Friday 3 November 2017

Prisons, developmental language disorder, and base rates

There's been some interesting discussion on Twitter about the high rate of developmental language disorder (DLD) in the prison population. Some studies give an estimate as high as 50 percent (Anderson et al, 2016), and this has prompted calls for speech-language therapy services to be involved in the working with offenders. Work by Pam Snow and others has documented the difficulties of navigating the justice system if your understanding and ability to express yourself are limited.

This is important work, but I have worried from time to time about the potential for misunderstanding. In particular, if you are a parent of a child with DLD, should you be alarmed at the prospect that your offspring will be incarcerated? So I wanted to give a brief explainer that offers some reassurance.

The simplest way to explain it is to think about gender. I've been delving into the latest national statistics for this post, and found that the UK prison population this year contained 82,314 men, but a mere 4,013 women. That's a staggering difference, but we don't conclude that because most criminals are men, therefore most men are criminals. This is because we have to take into account base rates: the proportion of the general population who are in prison. Another set of government statistics estimates the UK population as around 64.6 million, about half of whom are male, and 81% are adults. So a relatively small proportion of the adult population is in prison, and the numbers of non-criminal men vastly outnumber the number of criminal men.

I did similar sums for DLD, using data from Norbury et al (2016) to estimate a population prevalence of 7% in adult males, and plugging in that relatively high figure of 50% of prisoners with DLD. The figures look like this.

Numbers (in thousands) assuming 7% prevalence of DLD and 50% DLD in prisoners*
As you can see, according to this scenario, the probability of going to prison is much greater for those with DLD than for those without DLD (2.24% DLD vs 0.17% without DLD), but the absolute probability is still very low – 98% of those with DLD will not be incarcerated.

The so-called base rate fallacy is a common error in logical reasoning. It seems natural to conclude that if A is associated with B, then B must be associated with A. Statistically, that is true, but if A is extremely rare, then the likelihood of B given A can be considerably less than the likelihood of A given B.

So I don't think therefore that we need to seek explanations for the apparent inconsistency that's being flagged up on Twitter between rates of incarceration in studies of those with DLD, vs rates of DLD in those who are incarcerated. It could just be the consequence of the low base rate of incarceration.

Anderson et al (2016) Language impairments among youth offenders: A systematic review. Children and Youth Services Review, 65, 195-203.

Norbury, C. F.,  et al. (2016). The impact of nonverbal ability on prevalence and clinical presentation of language disorder: evidence from a population study. Journal of Child Psychology and Psychiatry, 57, 1247-1257.

*An R script for generating this figure can be found here.

Postscript - 4th November 2017
The Twitter discussion has continued and drawn attention to further sources of information on rates of language and related problems in prison populations. Happy to add these here if people can send sources:

Talbot, J. (2008). No One Knows: Report and Final Recommendations. Report by Prison Reform Trust. 

House of Commons Justice Committee (2016) The Treatment of Young Adults in the Criminal Justice System.  Report HC 169.


  1. I'm not sure 2.24% is reassuring. Would parents be happy to be put in a random draw with a 1 in 45 chance of their child being in prison? Secondly it's a point-in-time probability of being in prison - lifetime likelihood could be much higher. Thirdly risk (which is what causes people to be alarmed) is about consequences as well as likelihood. The consequences of going to prison (for mental health, employment, life expectancy and so on) are pretty severe.

  2. Your post is really very interesting! It got me thinking about the comorbidity between ADHD and DLD, described by many studies, and the high prevalence of adult ADHD among inmates, described by other studies. I would love to read your opinion.

  3. Thanks for an excellent post on base rates. It seems to be an incredibly difficult concept to master and I am forever having to force myself to consider it---and then grab pencil and paper to check that my first reading of something really was wrong (again!).

    This is a nice example/reminder for me and for others to whom I can pass in on.

  4. Thanks for blogging about this important issue Dorothy. I am constantly reminding journalists that elevated rates of DLD in youth justice populations do not mean that parents should be anxious about future incarceration, as that is obviously a low-probability (though rather catastrophic) outcome.
    We should all be concerned, however, about the confluence of risks present in the lives of young people who are in what has been referred to as the "school-to-prison pipeline" (see the US work of Christle & Jolivette). This is invariably associated with academic under-achievement, with poor literacy skills as a central feature. I am increasingly at pains to point out too that we should not interpret the word "prison" too literally, as social marginalisation and being locked out of the economic mainstream is a form of longterm imprisonment, though not necessarily as conspicuous to others.
    These young people also typically have lives characterised by high numbers of adverse childhood experiences (ironically abbreviated as "ACEs" - see It's not possible from our research to tease out the nature/nurture question, but the presence of ACEs suggests that early language development is vulnerable in the face of various forms of early maltreatment (neglect, abuse, high stress etc) - all of which work against a positive interpersonal space in which language development can flourish.
    However the very small numbers of young people who are incarcerated (with the unfortunate exception of the USA) are just the tip of a much bigger iceberg, and there are many who do not end up formally incarcerated, but are never-the-less excluded from the mainstream.
    It would be great to see some large-scale longitudinal cohort studies in this space to tease out the nature of the complex inter-relationships.