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CBECS Home Page 1995 CBECS Detailed Tables
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Statistical Significance of Survey Data 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 the 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. Statistical Significance Between Two Statistics The difference between any two estimates given in the Detailed Tables may or may not be statistically significant. Statistical significance is computed as: 
where S is the standard error, x1 is the first estimate, and x2 is the second estimate. The result of this computation is to be multiplied by 1.96 and, if this result is less than the difference between the two estimates, the difference is statistically significant. For example, in 1995, mercantile and service buildings consumed an estimated 395 trillion Btu of natural gas, while health care buildings consumed an estimated 258 trillion Btu, for an estimated difference of 137 trillion Btu. The standard error for the 395 trillion Btu estimate (x1) is 48.70, and the standard error for the 258 trillion Btu estimate (x2) is 35.55 and Sx1-x2=(48.702+35.552)½ and Sx1-x2=60.30. Multiplying 60.30 by 1.96 yields 118.2. Since 118.2 is less than 137, the difference between the two estimates is statistically significant. Top Return to 1995 CBECS Detailed Tables Specific questions on these topics may be directed to: Joelle Michaels joelle.michaels@eia.doe.gov CBECS Manager Phone: (202) 586-8952 FAX: (202) 586-0018 URL: http://www.eia.doe.gov/cbecs/stat_significance.html |