44:. Barnard, at that time President of the Royal Statistical Society, was one of three Fellows appointed by the Council of the Royal Statistical Society to help provide a government-commissioned review of data security for the 1971 UK Census. The resulting report questioned whether rounding small numbers to the nearest five was the best approach to preserving respondent confidentiality. The formal government response to the report noted that an additional safeguard of small random adjustments had been introduced for 1971 Census, the suggestion for which they explicitly attributed to Professor Barnard, as did a New Scientist article dated July 1973. Muddying the waters slightly, a 1973 paper in the Journal of the Royal Statistical Society discussing this new safeguard reported that "after much discussion, a variant of a procedure suggested in Canada was adopted.". Presumably Professor Barnard was involved in these discussions, and was the inventor of the variant. In any case, no evidence can be found of any such safeguard being applied in Canada, with Statistics Canada seeming to stick instead to the use of random rounding of all counts to the nearest 0 or 5.
172:. Some aspects of an initial decision by the Commissioner were overturned on appeal to the House of Lords, and the Commissioner was invited to revisit his original decision. The Commissioner's final decision ruled that barnardisation provided insufficient disclosure protection for rare events (in this case, Childhood Leukaemia), reversing in part his original decision: "the barnardised data, by themselves, can lead to identification, and the effect of barnardisation on the actual figures, at least as deployed by the CSA, does not have the effect of concealing or disguising the data which he had originally considered that it would." However, in his written decision the Commissioner offered no statistical justification for this assertion. Instead the Commissioner's decision centred mainly around addressing points of law relating to the nature of the original and barnardised data, and how this related to legal definitions of (sensitive) personal data.
161:
the relatively high probability that
Barnardisation will leave a small count (in particular a 1) unadjusted and, secondarily, to the dangers of reverse engineering the original value if sufficient overlapping barnardised tables are released. For these and other reasons UK Censuses from 2001 onwards have abandoned the use of Barnardisation. See Spicer for a good review of the 2001, 2011 and 2021 alternatives to Barnardisation that have been adopted, and the rationale for this,.
59:, where it is used by two separate chapter authors and by the index compiler. However, by at least the late 1980s the term was already in widespread conversational usage during UK academic conferences and meetings. More recently the term 'Barnardisation' has also become firmly ensconced in the lexicon of official reports produced by official UK statistical agencies and others.
51:
The earliest use of the term 'Barnardisation' found in print so far dates to an Office for
Population Censuses and Surveys working paper written by Hakim in 1979, where the term is mentioned without citation, and without ascribing it to Prof G A Barnard. But, at the time, Hakim's coinage of this term
47:
Despite originating from Prof
Barnard, in documentation surrounding the 1971 Census the method of adjustment now known as Barnardisation was simply described as a 'procedure'; an 'adjustment of values'; a 'special procedure'; a 'process of random error injection'; or a 'modification' or 'adjustment'.
23:
for tables of counts. It involves adding +1, 0 or -1 to some or all of the internal non-zero cells in a table in a pseudo-random fashion. The probability of adjustment for each internal cell is calculated as p/2 (add 1), 1-p (leave as is), p/2 (subtract 1). The table totals are then calculated as the
160:
Since the late 1990s concerns over the efficacy of
Barnardisation in protecting confidentiality have increased to the point where it is now no longer recommended as a 'go to' tool, but rather as a technique only to be used in special circumstances. This change in attitudes appears to centre around
83:
rights of the individuals to whom the information relates (e.g.). In some cases this has involved further modifications to the
Barndardisation procedure. For example, as implemented by the Common Service Agency, adjustments of -1, 0 or +1 were only applied to counts of 1 to 4, whilst counts of 0,
67:
As originally conceived and implemented in the 1971 UK Census, Barnardisation had the added characteristic of pairing tables from separate areas, and applying equal and opposite adjustments to the two areas. For example, if a given table cell in Area A had its value increased by 1, then in paired
71:
For the 1991 UK Census the pairing of areas prior to the application of
Barnardisation was dropped; and for the more detailed Local Base Statistics, its scope was extended to include adjustments of -2, -1, 0, +1 or +2, achieved by applying the +1, 0 or +1 adjustment twice.
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Area B the equivalent table cell would have its value reduced by 1 (subject to not making the value negative). The purpose of this pairing was to cancel out, as much as possible, the amount of noise introduced via the
Barnardisation process at a more aggregate level.
