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Survey of Market Absorption of Apartments (SOMA)
NOTE TO DATA USERS
The SOMA adopted new ratio estimation procedures in 1990 to derive more accurate estimates of completions.2 This new procedure was used for the first time in processing annual data for 1990. Please use caution when comparing the number of completions in 1990 and following years with those in earlier years.
The U.S. Census Bureau designed the survey to provide data concerning the rate at which privately financed, nonsubsidized, unfurnished units in buildings with five or more units are rented or sold (absorbed). In addition, the survey collects data on characteristics such as number of bedrooms, asking rent, and asking price.
Buildings for the survey came from those included in the Census Bureau's Survey of Construction (SOC)3. For the SOC, the United States is first divided into primary sampling units (PSUs), which are stratified based on population and building permits. The PSUs to be used for the survey are then randomly selected from each stratum. Next, a sample of geographic locations that issue permits is chosen within each of the selected PSUs. Finally, all newly constructed buildings with five units or more within sampled places and a subsample of buildings with one to four units are included in the SOC.
2See ESTIMATION section below.
3See http://www.census.gov/const/www/newresconstdoc.html#sample for further details on the SOC sample design.
For the SOMA, the Census Bureau selects, each quarter, a sample of buildings with five or more units that have been reported in the SOC sample as having been completed during that quarter. The SOMA does not include buildings in areas that do not issue permits. In each of the subsequent four quarters, the proportion of units in the quarterly sample that were sold or rented (“absorbed”) are recorded, providing data for absorption rates 3, 6, 9, and 12 months after completion.
Beginning with data on completions in the fourth quarter of 1990 (which formed the basis for absorptions in the first quarter of 1991), the Census Bureau modified the estimation procedure and applied the new estimation procedure to data for the other three quarters of 1990 so that annual estimates using the same methodology for four quarters could be derived. The Census Bureau did not perform any additional re-estimation of past data.
Using the original estimation procedure, the Census Bureau created design-unbiased quarterly estimates by multiplying the counts for each building by its base weight (the inverse of its probability of selection) and then summing over all buildings. Multiplying the design-unbiased estimate by the following ratio-estimate factor for the country as a whole provides the following estimate:
total units in buildings with five units or more in permit-issuing areas as estimated by the SOC for that quarter divided by total units in buildings with five units or more as estimated by the SOMA for that quarter
In the modified estimation procedure, instead of applying a single ratio-estimate factor for the entire country, the Census Bureau computes separate ratio-estimate factors for each of the four census regions. Multiplying the unbiased regional estimates by the corresponding ratio-estimate factors provides the final estimates for regions. The Census Bureau obtains the final estimate for the country by summing the final regional estimates.
This procedure produces estimates of the units completed in a given quarter that are consistent with published figures from the SOC and reduces, to some extent, the sampling variability of the estimates of totals. Annual absorption rates are obtained by computing a weighted average of the four quarterly estimates.
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 about which data were obtained. The noninterviewed and not-accounted-for cases constitute less than 2 percent of the sample housing units in this survey.
ACCURACY OF THE ESTIMATES
The SOMA is a sample survey and consequently all statistics in this report are subject to sampling variability. Estimates derived from different samples would differ from one another. The standard error of a survey estimate is a measure of the variation among the estimates from all possible samples. The methodology for calculating standard errors is explained in the section on Accuracy of the Estimates.
Two types of possible errors are associated with data from sample surveys: nonsampling and sampling 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 interpretation of questions, inability or unwillingness of the respondents to provide correct information, and errors made in processing the data. Although no direct measurements of the biases have been obtained, the Census Bureau thinks that most of the important response and operational errors were detected during review of the data for reasonableness and consistency.
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 design. Even if the same questionnaires, instructions, and interviewers were used, estimates from each of the different samples would likely differ from each other. The deviation of a sample estimate from the average from all possible samples is defined as the sampling error. The standard error of a survey estimate provides a measure of this variation 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 responses and by the 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 capture all of the effect of sampling error and, in this case, some nonsampling error as well.
If all possible samples were selected, if each of them was surveyed under the same general conditions, if there were no systematic biases, and if an estimate and its estimated standard error were calculated from each sample, then:
This report uses a 90-percent confidence level as its standard for statistical significance.
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 reliability of an estimated absorption rate (i.e., a percentage) computed by using sample data for both the numerator and denominator depends on both the size of the rate and the size of the total on which the rate is based. Estimated rates of this kind are relatively more reliable than the corresponding estimates of the numerators of the rates, particularly if the rates are 50 percent or more.
Tables A and B present approximations to the standard errors of various estimates shown in the report. Table A presents standard errors for estimated totals, and Table B presents standard errors of estimated percents. To derive standard errors that would be applicable to a wide variety of items and could be prepared at moderate cost, a number of approximations were required. As a result, the tables of standard errors provide an indication of the order of magnitude of the standard errors rather than the precise standard error for any specific item. Standard errors for values not shown in Tables A-1 to A-3 or B-1 to B-3 can be obtained by linear interpolation.
ILLUSTRATIVE USE OF THE STANDARD ERROR TABLES
Table 2 of this report shows that 9,500 apartments were built in the Midwest in 2007. Table A-1 shows the standard error of an estimate of this size to be approximately 1,650. To obtain a 90-percent confidence interval, multiply 1,650 by 1.6 and add and subtract the result from 9,500, yielding limits of 6,860 and 12,140. The average estimate of these units may or may not be included in this computed interval, but one can say that the average is included in the constructed interval with a specified confidence of 90 percent.
Table 2 also shows that the rate of absorption after 3 months for those 9,500 units built in the Midwest was 58 percent. Table B-1 shows the standard error on a 58 percent rate on a base of 9,500 to be approximately 8.7 percent. Multiply 8.7 by 1.6 (yielding 13.9) and add and subtract the result from 58. The 90-percent confidence interval for the absorption rate of 58 percent is from 44.1 percent to 71.9 percent.
The median asking rent for these 9,500 unfurnished rental apartments built in the Midwest was $772. The standard error of this median is about $52.
Several statistics are needed to calculate the standard error of a median.
|length of interval containing|
|the sample median|
|standard error of median = σ50% x||_____________________________|
|estimated proportion of the base|
|falling within the interval|
|containing the sample median|
For this example, the standard error of the median of $772 is:
8.9 x 100/17 = $52
Therefore, 1.6 standard errors equals $83. Consequently, an approximate 90-percent confidence interval for the median asking rent of $772 is between $689 and $855 ($772 plus or minus $83).