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1992 CBECS Detailed Tables
 
  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.
 
2. Multiply the standard error by 1.96 to determine the confidence 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 1992 CBECS is 67,876 million square feet and the estimate’s RSE is 3.7 percent. The standard error is (3.7÷100)×(67,876 million square feet) or 2,511 million square feet. The 95-percent confidence error is (1.96)×(2,511 million square feet), or 4,922 million square feet. Therefore, with 95 percent confidence, the true amount of floorspace in commercial buildings in the United States in 1992 was 67,876 (± 4,922) million square feet or, stated another way, the range was from 62,954 to 72,798 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 1992, mercantile and service buildings consumed an estimated 381 trillion Btu of natural gas, while health care buildings consumed an estimated 189 trillion Btu, for an estimated difference of 192 trillion Btu. The standard error for the 381 trillion Btu estimate (x1) is 60.96, and the standard error for the 189 trillion Btu estimate (x2) is 33.64 and
 
Sx1-x2=(60.962+33.642)½
 
and
 
Sx1-x2=69.63.
 
Multiplying 69.63 by 1.96 yields 136.5. Since 136.5 is less than 192, the difference between the two estimates is statistically significant.
 
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Return to 1992 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_92.html

File last modified November 16, 1999


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