Payment by Results and lamp posts

Many years ago at school, I studied SMP Maths. I always remember the cartoon at the front of the chapter on statistics. It showed a drunken man leaning against a lamp post. The caption read: some people use statistics like a drunk uses a lamp post, for support rather than illumination.

And so yesterday, the Ministry of Justice published

Statistical Notice: Interim re-conviction figures for the Peterborough and Doncaster Payment by Results pilots

I was drawn towards this document by a combination of Russell Webster's excellent blog and the BBC news at midday. It kind got up my gander a little bit as it seemed to be exercise in political punditry rather than a clear analysis of whether the new Payment by Results regime may actually be working (or not). With my gander raised, I emailed the statistician involved with a number of questions which I reprint below.

The questions are a bit geeky, I know. But I do think it is vital for us all to know the precise evidence for whether PbR can work or not. Feel free of course to comment or indeed write with your own questions too.
________________________

Dear Mike Elkins

I have just read through your publication. I have a number of questions and I would be most grateful for your thoughts:

1.       The pilots began on 9 September 2010 and the 1 October 2011 (Peterborough and Doncaster respectively.) Please can you qualify “began”?
2.       Given that “the next Proven Reoffending Statistics quarterly bulletin will not be published until 25 July 2013”, why did you publish your results today rather than a few weeks from now?
3.       I understand that “the interim re-conviction figures being published in this statistical bulletin are based on periods half the length of those that will be used for the final results” – daft question I am sure, but presumably this applies to both the ‘experimental’ subject averages and the national comparators?
4.       You say that these “interim 6 month re-conviction figures are available for almost all of Peterborough cohort 1 (around 850 offenders) and half of Doncaster cohort 1 (around 700 offenders)”, please can you explain what has happened to the other portions of the cohorts and why they are included?
5.       In terms of methodology, you say “offenders enter the PbR pilots after their first eligible release from the prison within the cohort period”, please can you explain “eligible” in this context and whether the national comparator figures also cover the same “eligible” group?
6.       You explain that the key difference is that reconvictions only count offences for which the offender was convicted at court, whereas the National Statistics proven re-offending measure also includes out of court disposals (cautions)” and “Additionally, there are a number of other differences between the pilots and the
7.       National Statistics proven re-offending measure in terms of which offenders are counted within the cohort”. Are you able to say what difference these differences might make to the figures? For example, what number of offenders per hundred are usually subject to a caution (or similar disposal) as opposed to a court conviction?
8.       Again I assume that given that the “Peterborough pilot includes offenders released from custodial sentences of less than 12 months, whereas the Doncaster pilot includes all offenders released from custody regardless of sentence length”, the national comparisons are on a like for like basis?
9.       You explain that the “success of each Peterborough cohort will be determined by comparison with a control group (of comparable offenders from across the country)”. How will this ‘control’ group be selected to ensure there is no inadvertent or unknown bias? Indeed was there (will there be) any form of randomised control trial element to either of these two trials (and extensions)? If not, what is your considered professional judgement as a statistician as to the validity of these results to guide future practice?
10.   For Doncaster, success “will be determined by comparison with the reconviction rate in the baseline year of 2009”. How will this accommodate national and/or local trends in (say) sentencing practice or levels of crime?
11.   Given that normally reconviction rates are measured on a 12 month basis and these interim results are measured on a 6 month one, how much is that likely (based on past data) to have depressed the reconviction rates?
12.   You say “Whereas in this publication, to eliminate the risk of seasonality and enable a consistent comparison over time, all figures relate to offenders released in the 6 month period from October to March”. I may well be missing something here, but by only using the six winter months, are you not likely to increase the risk of a seasonal effect in the data? Please explain further.
13.   Given that the Peterborough cohort finished on 1/7/12, and allowing for the 6 months plus 3 (for court delays), this takes us up to March 2013. So on this basis, why have the last three months of data (April, May and June 2012) been excluded? (As far as I can see there is no explanation of this decision, but forgive me if I have overlooked it.)
14.   Given that I assume that data is ordinarily collected on a quarterly basis, it would have been helpful to have presented your data in a similar way so that trends could be spotted over time rather than use the fairly arbitrary 19 month period to show the data. Why did you present it this way? Please could I have the data on a quarterly basis.
15.   Given that you must have the data for Peterborough for the missing 19 month period (September 08 to March 11), and acknowledging that this overlaps with the pilot beginning, please could I have this data nonetheless.
16.   Likewise, please could I have the data for the quarter beginning April 2012.
17.   You say “Nationally the equivalent figures show a rise of 16% from 69 to 79 re-conviction events per 100 offenders”. How do you get 16%? I can see a rise of 10 ‘points’ or a rise of (10/69*100) 14.5%.
18.   (As an aside, this is quite a large rise nationally in re-conviction rates comparing the period from just before the last election to period after. Have national rates continued to rise or have they levelled off now?)
19.   You say “these interim figures show a fall in the frequency of re-conviction events at Peterborough” which is drop from 41.6% to 39.2%. At what threshold of probability is this statistically significant?
20.   Please can you confirm that the OGRS scores cited relate to the cohort groups in both Peterborough and Doncaster (rather than all offenders who were released)?
21.   Why are the national re-conviction scores given next to Doncaster data (which average 32.9%) differ from the scores given next to the Peterborough data (average 37.9%)? I know the period is different and there is some missing data, but this still seems like a large difference…

I look forward to your thoughts

Many thanks

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And now I wait...

UPDATE: FoI inquiry has been acknowledged. 20 working days or less to go... (140613)