS-IC in the computation of Gross Domestic Product (GDP). The MEPS-IC is an annual panel survey. Data are collected from the selected organizations through a prescreening telephone interview, a mailed questionnaire, and a telephone follow-up for nonrespondents. Survey Management MEPS data are collected under the authority of the Public Health Service Act. They are edited and published in accordance with the confidentiality provisions of this act and the Privacy Act. NCHS provides consultation and technical assistance. As soon as data collection and editing are completed, the MEPS survey data are released to the public in staged releases of summary reports and microdata files. Summary reports are released as printed documents and electronic files. Microdata files are released on CD-ROM and/or as electronic files. Printed documents and CD-ROMs are available through the AHRQ Publications Clearinghouse. Write or call:
AHRQ Publications Clearinghouse To order online, send an e-mail to: ahrqpubs@ahrq.gov. Be sure to specify the AHRQ number of the document or CD-ROM you are requesting. Selected electronic files are available through the Internet on the MEPS Web site: http://www.meps.ahrq.gov/ For more information, visit the MEPS Web site or e-mail mepspd@ahrq.gov. The Insurance Component of the Medical Expenditure Panel Survey (MEPS-IC) is an annual national survey of business establishments (locations) and governments sponsored by the Agency for Healthcare Research and Quality (AHRQ) and conducted by the United States Census Bureau. The survey is designed to collect information on employer-sponsored health insurance, such as whether insurance is offered and if so, enrollments, premiums, employee contributions, and plan characteristics. Information about the establishment or government, such as size and workforce characteristics, are also collected to allow for modeling of results and estimation by different business or government characteristics. The MEPS-IC has two major purposes. The first is to collect information from employers of household respondents to the MEPS Household Component (HC), a household survey collecting information on health expenditures, use, insurance and demographics of the noninstitutionalized population of the United States. This sample of employers of the household respondents is known as the household sample (Cohen, 1996). These data are primarily used for modeling and are not collected annually. Instead, the data are collected on a periodic basis. The second purpose of the survey is to produce national- and state-level estimates of enrollments, premiums, and contributions for a variety of categories, such as industry, firm size, and average payroll per employee. This requires a random sample of business locations and governments, which for the MEPS-IC is referred to as the list sample, because it is selected from lists maintained by the Census Bureau. The original list sample, designed for the first MEPS-IC used for collection of data for the year 1996 (years in this document will always refer to the year of the data, not year of collection; collection of data crosses years), supported estimates for the 40 largest states and the nation as a whole. However, in subsequent years, sample sizes for the 20 smallest states were changed annually so that, although there were published estimates for only 40 states in a given year, all 50 states and the District of Columbia would have state-level estimates at least once every four years (MEPS Insurance Component: Technical Notes and Survey Documentation). The original list sample design and allocation (Sommers, 1999) considered governments and private sectors together in order to yield allocations that produced estimates with a desired level of error at the state and national level for the entire set of employers, both public and private sectors. This basic design, which was used with little change through the 2002 survey, will be called the old, original, or current design within this document. The updated design, which will be completely in place for the 2004 survey, will be called the new design. After the original allocation took place, the sample was then allocated within each state between the public and private sectors based upon each sector’s proportion of total state employment. Within each sector, these allocations were further allocated to individual strata. This design allowed for sufficient sample in the largest states to support national and state estimates, while smaller states below a certain size had minimum sample sizes assigned. These minimum sample sizes were generally much larger than the sample otherwise required to support reliable national estimates. However, the minimum sample sizes were required to support estimates for the individual states. Within each state, strata were formed based upon employment sizes, and sequential sample selection methods were used to select the final samples. Because the public and private sector lists of employers were maintained on two different lists, sampling for public and private sectors was done separately once allocations were determined. A unique feature of the MEPS-IC list sample is a restriction on the expected numbers of establishments in the sample for a private sector firm. (A firm is an entity that controls one or more business establishments or locations; for instance, General Motors is a firm and an individual General Motors plant location is an establishment.) The reason for this restriction was to limit the amount of collection burden on an individual firm, since most firms require collection of information for all their establishments at a central location. Because the MEPS-IC required collection of both the household and list samples of establishments and the sample of establishments in the household sample was predetermined, the restriction on firm size took place only on the list sample and was very strict. This restriction significantly raises the design effect of the list sample estimates. (Sommers, 1999 and Kish, 1965) New Conditions and Information That Allow Updating the Sample Design Considerable knowledge has been gained since the 1996 MEPS-IC that can be used to improve the sample design. During the same time period, operational conditions of the survey have changed. These changes in operational climate also allow implementation of methods that can improve the sample design. Following are the key new factors that support improvement in the sample design of the survey:
