What is an RSE?

The estimates in the Commercial Buildings Energy Consumption Survey (CBECS) are based on data reported by representatives of a statistically-designed subset of the entire commercial building population in the United States, or a "sample".  Consequently, the estimates differ from the true population values.  However, the sample design permits us to estimate the sampling error in each value.

It is important to understand: CBECS estimates should not be considered as finite point estimates, but as estimates with some associated error in each direction.

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 to determine the standard error.

2.  Multiply the standard error by 1.96 to determine the confidence error.

3.  The survey estimate plus or minus the confidence error is the 95-percent confidence range.

For example, from Table B1, the estimate for total floorspace for all commercial buildings in the 1999 CBECS is 67,338 square feet and the estimate's RSE is 3.5 percent.  The standard error is (3.5/100)*(67,338 million square feet) or 2,357 million square feet.  The 95-percent confidence error is (1.96)*(2,357 million square feet), or 4,620 million square feet.  Therefore, with 95 percent confidence, the true amount of floorspace in commercial buildings in the U.S. in 1999 was 67,338 plus or minus 4,620 million square feet, or, the range was from 62,718 to 71,958 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, from Table C15, education buildings consumed an estimated 227 trillion Btu of natural gas in 1999, while retail (other than mall) buildings consumed an estimated 110 trillion Btu, for an estimated difference of 117 trillion Btu. The standard error for education buildings (x₁) is (11.8/100)*227, or 26.79 trillion, and the standard error for retail (other than mall) buildings (x₂) is (17.4/100)*110, or 19.14 trillion. So,
 
S_x1-x2=(26.79²+19.14²)^½
 
and
 
S_x1-x2=32.92.
 
Multiplying 32.92 by 1.96 yields 64.52. Since 64.52 is less than 117, the difference between the two estimates is statistically significant.

Specific questions on these products 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/emeu/cbecs/rse.html