Confidence intervals

The Accuracy the 2001 Census Result

The estimates of under-enumeration, and thus the census results, are based upon a sample survey, the Census Coverage Survey (CCS) and are therefore subject to sampling error. This is an important difference with previous census results, as the final numbers are all estimates rather than a simple count, and the error levels can be used as a guide for assessing the accuracy of the estimates. Standard statistical techniques have been used to calculate these error levels, and therefore produce confidence intervals for the One Number Census (ONC) results.

For England and Wales, the confidence interval - reflecting error levels arising for a number of reasons - on the whole population is +/-0.2 per cent, or a total of 104,000.

Interpreting error levels

A 95 per cent confidence interval is a range within which the true population would fall for 95 per cent of the times the sample survey was repeated. It is a standard way of expressing the statistical accuracy of a survey based estimate. If an estimate has a high error level, the corresponding confidence interval will be very wide.

The error levels associated with the ONC estimates are mainly dependent on the CCS sample size, the size of the population, the census response rate, the CCS response rate and the homogeneity of the population the error level relates to.

Therefore, at a national level the overall error will be smaller than the error associated with a local authority that has a low response rate or an area that has a diverse population. However, sample sizes do vary between local authorities and age-sex groups and therefore some error levels may be smaller or larger than expected.

This is the first time it has been possible to estimate the level of precision for a census with any confidence. It should be noted that as with all statistical analysis these standardised calculations do not capture all sources of variation and there will also be, for example, response, capture and coding errors - these will be outlined in full in the 2001 Census Quality Report which will be available in 2003. However, our assessment is that, having made an adjustment for dependency, the ONC results remain the best central estimates possible of the population as at census day 2001.

What the Numbers Show

The attached Excel spreadsheet gives details of 95 per cent confidence intervals.

• Table 1 gives the 95 per cent confidence intervals for the total England and Wales census estimates. It shows that for England and Wales as a whole, the confidence interval on the population is +/- 0.2 per cent or numerically +/- 104,000.

• Table 2 shows the error levels by age and sex for England and Wales, showing that the confidence intervals are wider for those age-sex groups that have the highest under-enumeration - that is males in their twenties.

• Tables 3 and 4 show the age and sex intervals for England and Wales respectively.

• Table 5 gives the total population error levels for each of the 376 local authorities in England and Wales.