Combinations of these items have motivated the following changes to the sample design:
The following sections discuss specific changes in the MEPS-IC sample design that will result in an updated design by the year 2004. Included are descriptions of the changes, how they were developed and the improvements in sampling errors that are expected as a result of these changes. Allocation to States: Private Sector Allocation of private sector sample to states for the new design was done in a manner similar to the allocation of total sample, government and private sector, for previous surveys. First, the proportions of national payroll, employment, and number of establishments were calculated for each state. For each state, these proportions were averaged to give an average proportion across the three items. Using these average proportions, 17,000 responding sample units were allocated proportionally to the states. Any state with fewer than 560 units then had its allocation increased to 560 units. (Note that in the samples prior to 2003, each state was allocated a responding sample of 600, but this included governments. This new allocation is for the private sector only and thus has a smaller minimum sample size than the old allocation. [Sommers, 1999] ) This initial sample allocation could not be afforded under the IC budget. To reduce costs, the expected responding sample size for the smallest 11 states was reduced to 520. This new allocation should give national results at least comparable to the current sample if no other changes were made. For instance, the relative standard error for estimates of the percentage of establishments that offer health insurance and the average single premium would both be about 0.5 percent. The slight reduction in sample for the smallest states would still allow the survey to meet this goal, since the larger sample in these states has little effect on national estimates due to the very small portion of the nation that these states represent. Assuming the same variance structure within each state, the overall sampling of states in this manner, with the resulting unequal weighting, creates a 20 percent increase in standard errors for national estimates compared to a proportional allocation with equal weights. Note that for the current sample (Sommers, 1999), where only 40 states had a minimum sample size, there was only a 10 percent increase in standard errors in national estimates due to the over sampling. However, the overall sample size was smaller. This increase in sample size offsets the extra inefficiency caused by the increase in over sampling of small states. With the extra sample, if no other changes were made to the sample design except for the change in allocations to the states, the errors for national estimates would be very comparable for both allocations. The new allocations to states are presented in Appendix A. Allocation within States: Private Sector In order to reduce sampling error in IC estimates, new sampling strata were developed. The original strata boundaries were developed by Westat as part of the work done on the 1993 National Employer Health Insurance Survey, a precursor to the IC. These strata were based upon firm and establishment employment sizes (Marker, 1996). While employment sizes correlate well with such important variables as whether an establishment offers health insurance, the percentage of employees enrolled, and the average premiums and contributions towards health insurance made by employers and employees, over the years information that has been gathered has shown several other independent descriptive variables also correlated with these outcome variables. Among these variables are state, age of firm, industry, and average payroll of an establishment. AHRQ decided that these variables also should be considered in production of IC strata along with the important employment size variables. The old stratification of the IC sample was done by simply crossing categories of firm size and categories of establishment size to create 14 strata. However, due to the many cells that would be created by crossing the categories of six different variables, another method was needed to consider all the new variables in creating strata. Such a method was required to limit the number of strata used. The method chosen was to use the set of variables to create models that would predict the probability that an establishment would offer health insurance and the expected percentage of employees at the establishment that would enroll in insurance if offered. It was assumed that because the models were based upon a large number of variables, each of which correlated with the key variables, that the predicted values would correlate better with the final results than just the employment size classes alone. To test this hypotheses, three years of data were used, 1998–2000. Using 1999 data, logistic regressions were run, the first to model the probability that an establishment had health insurance and the second to model, for those with health insurance, the probability that an employee would enroll. The models were used to predict values for the entire frame for