Sample Results 

Constraints

The synthetic microdata available for downloading have been constrained to fit 817 small-area Census counts drawn from 14 small-area Census tabulations.  The nature of these constraints is summarised here.

SAR household combinations

For each small area, a file is available listing the identifiers (household numbers) of those households from the 1991 Census household Sample of  Anonymised Records that best fit known small-area constraints (example).  Full or partial details associated with each SAR household record may be extracted as required (further details). 

Goodness-of-fit

The fit of the synthetic microdata to known constraints is measured in two main ways: Absolute error and Z-score.  These measure respectively the absolute and relative (proportional) difference between Census and synthetic counts. 

In order to protect respondent confidentiality, all 1991 Census small-area counts were randomly modified by +/- 0 or 1 before release.  In consequence,  perfect fit  between synthetic microdata and the Census counts used to constrain their estimation (Total Absolute Error = 0) is known not to be possible.   Instead, for individual table cells, a Z-score of > +/-1.96 is taken to indicate poor fit, whilst for whole tables, poor fit is indicated by a sum of cell Z-scores greater than the chi-square critical value with degrees of freedom = number of table cells.  For a fuller discussion, see Huang and Williamson (2001).

The fit of the synthetic microdata estimated for the 1379 EDs in Leeds is summarised here.  For nearly 95% of all EDs, the fit to all 817 constraining counts is good.  For no ED is an entire constraining table poorly fitted.  Even when synthetic microdata are aggregated to ward level (33 wards in Leeds), the fit is good for an average of over 98% of all cell constraints.  

The fit of the synthetic microdata estimated for one Enumeration District (ED) in the city of Leeds to all 817 constraining Census count is presented here.  The goodness-of-fit for this ED is equal to the average achieved across all 1379 EDs in the city.  Equivalent reports are available for every synthetic ED in the UK, as are a range of other measures, as outlined here.