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Tackling selection bias in sentencing data analysis: a new approach based on a scale of severity

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  • Jose Pina-Sánchez

    (University of Leeds)

  • John Paul Gosling

    (University of Leeds)

Abstract

For reasons of methodological convenience statistical models analysing judicial decisions tend to focus on the duration of custodial sentences. These types of sentences are however quite rare (7% of the total in England and Wales), which generates a serious problem of selection bias. Typical adjustments employed in the literature, such as Tobit models, are based on questionable assumptions and are incapable to discriminate between different types of non-custodial sentences (such as discharges, fines, community orders, or suspended sentences). Here we implement an original approach to model custodial and non-custodial sentence outcomes simultaneously avoiding problems of selection bias while making the most of the information recorded for each of them. This is achieved by employing Pina-Sánchez et al. (Br J Criminol 59:979–1001, 2019) scale of sentence severity as the outcome variable of a Bayesian regression model. A sample of 7242 theft offences sentenced in the Crown Court is used to further illustrate: (a) the pervasiveness of selection bias in studies restricted to custodial sentences, which leads us to question the external validity of previous studies in the literature limited to custodial sentence length; and (b) the inadequacy of Tobit models and similar methods used in the literature to adjust for such bias.

Suggested Citation

  • Jose Pina-Sánchez & John Paul Gosling, 2020. "Tackling selection bias in sentencing data analysis: a new approach based on a scale of severity," Quality & Quantity: International Journal of Methodology, Springer, vol. 54(3), pages 1047-1073, June.
    • Handle: RePEc:spr:qualqt:v:54:y:2020:i:3:d:10.1007_s11135-020-00973-z
    DOI: 10.1007/s11135-020-00973-z
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    3. Nancy J. King & Rosevelt L. Noble, 2005. "Jury Sentencing in Noncapital Cases: Comparing Severity and Variance with Judicial Sentences in Two States," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 2(2), pages 331-367, July.
    4. Tsang, Eric W. K., 2014. "Old and New," Management and Organization Review, Cambridge University Press, vol. 10(03), pages 390-390, November.
    5. Frederick Mosteller, 1951. "Remarks on the method of paired comparisons: II. The effect of an aberrant standard deviation when equal standard deviations and equal correlations are assumed," Psychometrika, Springer;The Psychometric Society, vol. 16(2), pages 203-206, June.
    6. Gibson, James L., 1978. "Judges' Role Orientations, Attitudes, and Decisions: An Interactive Model," American Political Science Review, Cambridge University Press, vol. 72(3), pages 911-924, September.
    7. Frederick Mosteller, 1951. "Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations," Psychometrika, Springer;The Psychometric Society, vol. 16(1), pages 3-9, March.
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