Standard Errors for Annual Business Inquiry

New 2005 ABI standard errors and coefficients of variation are available for local authority areas. The measures relate to total employee jobs (excluding agriculture) for each area. The new 2005 figures have been added to those previously released to provide a time series from 2000 to 2005.

ABI standard errors (xls, 112 Kb)


Background

In principle it would be possible to collect information each month for all businesses in Great Britain and use it to construct employee totals by region and industry which would provide a true total. However, this would be very time consuming and expensive and would impose an unacceptable burden on businesses, so the ABI is based on a sample of approximately 78,000 businesses and is used to provide an estimate of the number of employees. If a different sample of 78,000 businesses were selected it would produce a different estimate.

The difference between the estimate and its true value is known as the sampling error. The actual sampling error for any estimate is unknown but we can estimate, from the sample, a typical error, known as the standard error. This provides a means of assessing the precision of the estimate; the lower the standard error, the more confident we can be the estimate is close to the true value.

If estimates were obtained from many different samples, then approximately two thirds of these estimates would be less than one standard error away from the true estimate and approximately 95 per cent would be less than two standard errors away from the true value. Another way to express a standard error is as a percentage of the estimate itself. This is referred to as the coefficient of variation or cv of the estimate.


About the standard errors

  • The ABI is based on a sampled survey, estimating the number of employees which gives rise to sampling errors. Standard errors can be applied to the estimates to provide an upper and lower boundary, of which we are 95 per cent confident the true value lies.
    e.g. The City of London estimate for 2005 is 280,097 with a standard error of 5,253. This interpreted suggests that we are 95 percent sure that the true value lies within twice the standard error, so within the range 269,591 to 290,603. The corresponding coefficient of variation is 0.02 (or 2 per cent expressed as a percentage). That is we are 95 per cent sure the true value lies within 4 percent of the estimate.
  • The coefficient of variation can be calculated by dividing the standard error divided by the estimate. Data have been calculated on unrounded figures. The coefficient of variation indicates the quality of a figure, the smaller the coefficient of variation the higher the quality.
  • The coefficient of variation and standard errors are at local authority/district level.
  • Data are available for 2000 - 2005.
  • The coefficient of variation and standard errors are calculated based on current geography ABI estimates. The coefficient of variation for each current district can be applied to the relevant CAS geography district estimates to produce standard errors on this basis.
  • The coefficients of variations are calculated excluding agriculture data as these data are supplied externally and not necessarily through a sample. However, it is assumed the agriculture data are of the same quality and will not effect the value of the CV and can be applied to the total estimate for the region.

Any further queries regarding standard errors for the ABI please contact the ABI team:

email: annual.employment.figures@ons.gov.uk
tel: 01633 456903