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

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 noncustodial 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.