the 2000 survey year. Using the “cum square root f rule” (Cochran, 1977), the 2000 frame was broken into six strata based upon the establishment’s probability of offering insurance. After this was done, the three strata that contained establishments with the highest probabilities of offering health insurance were broken into substrata using the “cum square root f rule” applied to the expected number of enrollees in health insurance. The stratum that contained the establishments with highest probability of offering health insurance was broken into six substrata, the stratum that contained establishments with the second most likely chances of offering health insurance was broken into three substrata, and the stratum that contained establishments with the third highest probability of offering health insurance was broken into two substrata. The reason for the decreasing number of substrata was that as the probability of offering heath insurance decreases, the range of sizes of establishments in the strata based upon this probability decreases. Thus, the three strata with establishments that have the least likely chance of offering health insurance, consist of only small establishments that do not require substratification for the size of the potential enrollment. On the other hand, the expected number of enrollees varies considerably within the stratum with establishments with a high probability of offering health insurance. Breaking this stratum into substrata assures that the variance across the total enrollment within each substratum will be smaller, which is highly desirable. This created 14 strata of establishments for the year 2000 frame based upon 1999 data. Using the models based upon 1999 data, predictions were produced for the establishments on the frames for the year 1998 and 2000. Using each of these predictions, the establishments on these frames were placed into the 14 strata developed using 1999 models. The establishments in the samples from the years 1998 and 2000 were used to calculate estimates of variance components for each of the strata. Using these variance components and variance components calculated using the same data for the old strata, and counts from the 2000 frame, errors for a variety of allocations for the new and old strata could be evaluated using the following formula:
where
Estimates of standard errors were made for two variables: the total number of establishments offering health insurance and the total number of employees enrolled. These variables were chosen because they represent the two different types of estimates made with IC data. The first is driven by numbers of establishments. Such estimates are dominated by the large number of small establishments on the frame. The second is dominated by establishments with large employments and enrollments. The former requires a large sample of small establishments, and the latter requires that the sample be dominated by large establishments. These two opposite types of variables require a sampling strategy that in some way balances the sample between numbers of establishments and numbers of employees. Several methods have been recommended to accomplish this type of allocation (Cochran, 1977). One is to produce variance components for each stratum that are weighted averages of the variance components for each variable for the stratum. A second is to assign the allocation to the cell as a weighted average of the optimal allocations for the stratum for the individual variables. Another method, used for the 1993 National Employer Health Insurance Survey, a one-time survey with similar data needs as the IC, is to allocate sample to strata based upon the measure of size equal to the square root of the employment at each establishment. This allocation tends to balance enrollment and numbers of establishments. The results for several of the allocation tested are shown in Table 1.
The table demonstrates the following:
Given the possibilities for improvements, further research was undertaken to find an improved allocation given the proposed new strata definitions. As part of this process, another variable was added to the analysis: the total single employee contribution. This variable was added because AHRQ decided that many more estimates were being requested by users that related to employment than to numbers of establishments. Thus, it was decided to weight the new allocation more towards that type of variable. One of the results of this analysis was the development of a 15th stratum for the proposed new set of strata. This is a certainty stratum of approximately 200 of the largest establishments. Adding such a stratum to the new strata had a significant effect on results for the two variables correlated with employment. When added to the current stratification definitions, a certainty stratum had far less effect. After much analysis, a final allocation method was accepted that was a weighted average of 50 percent of the optimal allocation for estimates of the number of establishments that offer health insurance plus 25 percent each of the optimal allocations for the estimates of the total enrollment and total single contributions. The decision on the final allocation was based primarily upon the improvement in variance of the estimates compared with the current sample. However, some allocations that were slightly better than the final choice were rejected because of the percentage of the sample required from the largest firms. There was concern that extra burden on these respondents and the potential loss in response rate was not worth the risk compared with the slightly better forecasted errors from the allocations. Table 2 gives results for the final optimal allocation for the three analysis variables along with results for the current sample allocation and the chosen new allocation.