534:
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From a user point-of-view, another advantage of
Barnardisation is that it has been shown to have a smaller impact on typical user analyses than the following Statistical Disclose Control measures: random rounding to base 5; as used by
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The adjustment can be unpicked via differencing if other tables are available that share the same counts or totals, or that provide an unadjusted total for a larger spatial area within which the barnardised tables
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The question of whether barnardisation may fall short of the complete anonymisation of data, and the status of barnardised data under the complex provisions of the
52:
appears to have been either widely overlooked or widely ignored, at least in print, as demonstrated by the wide range of later publications already cited above.
79:, barnardisation became increasingly employed by public agencies in order to enable them to provide information for statistical purposes without infringing the
571:"Decision 021/2005 Mr Michael Collie and the Common Services Agency for the Scottish Health ServiceChildhood leukaemia statistics in Dumfries and Galloway"
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methods in the run up to the 2011 UK Census identified the following list of pros/cons of
Barnardisation from the point-of view of the data provider:
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Leads to inconsistent values for the same cell counts and table totals if they are present in two or more separately barnardised tables
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The term 'Barnardisation' does not appear to have reemerged in print until the 1995 publication of Stan
Openshaw's
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141:
428:
Marsh (1993). "Privacy, confidentiality and anonymity in the 1991 Census". In Dale, A; Marsh, C (eds.).
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The probability of adjustment used is typically small, meaning that many cell values are left unadjusted
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535:"Statistical Disclosure Control (SDC) methods short-listed for 2011 UK Census tabular outputs, Paper 1"
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Willliamson, Paul (2007). "The impact of cell adjustment on the analysis of aggregate census data".
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Hakim, Catherine (1979). "Census confidentiality in Britain". In Bulmer, M (ed.).
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Techniques for ensuring the confidentiality of census information in Great Britain
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Geographical analysis and mapping of the 1971 UK Census data, Working Paper 3
225:(Working Paper 3: Risk Management ed.). Office for National Statistics.
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instead of being left unchanged, were adjusted by the addition of 0 or +1.
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The technique of Barnardisation appears to have been named after Professor
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Review of the dissemination of health statistics: confidentiality guidance
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J. C. Dewdney (1983). "Censuses past and present". In Rhind, D W (ed.).
361:(Introduction to volume I (part 1) ed.). Ottawa: Statistics Canada
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144:; and Small Cell Adjustment, as used at various points in time by the
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384:. Dept of Geography, University of Durham: Census Research Unit.
300:"Population census: recent British developments in methodology"
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EAP125 on Statistical disclosure control (SDC) for Census 2021
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1971 Census of Canada : population : vol. I - part 1
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Journal of the Royal Statistical Society. Series A (General)
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Dept. of Geography and Planning, University of Liverpool
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399:(Occasional Paper 3 ed.). Census Division, OPCS.
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Census confidentiality, microdata and census analysis
198:(Occasional Paper 4 ed.). Census Division, OPCS.
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Table totals are consistent with internal cell values
513:Williamson, Paul (2022). "Personal communication".
298:Jones, H. J. M.; Lawson, H. B.; Newman, D. (1973).
280:New Scientist (1973). "Census data not so secret".
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140:; random rounding to base 3, as used by
243:"'Security of the Census of Population"
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459:. London: Palgrave. pp. 132–157.
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36:(1915–2002), a Professor of
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414:. London: Methuen. pp. 1–16.
170:Scottish Information Commissioner
150:Australian Bureau of Statistics
542:Office for National Statistics
146:Office for National Statistics
94:Statistical Disclosure Control
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456:Censuses, Surveys and Privacy
465:10.1007/978-1-349-16184-3_10
430:The 1991 Census User's Guide
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596:Environment and Planning A
352:Statistics Canada (1974).
114:The adjustment is unbiased
395:Hakim, Catherine (1978).
168:, were considered by the
412:A Census User's Handbook
166:Data Protection Act 1998
488:Openshaw, Stan (1995).
194:Newman, Dennis (1978).
533:SDC UKCDMAC Subgroup.
492:. Cambridge: Pearson.
142:Statistics New Zealand
57:Census Users' Handbook
490:Census Users' Handbok
34:George Alfred Barnard
156:Efficacy reappraised
666:Information privacy
380:Rhind, D W (1975).
241:Moore, P G (1973).
81:information privacy
63:Operational details
42:University of Essex
661:Survey methodology
105:Easy to understand
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