Sampling error
The difference between estimates obtained from a sample of businesses, and the estimates that would have been produced if the information had been obtained from all businesses, is called sampling error. The expected magnitude of the sampling error associated with any estimate can be estimated from the sample results. One measure of sampling error is given by the standard error (SE), which indicates the degree to which an estimate may vary from the value that would have been obtained from a full enumeration (the 'true' figure). There are about 2 chances in 3 that a sample estimate differs from the true value by less than one standard error, and about 19 chances in 20 that the difference will be less than two standard errors.
The following is an example of the use of standard error on the estimated proportion of innovation-active businesses. If the estimated proportion of innovation-active businesses was 45.6% and the standard error of this estimate was 2.0, there would be approximately 2 chances in 3 that a full enumeration would have given a figure in the range of 43.6% and 47.6%, and 19 chances in 20 that it would be in the range of 41.6% to 49.6%.
In this publication, indications of sampling variability are measured by relative standard errors (RSEs). The relative standard error is a useful measure in that it provides an immediate indication of the percentage errors likely to have occurred due to sampling and thus avoids the need to refer to the size of the estimate. Relative standard errors are shown in the Relative Standard Error table in this section.
To annotate proportion estimates, a value of 50% has been used in the calculation of RSE rather than the estimated proportion from the survey data. This avoids inconsistencies between the way very low and very high proportions are annotated. Relative standard errors for estimates in this publication have been calculated using the actual standard error and the survey estimate (referred to as x) in the following manner: RSE%(x) = (SE(x)*100)/50.
Using the previous example, the standard error for the estimated proportion of innovation-active businesses was 2.0%. Multiplied by 100 and then divided by 50 gives an RSE calculated on this basis of 4.0%. It is these figures that appear in the table appended to this chapter.
Estimates may have corresponding RSE range values annotated. Depending on the level of RSE, data should be used with caution. Estimates with RSEs between 10% and 25% are subject to sampling variability too high for some purposes. Estimates with RSEs between 25% and 50% are subject to sampling variability too high for most practical purposes and estimates with an RSE greater than 50% indicate that the sampling variability causes the estimates to be considered too unreliable for general use.
Estimates with an annotated RSE of between 10% and 25% should be used with caution as the estimate from full enumeration could lie more than a decile away. For example, a proportion estimate of 30% with this RSE annotation, means the full enumeration value could lie beyond the range 20% to 40%. Estimates with an annotated RSE of between 25% and 50% could lie more than a quartile away and is subject to sampling variability too high for most practical purposes. A proportion estimate of 30% annotated with this RSE annotation, means the full enumeration value could lie beyond the range 5% to 55%. Proportion estimates annotated with RSE greater than 50% have a sampling error that causes the estimates to be considered too unreliable for general use.