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  Standard Errors


| | Estimation of Standard 
      Errors Sampling 
      error is the difference between the survey estimate and the true 
      population value due to the use of a random sample to estimate the 
      population. This difference arises because a random subset, rather than 
      the whole population, is observed. The typical magnitude of the sampling 
      error is measured by the standard error of the estimate. The standard 
      error is the root-mean-square difference between the estimate based on a 
      particular sample and the value that would be obtained by averaging 
      estimates over all possible samples.
       
      If the estimates are 
      unbiased, meaning there is no systematic error, this average over all 
      possible samples is the true population value. In this case, the standard 
      error is simply the root-mean-square difference between the survey 
      estimate and the true population value. If systematic error is present, 
      however, this bias is not included in the error measured by the standard 
      error. Thus, the standard error tends to understate the total estimation 
      error if there are non-negligible biases.
       
      In principle, 
      random errors can be attributed to the estimate by sources other than the 
      sampling process. Such additional sources of random error include random 
      errors by respondents and data entry staff and random unit nonresponse. To 
      recognize these additional sources of variation, the definition of the 
      sampling process can be expanded to include not just the selection of 
      buildings but all steps required to obtain a set of responses. Under this 
      expanded definition, all random errors can be regarded as sampling errors. 
      The procedures designed to estimate the sampling error for CBECS 
      incorporate all random components of the estimation 
      process.
       Jackknife 
      Replication Throughout this report, standard 
      errors are given as percents of their estimated values, that is, as 
      relative standard errors (RSEs). Computations of standard errors are more 
      conveniently described, however, in terms of the estimation variance, 
      which is the square of the standard error.
       
      For some types of 
      surveys, a convenient algebraic formula for computing variances can be 
      obtained. The CBECS used a list-supplemented, multistage area sample 
      design  of such complexity that it is virtually 
      impossible to construct an exact algebraic expression for estimating 
      variances. In particular, convenient formulas based on an assumption of 
      simple random sampling, typical of most standard statistical packages, are 
      entirely inappropriate for the CBECS estimates. Such formulas tend to give 
      severely understated standard errors, making the estimates appear much 
      more accurate than is the case.
       
      The method used to estimate 
      sampling variances for this survey was a jackknife replication method. The 
      idea behind replication methods is to form several pseudoreplicates of the 
      sample by selecting subsets of the full sample. The subsets are selected 
      in such a way that the observed variance of estimates based on the 
      different pseudoreplicates estimates the sampling variance in the overall 
      estimate.
       
      The sampling strata are first divided into k groups, and within each group, divided into 2 (or occasionally 3 members). The kth jackknife pseudoreplicate sample 
      set is obtained by deleting all observations from one of the members in 
      the kth group and multiplying the weights on all cases in the other group 
      members by 2 if there are 2 members in the group and by 1.5 if there are 3 
      members in the group. Observations in all other groups are unaffected. The 
      kth pseudoestimate is then obtained from this pseudoreplicate 
      sample by following all the steps used to construct the full-sample 
      estimate.
       
      The variances are estimated from the 
      pseudoestimates in the following way. Let X' be a survey estimate (based 
      on the full sample) of characteristic X for a certain category of 
      buildings. For example, X may be the total square footage of buildings 
      using natural gas in the Midwest. Let Xk' be the pseudoestimate 
      of X based on the kth pseudoreplicate sample. The estimated 
      variance of the full-sample estimate X' is then given 
      by:
       
           equation
       
      The standard 
      error of X' is given by:
       
           equation
       
      The relative standard error (percent) of X' is obtained from 
      this standard error as:
       
           equation      
      Specific questions on these topics may be 
        directed to:Jay Olsenjay.olsen@eia.doe.gov-or-Joelle Michaelsjoelle.michaels@eia.doe.gov
        CBECS 
        ManagerFile last modified November 08, 2012URL: http://www.eia.gov/consumption/commercial/data/archive/cbecs/tech_std_errors.htmlIf you have any technical problems with this site, please contact the 
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