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Survey of Market Absorption of Apartments (SOMA)



Source and Accuracy of the Estimates - Third Quarter 1997

The Survey of Market Absorption (SOMA) is a sample survey and consequently all statistics are subject to sampling variability. Estimates derived from different samples would likely differ from these.

The standard error of a survey estimate is a measure of the variation among the estimates from all possible samples. It allows us to construct an interval with prescribed confidence that the interval includes the average of the estimates from all possible samples. (Estimates of standard errors have been computed from the sample data and are presented in the tables.)

For all the statements about changes made in this report, 90-percent confidence intervals for statistical comparisons can be constructed by using the 90-percent deviate shown in the parentheses after the change; however, when a 90-percent confidence interval contains zero, we are uncertain whether or not the change has occurred. In addition, any statistical findings that are not part of the tables or that are derived by collapsing intervals within a table are also provided with 90-percent confidence intervals.

NOTE TO DATA USERS

The SOMA adopted new ratio estimation procedures in 1990 to derive more accurate estimates of completions. Caution must be used when comparing the number of completions in 1990 and later with those in earlier years.

SAMPLE DESIGN

The buildings selected for the SOMA are those included in the Census Bureau's Survey of Construction (SOC). For the SOC, the United States is first divided into primary sampling units (PSUs) which are stratified on the basis of population and building permits. The PSUs to be used for the survey are then randomly selected from each stratum. Next, a sample of permit-issuing places is chosen within each of the selected PSUs. Finally, all newly constructed buildings with five units or more within sampled places, as well as a subsample of buildings with one to four units, are included in the SOC.

Each quarter, a sample of buildings with five units or more in the SOC sample reported as completed during that quarter are chosen for the SOMA. Buildings completed in nonpermit-issuing areas are excluded from consideration. Information on the proportion of units absorbed three, six, nine, and twelve months after completion is obtained for units in buildings selected in a given quarter in each of the next four quarters.

ESTIMATION

Estimates published for a given quarter are preliminary and are subject to revision in ensuing quarters. Each quarter, the absorption data for some buildings are received too late for inclusion in the tabulations. These late data are included in a revised table in the next quarter. They are finalized in an annual report.

Beginning with data on completions in the fourth quarter of 1990 (which formed the base for absorptions in the first quarter of 1991), the estimation procedure was modified. The modified estimation procedure was also applied to the data for the other three quarters of 1990 so that annual estimates could be derived using the same methodology for four quarters. No additional re-estimation of past data is planned.

Before this change in the estimation procedure, unbiased estimates were formed by multiplying the counts for each building by its base weight (the inverse of its probability of selection) and then summing over all buildings. The final estimate was then obtained by multiplying the unbiased estimate by the following ratio estimate factor for the Nation as a whole:

For the modified estimation procedure, instead of applying a single ratio-estimate factor for the entire nation, separate ratio-estimate factors are computed for each of the four Census regions. The final estimates for regions are obtained by multiplying the unbiased regional estimates by the corresponding ratio-estimate factors. The final national estimate is obtained by summing the final regional estimates.

This procedure produces estimates of the units completed in a given quarter which are consistent with the published figures from the SOC and also reduces, to some extent, the sampling variability of the estimates of totals.

Absorption rates and other characteristics of units not included in the interviewed group or not accounted for are assumed to be identical to rates for units where data were obtained. The noninterviewed and not-accounted-for cases constitute less than two percent of the sample housing units in this survey.

ACCURACY OF THE ESTIMATES

There are two types of possible errors associated with data from sample surveys: nonsampling and sampling errors. The following is a description of the nonsampling and sampling errors associated with the SOMA.

Nonsampling Errors

In general, nonsampling errors can be attributed to many sources: inability to obtain information about all cases in the sample; difficulties with definitions; differences in the interpretation of questions; inability or unwillingness of the respondents to provide correct information; and errors made in processing the data. These nonsampling errors also occur in complete censuses. Although no direct measurements of the biases have been obtained, we believe that most of the important response and operational errors were detected during review of the data for reasonableness and consistency.

Sampling Errors

The particular sample used for this survey is one of many possible samples of the same size that could have been selected using the same sample design. Even if the same questionnaires, instructions, and interviewers were used, estimates from different samples would likely differ from each other. The deviation of a sample estimate from the average of estimates from all possible samples is defined as the sampling error. The standard error of a survey estimate attempts to provide a measure of this variation among the estimates from the possible samples and, thus, is a measure of the precision with which an estimate from a sample approximates the average result from all possible samples.

As calculated for this survey, the standard error also partially measures the variation in the estimates due to errors in response and by interviewers (nonsampling errors), but it does not measure, as such, any systematic biases in the data. Therefore, the accuracy of the estimates depends on the standard error, biases, and some additional nonsampling errors not measured by the standard error. As a result, confidence intervals around estimates based on this sample reflect only a portion of the uncertainty that actually exists. Nonetheless, such intervals are extremely useful because they do capture all of the effect of sampling error and, in this case, some nonsampling error as well.

If all possible samples were selected, each of them were surveyed under essentially the same general conditions, there were no systematic biases, and an estimate and its estimated standard error were calculated from each sample, then--

For very small estimates, the lower limit of the confidence interval may be negative. In this case, a better approximation to the true interval estimate can be achieved by restricting the interval estimate to positive values, that is, by changing the lower limit of the interval estimate to zero.

The average result from all possible samples either is or is not contained in any particular computed interval. However, for a particular sample, one can say with specified confidence that the average result from all possible samples is included in the constructed interval.


Contact George Boyd at 301-763-3199 or mail to george.t.boyd@census.gov for further information on the Survey of Market Absorption of Apartments Data.

Source: U.S. Census Bureau, Social, Economic, and Housing Statistics Division
Last Revised: September 30, 2011