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Using SAS to Inform a Performance Indicator on Scotland Performs: A Study of Reconvictions
Ian Morton, Statistician,Justice Analytical Services, Scottish Government
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Contentso Scotland Performs
o Technical Notes and Reconvictions
o Baseline, Progress and Targets
o Stakeholders
o National Results
o Local Level Performance
o The good, the bad and the ugly
o Summary
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Scotland Performs
Measures and reports on progress of government in Scotland (http://www.scotland.gov.uk/About/scotPerforms)
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Purpose Targets, National Outcomes & Indicatorso Scotland Performs is tracked by …o 7 purpose targets (e.g. Solidarity: To increase overall income and the
proportion of income earned by the three lowest income deciles as a group by 2017),
o 16 National Outcomes (e.g. We live our lives safe from crime, disorder and danger http://www.scotland.gov.uk/About/scotPerforms/outcome),
o 50 National Indicators (e.g. reduce reconviction rates http://www.scotland.gov.uk/About/scotPerforms/indicator)
o One such indicator is the reconviction rate of offenders (http://www.scotland.gov.uk/About/scotPerforms/indicator/reconviction)o Current Status: The reconviction frequency rate decreased by 1.8
reconvictions per 100 offenders, from 59.7 in the baseline year of 2006-07 to 57.9 in 2008-09.
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Reconvictions Technical Note
o Each indicator has a technical note …o Reconvictions
http://www.scotland.gov.uk/About/scotPerforms/TechNotes/reconvictions
o Explains:o Baseline year and magnitude of measure
o How we measure progress
o If there is a target
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Baseline
o A baseline year of 2006-07 was chosen because this related to the financial year coinciding with the previous government
o Baseline reconviction frequency rate (59.7 reconvictions for every 100 offenders)
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Progresso Progression seen through a 'direction of travel' arrow showso improving (↓ for reconviction), worsening (↑) or maintaining (↔).
o How do we choose this ? Confidence Intervals:o Parametric model (Poisson) or Non-parametric model (Bootstrap).
o References:o [Poisson] Spiegelhalter D (2009) A predictable pattern of murder
http://understandinguncertainty.org/node/200
o [Bootstrap] Miller, D.P. (2004) Bootstrap 101: Obtain Robust Confidence Intervals For Any Statistic SUGI 29 Proceedings Paper 193-29 Montréal, Canada May 9-12, 2004 (http://www2.sas.com/proceedings/sugi29/193-29.pdf)
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Targetso Previous targeto Baseline of 2004-05, Reduce reconvictions rates by 2% by 2011
o Historically the previous target was chosen because it looked plausible and sounded stretching
o Use survival analysis – where survival time is the number of months to reconviction for those convicted previously
o References:o Allison P (1995) Survival Analysis Using the SAS System, SAS
Institute.
o Fox J (2006) Introduction to Survival Analysis (http://socserv.mcmaster.ca/jfox/Courses/soc761/survival-analysis.pdf)
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Stakeholderso Community Justice Authoritieso Local authoritieso Scottish Prison Serviceo Scottish Police Forceso Scottish Court Serviceo Risk Management Authorityo Parole Board for Scotlando Crown Office and Procurator Fiscal Serviceo Health Boardso Victim Supporto Third Sector Partnerso COSLAo Association of Directors of Social Work
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National Resultso Current Status: The reconviction frequency rate decreased
by 1.8 reconvictions per 100 offenders, from 59.7 in the baseline year of 2006-07 to 57.9 in 2008-09.
o Confidence Intervals for 2006-07o Parametric model [59.0,60.4]o Non-parametric model [58.7,60.7]o Suggests +-1 = maintainingo Conclusion for 2008-09: Performance Improving
o Target (Survival Analysis: not completed yet)
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Local Level Performanceo The Management of Offenders etc. (Scotland) Act 2005
established provisions for 8 local CJAs.
o Established to provide planning, manage performance and to report on performance of the 32 local authorities.
o Aim is to target services to reduce reoffending and to ensure close co-operation between community and prison services to aid the rehabilitation of offenders.
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The Bad and The Uglyo A league table ignores sample size and uncertainty
o Ref: Bird et al (2005) Performance indicators: good, bad, and ugly J R Stat Soc A 168, Part 1, pp. 1–27
2008-09
Back to index sheet
Scotland 49,613 15,392 31.0 28,743 57.9
Fife & Forth Valley 5,831 1,872 32.1 3,378 57.9Clackmannanshire 616 228 37.0 432 70.1Falkirk 1,489 484 32.5 898 60.3Fife 2,850 867 30.4 1,515 53.2Stirling 876 293 33.4 533 60.8Glasgow 10,041 3,285 32.7 6,378 63.5Glasgow City 10,041 3,285 32.7 6,378 63.5
Reconviction frequency
rate
One year Reconviction Rates by Community Justice Authority and Local Authority, 2008-09
Local authority area / community justice area
Number of Offenders
Number of offenders
reconvictedReconviction
RateNumber of
reconvictions
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The Good
o Reference: Spiegelhalter, D. J. (2005) Funnel plots for comparing institutional performance Statistics in Medicine 24 1185-1202.
o Can remove offender mix using logistic regression (see bulletin ref on next slide): Allison, P. D. (1999) Logistic Regression Using the SAS System SAS Institute and Wiley, North Carolina.
One Year Reconviction Rate: 2008-09 Offender Cohort
West Lothian
Highland
Glasgow City
Edinburgh and Midlothian
Dundee City
ClackmannanshireAngus
30
40
50
60
70
80
0 2000 4000 6000 8000 10000
Number of Offenders
1 y
ear
reco
nvic
tio
n f
req
uen
cy r
ate
LAs
Average
2SD limits
3SD limits
Source: Reconviction Rates in Scotland: 2007 and 2008-09 Offender Cohorts, Scottish Government
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Further Information
o If you want to delve deeper see the latest bulletin – pages 15 and 16 (http://www.scotland.gov.uk/Publications/2011/08/29151240/0)
o Or see my slideshows / papers on Linkedin
o http://uk.linkedin.com/in/idmorton
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Summaryo Scotland Performs measures and reports on progress of government in
Scotland.
o Described the use of SAS to provide statistical information for Scotland Performs.
Key Factso Recorded crime in Scotland is at its lowest level since 1976 and is down by 23%
since 2006-07.
o One year reconviction rates are at their lowest point in the past 12 years, with 31% of the 2008-09 cohort reconvicted within a year.
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Questions