The first three rows of the table give the standard error that can be obtained with the optimal allocation for that variable with that stratification. No one allocation can reach the minimum value for all the variables. However, as one can see in the table, the proposed weighted allocation using the new strata gives standard errors that are close to the best possible values for each of the variables and better than the current allocation for the total number of establishments. The projected improvements in standard errors from the new stratification and allocation methods, shown in the fourth row, over the current methods shown in the fifth row, are 11 percent for total establishments offering health insurance, 58 percent for total enrollment, and 51 percent for total single employee contributions. Appendix B gives the overall percentages of the total establishments, total employment, enrollment, and sample for each of the 15 strata in the new sample design. Changes in Restrictions on Maximum Sample Size per Firm The IC list sample design contains a process that limits the total expected sample of establishments that can be selected from an individual firm. This was done to limit the burden on individual respondents. The total burden for the IC includes sample from the household sample and the list sample. The members of the household are predetermined in the sense that they are the employers of respondents to the household survey, and AHRQ cannot control this sample of employers. On the other hand, the list sample is designed by AHRQ and Census and selected by the Census. Thus, the expected sample for a firm within this sample can be controlled. Given that the total sample size for the private sector from the combined household and list samples is about 44,000 private sector establishments, if samples were selected proportional to firm’s share of total employment then, given a total employment of 110 million employees in the private sector, a company with over 100,000 employees could expect to have over 40 (44,000x100,000/110,000,000) establishments in the sample. To avoid these large samples, the sum of the probabilities of selection for establishments within the same firm were limited for the list sample. In order to maintain the same overall sample size, the probabilities of selection for establishments from smaller firms within the same strata must be increased so the total probabilities of selection within a stratum remain equal to the allocated sample size. This leads to the situation that, within a stratum, establishments with about the same expected values for variables, such as enrollment, can have different selection probabilities and thus different weights. This leads to an increase in the sampling error. Given that there was an opportunity to change this restriction on the sample design, an effort was first made to determine the effect of the current restrictions on sampling errors. To measure this effect, several types of design effects were calculated using SUDAAN, a specialized error estimation software for complex surveys. These estimates allow one to measure the effects on errors of the several different aspects of a sample design, stratification, clustering, over sampling, and unequal weighting (Research Triangle Park, 2002). Of particular interest to the current problem is the ability to measure the design effect of the sample design with and without unequal weighting. These effects were run for a variety of variables, such as total enrollment, average premiums and contributions, etc.. While the results varied by variable, in general the design effect that took into account unequal weighting within each stratum was twice that when this effect was removed. Thus to lower this effect could result in significant improvements in the overall errors for many variables. After considering the distribution of expected sample sizes per firm, before reduction, a new reduction method was developed that the Census Bureau believed would result in acceptable sample sizes per firm and would not place an unreasonable burden on firms nor the IC budget. The key difference in the two methods is that, under the old method, the maximum expected sample size for all but two large firms was 10 and some type of downward adjustment was used for any firm with an original expected sample size of two or more. The new method applies no adjustments to firms with expected sample size values less than three and allows for a maximum expected number of units of 50. Even with these lessened restrictions on the list sample, the actual burdens on firms when combined with dropping the household sample, are decreased overall. The two reduction methods are shown in Appendix C. To assess the possible improvement in sampling errors for this method, the following assessment was performed.
Within each stratum with N establishments in the IC, an independent sample of size n is
selected. Assuming that each establishment selected has a common mean
To compare the variance of this estimate with that of the one with equal probability of selection, we simply calculate the relative value of the variance of the unequal probability estimate to that of the equal probability of selection estimate by taking the ratio of the two variances:
To obtain a rough estimate of the differences in variances, the value of
Using the approach, the current method yields a value of 1.966n. The new method has a value of 1.218n. The relative magnitude of the two values is 1.61. Applying the square root to this value yields 1.27. Thus, for estimates for the firms with more than 1,000 employees, the new method of reduction has approximately 27 percent smaller standard error than similar estimates where the sample was selected using the old method of burden reduction. While the reduction method is only one of the reasons that weights are unequal, AHRQ believes that using the new method will result in significant reductions in standard errors for most national estimates and estimates made for the groups of firms above 1,000 employees. Government Sample Improvements In surveys prior to the 2003 IC, the sample of governments consisted of two parts, (1) a set of certainties that included all governments with more than 5,000 full-time equivalent employees and (2) a sample of smaller governments that was allocated so that governments in smaller states were over sampled relative to those in larger states. This happened because, using the old allocation method, the over sampling for smaller states was applied to both