Selection Bias


Tackling Selection Bias in Sentencing Data Analysis: A New Approach Based on a Scale of Severity

Article (Quality & Quantity)

Presentation (Royal Statistical Society)

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 problem of selection bias. Here we implement an original approach to model custodial and non-custodial sentence outcomes simultaneously while making the most of the information recorded for each of them using a scale of sentence severity. The severity scale is estimated using a Bayesian approximation of Thurstone’s pair comparisons and a sample of 21 magistrates. The severity scores for different types of sentence outcomes are specified using a series of linear models and a sample of 7,242 theft offences sentenced in the Crown Court. Comparing results from a model limited to custodial sentences with another model using all sentence outcomes we can illustrate how pervasive the problem of selection bias, and call to question the external validity of previous studies limited to custodial sentence length.