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The methodology for collecting information on new manufactured homes for 1974 through 1979 involved contacting a sample of manufactured home dealers each month within 137 geographic areas or primary sampling units. The dealers were requested to provide data on the number of manufactured homes received from manufacturers, the number placed on a site for residential use, and the number held in inventory.
The methodology used after 1979 involves a monthly sample of new manufactured homes shipped by manufacturers. The dealer to whom the sampled unit was shipped is contacted by telephone and asked about the status of the unit. This is done each month until that unit is reported as placed.
The various estimates shown in the tables are based on sample surveys and may differ from statistics that would have been obtained from a complete census using the same schedules and procedures. For a particular estimate, statisticians define this difference as the total error of the estimate. When describing the reliability of survey results, total error is defined as the sum of sampling error and nonsampling error. Sampling error is the error arising from the use of a sample, rather than a census, to estimate population values. Nonsampling error encompasses all other factors that contribute to the total error of a sample survey estimate. The sampling error of an estimate can usually be estimated from the sample, whereas the nonsampling error of an estimate is difficult to measure and can rarely be estimated. Consequently, the actual error in an estimate exceeds the error that can be estimated. Further descriptions of sampling error and nonsampling error are provided in the following sections. Data users should take into account the estimates of sampling error and the potential effects of nonsampling error when using the published estimates.
Sampling error reflects the fact that only a particular sample was surveyed rather than the entire population. Each sample selected for the MHS is one of a large number of similar probability samples that, by chance, might have been selected under the same specifications. Estimates derived from the different samples would differ from each other. The standard error(SE), or sampling error, of a survey estimate is a measure of the variation among the estimates from all possible samples and, thus, is a measure of the precision with which an estimate from a particular sample approximates the average from all possible samples.
Estimates of the standard errors have been computed from the sample data for selected statistics. They are presented in the form of relative standard errors. The relative standard error equals the standard error divided by the estimated value to which it refers.
The sample estimate and an estimate of its standard error allow us to construct interval estimates with prescribed confidence that the interval includes the average result of all possible samples with the same size and design. To illustrate, if all possible samples were surveyed under essentially the same conditions, and estimates calculated from each sample, then:
1. Approximately 68 percent of the intervals from one standard error below the estimate to one standard error above the estimate would include the average value of all possible samples.
2. Approximately 90 percent of the intervals from 1.645 standard errors below the estimate to 1.645 standard errors above the estimate would include the average value of all possible samples.
Thus, for a particular sample, one can say with specified confidence that the average of all possible samples is included in the constructed interval.
For example, suppose that an estimated 30,000 manufactured homes were placed in a particular month and that the average relative standard error of this estimate is 4 percent. Multiplying 30,000 by .04, we obtain 1,200 as the standard error. This means that we are confident, with 68% chance of being correct, that the average estimate from all possible samples of manufactured homes placed during the particular month is between 28,800 and 31,200 homes. To increase the probability to a 90% chance that the interval contains the average value over all possible samples (this is called a 90-percent confidence interval), multiply 1,200 by 1.645, yielding limits of 28,026 and 31,974 (30,000 units plus or minus 1,974 units). The average estimate of manufactured homes placed during the specified month may or may not be contained in any one of these computed intervals; but for a particular sample, one can say that the average estimate from all possible samples is included in the constructed interval with a specified confidence of 90 percent. It is important to note that the standard error and the relative standard error only measure sampling variability. They do not measure any systematic nonsampling errors in the estimates.
Nonsampling error encompasses all other factors, other than sampling
error, that contribute to the total error of a sample survey estimate
and may also occur in censuses. It is often helpful to think of
nonsampling error as arising from deficiencies or mistakes in the
survey process. Nonsampling errors are usually attributed to many
possible sources: (1) coverage error - failure to accurately represent
all population units in the sample, (2) inability to obtain information
about all sample cases, (3) response errors, possibly due to definitional
difficulties or misreporting, (4) mistakes in recording or coding
the data obtained, and (5) other errors of coverage, collection
and nonresponse, response, processing, or imputing for missing or
inconsistent data. Although nonsampling error is not measured directly,
the Census Bureau employs quality control procedures throughout
the process to minimize this type of error.
For analyzing general trends in the economy, seasonally adjusted data are usually preferred since seasonal adjustment eliminates the effect of changes that normally occur at about the same time and in about the same magnitude every year. For example, suppose that the normal month-to-month change in an unadjusted series between February and March was an increase of 20 percent. Then, an increase in the unadjusted series of less than 20 percent would be viewed as a decrease in the seasonally adjusted series; an increase of exactly 20 percent would be viewed as no change in the adjusted series; and an increase of more than 20 percent would be viewed as an increase in the adjusted series.
The recurring changes in a series that are removed by seasonal adjustment result from such factors as normal changes in weather and differing lengths of months. It should be emphasized that seasonal adjustment does not account for abnormal weather conditions or for year-to-year changes in weather.
Most of the seasonally adjusted series are shown as seasonally adjusted annual rates (SAAR). A SAAR is the seasonally adjusted monthly rate multiplied by 12.
The seasonal adjustment indexes were developed using X-13ARIMA-SEATS software. X-13ARIMA-SEATS software improves upon the X-12-ARIMA seasonal adjustment software by providing enhanced diagnostics as well as incorporating an enhanced version of the Bank of Spain's SEATS (Signal Extraction in ARIMA Time Series) software, which uses an ARIMA model-based procedure instead of the X-11 filter-based approach to estimate seasonal factors. The X-13ARIMA-SEATS and X-12-ARIMA software produce identical results when using the X-11 filter-based adjustment methodology. The X-13ARIMA-SEATS software will be avilable from the Census Bureau's Internet site in the coming months. Note that MHS estimates continue to be adjusted using the X-11 filter-based adjustment procedure.
The X-13ARIMA-SEATS program provides summary statistics to indicate the overall effect of the seasonal adjustment. The following table shows some of these statistics (summary measures PDF 14k). A description of X-13ARIMA-SEATS appears in The X-13A-S Seasonal Adjustment Program and Update on the Development of X-13ARIMA-SEATS by Brian C. Monsell, U.S. Census Bureau. For more information on X-12-ARIMA see the reference manuals posted on the Census Bureau's website.
An assumption underlying the seasonal adjustment process is that the original series can be separated into a seasonal component, a trading-day component, a trend-cycle component, and an irregular component. The seasonally adjusted series consists of the trend-cycle and irregular components taken together. The trend-cycle component includes the long-term trend and the business cycle. The irregular component is made up of residual variations, such as the sudden impact of political events and the effects of strikes, unusual weather conditions, reporting and sampling errors, etc.
Seasonal indexes are developed concurrently for each month for shipments, regional estimates of manufactured homes placements and manufactured homes on dealer lots. The seasonally adjusted U.S. total is the sum of the four regional components.
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