There are a large number of small counts in the cells at both OA and ward level in the tables which show movements between all pairs of areas from which, and to which, people moved or commuted. There are over 30 billion pairs of OAs and 78 million pairs of wards in England and Wales. In practice, there were some 6.3 million movers in England and Wales, of whom 370,000 came from outside the UK, and 23.6 million people in employment in 2001, of whom 2.2 million worked from home. The majority of the cells of potential combinations of areas therefore did not contain any people. Some 860,000 ward pairs and almost two million OA pairs are present in the migration tables, and around 1.3 million ward pairs (excluding Scotland) and six million OA pairs (England and Wales) are present in the workplace tables.
When users combine data in these tables, or compare totals with other Census counts, some differences are likely to arise. These differences occur as a consequence of the small cell adjustment process which was applied to small values in tables. This process was designed to add uncertainty to the data in order to provide a measure of protection against the identification of individuals and their information. It has been applied to small cells in all Census tables for England, Wales and Northern Ireland, and in workplace tables for Scotland. Totals are derived as the sum of these adjusted values.
General guidance on the variability of 2001 Census data is given in a PDF document. It explains that the method of small cell adjustment is internally consistent within a table, since totals are obtained by summing the component cells. The method is also unbiased, that is the expected value if small cell adjustment was repeated randomly would be the same as the unadjusted value. However, the method may introduce some variability, which will tend to be largest for small areas that are likely to contain small counts. There are other sources of variation in the data which arise from coverage error, respondent error, other forms of processing error, and from record swapping - another element of disclosure protection in the 2001 Census. These all contribute to variations in output compared with the notional true values. Small cell adjustment is somewhat different in that a comparison between tables may show differences due to the way in which the method was applied.
The small cell adjustment of the origin-destination tables differed from the adjustment of the standard tables (including Key Statistics and Census Area Statistics). This method introduced some additional variation into the adjusted values, and the following advice was prepared to assist users in interpreting the results.
"The implementation of the adjustment method in the origin-destination statistics has introduced a small element of systematic variation. Whilst this effect is small compared to the other components of variation, and will not significantly affect the counts for a single area, small systematic differences may become apparent when aggregating results for many areas and comparing the results with counts from other Census tables.
If users wish to obtain estimates which involve combining data for different areas, it is recommended that the minimum number of areas should be used in the calculation. For example, if the total of 18 OAs is required in a ward which has 20 OAs, the recommended method would be to subtract the data for the remaining two OAs from the ward total rather than adding together the data for the 18 individual OAs. This approach should minimise the extent of variation in the resulting output."