governments and private sector establishments. This was done because the goal was to produce quality estimates for the set of all employers in the state, public, and private sector combined. Once each state was given an overall allocation of private sector establishments and non-certainty governments, the state’s total allocation was broken proportional to the relative size of the private sector and noncertainty governments in each state. Because small states were over sampled relative to large states, then non-certainty governments were also over sampled relative to the same governments in large states. Assuming similar variances among non-certainty governments within each of the states, this over sampling would yield a less efficient sample for estimates at a larger geographic area, such as Census Regions, than a proportional allocation across all non-certainty government units within all states in the area. This over sampling was necessary if there was a demand for estimates for the combined public and private sector universe within each state. However, users have rarely requested an estimate of the combination of public and private sector employers. Users request estimates for the private sector only, and some have requested state estimates for governments only. By imposing a slightly lower minimum sample for each state for the private sector as was done in the state-level allocation discussed earlier in this paper, AHRQ assured that the former would be produced for all states with relatively good standard errors. Using the past combined allocation, the state estimates for governments could not be produced with a reasonable error rate except for the largest states, even with the over sample of non-certainty governments. Since, with the exception of very large states, good state estimates for the government sector are not possible with the over sampling of governments in smaller states, it was decided not to over sample any governments at the state level. Instead, the government sample for the non-certainty governments was redesigned as follows:
The first two items were part of the old government sample design for the IC from 1996 to 2002. The final allocation gives the same total national allocation for non-certainty governments as in past surveys. The totals within Census Divisions are also approximately equal to the past allocations at the Census Division level. However, within Census Divisions, the allocation for non-certainty governments is proportional to the government employment in each state. The effect of this change should be to improve the published estimates for each Census Division, since the allocation of the small sample size for each Census Division is now done optimally for each Census Division. This is because there is no over sampling within Census Divisions by state as before. The allocations are proportional to state size within Census Divisions. This increases the sample of the larger states that have the most government employment. Making better estimates for each Census Division also will improve national estimates for the government sector. This will also allow AHRQ to make better state-level estimates for the larger states where quality estimates are possible. In summary, several major changes are being implemented for the 2004 MEPS-IC sample:
Taken together, the IC will soon produce significantly better state and national estimates for the private sector, and there will be quality estimates for all states, rather than just 40 states. These improvements should occur for all variables and for estimates for all subnational and substate cells. There should also be improvements in estimates for the nation, Census Divisions, and the largest states for government results. Cochran WG. Sampling techniques. New York: John Wiley and Sons; 1977. Cohen S. Sample Design of the 1996 Medical Expenditure Panel Survey Household Component. Rockville(MD); Agency for Health Care Policy and Research; 1997. MEPS Methodology Report No. 2. AHCPR Pub No. 97-0027. Kish L. Survey sampling. New York: John Wiley and Sons; 1965. Marker D, Bryant E, Wallace L, Yansaneh L. National Employee Health Insurance Survey (NEHIS): Draft final methodology report, Volume I: Statistical Methodology. Rockville, (MD): Westat, Inc.: 1996. MEPS Insurance Component: Technical Notes and Survey Documentation. Agency for Healthcare Research and Quality, Rockville, MD. http://www.meps.ahrq.gov/mepsweb/survey_comp/ic_technical_notes.shtml Research Triangle Institute. SUDAAN User’s Manual, Release 8.0. Research Triangle Park, NC: Research Triangle Institute; 2002. Sommers JP. List sample design of the 1996 Medical Expenditure Panel Survey Insurance Component. Rockville (MD): Agency for Health Care Policy and Research; 1999. MEPS Methodology Report No. 6 Pub. No. 99-0037.
Appendix C. Methods for Reduction of Expected Sample for Private Sector Firms Current Method
New Method
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is the size of the stratum,
is the sample size for the hth stratum, and
is the variance within the hth stratum. Assuming that a typical state has a distribution of
establishments similar to that of the entire country, results could be produced for any
allocation using stratum sizes that are available from the frame and values of the
components of variance that were estimated using the sample data.
and the same variance
,
then if units are selected with equal probabilities the variance of an estimate
of a total for this variable is
.
In this case, the probability of selection of all
establishments is n/N. If instead, unequal probabilities pf selection are used and the
probability of selection for the ith establishment is written as
,
then the variance of the estimate is:
for the sample of all firms with more than 1,000 employees was calculated for each method.
This was done assuming that all the establishments were from the same strata and using
the actual values of the expected sample sizes before adjustment from the 2003 IC
sample. The two adjustment methods were applied to the expected samples for the
largest firms. This decreased the expected sample sizes and increased the weights for
these establishments. The expected sample sizes for remaining firms were adjusted
upwards so that the final expected overall sample size was the original value of n. This
then decreased the weights for these establishments. Although these are not the actual
final adjustments because each state has a different stratum for these firms and the strata
could have different values of