Sampling Error, Standard Errors, and Relative Standard Errors
The Commercial Buildings Energy Consumption Survey
The commercial sector consists of business establishments and other organizations that provide services. The sector includes service businesses, such as retail and wholesale stores, hotels and motels, restaurants, and hospitals, as well as a wide range of buildings that would not be considered commercial in a traditional economic sense, such as public schools, correctional institutions, and religious and fraternal organizations. Excluded from the sector are the goods-producing industries: manufacturing, agriculture, mining, forestry and fisheries, and construction.
Nearly all energy use in the commercial sector takes place in, or is associated with, the buildings that house these commercial activities. Analysis of the structures, activities, and equipment associated with different types of buildings is the clearest way to evaluate commercial sector energy use. The Commercial Buildings Energy Consumption Survey (CBECS) is a national-level sample survey of commercial buildings and their energy suppliers conducted quadrennially (previously triennially) by the Energy Information Administration (EIA). The 1995 CBECS was the sixth survey in the series begun in 1979. From 1979 to 1986, the survey was known as the Nonresidential Buildings Energy Consumption Survey, or NBECS.
The following two sections summarize CBECS survey methodology and sampling error. Complete discussion of these two topics can be found in Technical Information on CBECS on the CBECS Home Page.
The CBECS is conducted in two stages, a building characteristics survey and an energy supplier survey. The first, an in-person or telephone survey, collects information on physical characteristics of the building, building use and occupancy patterns, major equipment used, conservation practices, and types and uses of energy in the buildings. The supplier survey, a mail survey, collects information on amounts and costs of energy delivered to the building during the survey year.
The target population for the CBECS consists of all commercial buildings in the United States with more than 1,000 square feet of floorspace. A commercial building defined by CBECS is an enclosed structure with more than 50 percent of its floorspace devoted to activities that are neither residential, industrial, nor agricultural. To survey this population, a representative sample of buildings is selected. For example, in the 1995 CBECS, 6,639 buildings were selected; of those, building characteristics survey interviews were completed at 5,766 buildings for a response rate of 87 percent.
The CBECS uses a multistage area probability cluster sample design supplemented by a list sample of large buildings, recently constructed buildings, and special buildings (Federal buildings and post offices, hospitals, colleges, and universities). The area sample portion of the design draws a sample from the broad spectrum of commercial buildings with a four-stage cluster sampling design, a method that progressively samples smaller geographic areas. The supplemental list sample is an oversample of large buildings and special buildings to ensure adequate coverage of buildings that are significant energy users. Similarly, for recently constructed buildings, an area sample is drawn from the broad spectrum of new buildings and a supplemental list is used to oversample of large new buildings.
Since the purpose of the CBECS is to publish estimates of population values, the CBECS sample is designed so that survey responses estimate characteristics of the entire stock of commercial buildings in the United States. The method of estimation is to calculate basic sampling weights (base weights) that relate the sampled buildings to the entire stock of commercial buildings. In statistical terms, a base weight is the reciprocal of the probability of selecting a building into the sample. A base weight can be thought of as the number of actual buildings represented by a sampled building; for example, a sampled building that has a base weight of 1,000 represents itself and 999 similar (but unsampled) buildings in the total stock of buildings.
Sampling Error, Standard Errors, and Relative Standard Errors
The CBECS estimates of buildings and floorspace always differ from the true population values because the CBECS estimates are based on data collected from a randomly chosen subset of the entire commercial building population. One source of the difference between the estimated values and the actual values is sampling error. Sampling error is the random difference that occurs between the survey estimate and the population value because the survey estimate is calculated from a randomly chosen subset of the entire population. The sampling error, if averaged over all possible samples, would be zero, but since there is only one sample for each CBECS, the sampling error is nonzero and unknown for the particular sample chosen. However, the sample design permits sampling errors to be estimated.
The standard error is a measure of the reliability or precision of a survey statistic. The value for the standard error can be used to construct confidence intervals and to perform hypothesis tests by standard statistical methods. Relative Standard Error (RSE) is defined as the standard error (square root of the variance) of a survey estimate, divided by the survey estimate and multiplied by 100. The 95-percent confidence range for a given survey estimate can be determined with the RSE. To calculate the 95-percent confidence range:
1. Divide the RSE by 100 and multiply by the survey estimate in the table to determine the standard error.The survey estimate plus or minus the confidence error is the 95-percent confidence range. For example, the estimate for total floorspace in all commercial buildings in the 1995 CBECS is 58,772 million square feet and the estimate’s RSE is 3.4 percent. The standard error is (3.4÷100)×(58,772 million square feet) or 1,998 million square feet. The 95-percent confidence error is (1.96)×(1,998 million square feet), or 3,917 million square feet. Therefore, with 95 percent confidence, the true amount of floorspace in commercial buildings in the United States in 1995 was 58,772 (± 3,917) million square feet or, stated another way, the range was from 54,855 to 62,689 million square feet.
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Release date: 01/12/2000
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