Statistics, state benefits, and reproduction: some sort of unholy trinity

Over the past week, there has been some discussion regarding a book written by Adam Perkins (a Lecturer in the Neurobiology of Personality at King’s College London) regarding the impact of state benefits on personal outcomes (the title of the book – “The Welfare Trait: how state benefits affect personality” – probably gives that away).

Of particular focus has been one table that Perkins claims demonstrates that being on benefits is associated with a higher number of children in that household – i.e. that being on state benefits encourages reproduction (according to Perkins). The table, reproduced from here below, appears to indicate that households in which no-one is employed have higher numbers of children than do households with one or two workers.

[Children%2520per%2520household%255B4%255D.png]

Perkins’ conclusions were criticised by Jonathan Portes (a Senior Fellow at the NIESR) for a number of reasons, to which Perkins provided a response – see here.

However, this response is entirely unsatisfactory as it fails to acknowledge the actual problems with using the table above to make meaningful inferences. First, it does nothing to demonstrate that the results in the table are statistically significant – that is to say that the results in the are not just due to “random chance” (i.e. an artefact of the data used) and are, in fact, a “true” result. Without testing the results for statistical significance, there is no way to determine whether or not there is actually a meaningful difference between the number of children in working households as compared to workless household. Indeed, Perkins does not appear to even acknowledge this as an issue of his reliance on this table.

Second, Perkins’ numbers deliberately exclude households in which there are no children. This is an egregious decision that Perkins has tried to justify using baseless arguments. The issue is that Perkins could have deliberately introduced a bias into the numbers in the table that directly affects the inferences drawn from the results in the table. To see this, suppose that a higher proportion of workless households have no children than the proportion of working households that have no children.

Indeed, suppose that 500,000 working households do not have children, but 1,000,000 workless households do not have children. The table below, shows the impact of this hypothetical example – including households that do not have children actually reverses the direction. Once childless households are included in this hypothetical example, workless households actually have fewer children that do working households. Hence, it is essential that the number of childless households are included when trying to see if state benefits affect reproduction.

Hypothetical childless

In fact, when one uses the actual total number of households available from the ONS (rather than the hypothetical example above), we actually find a mixed set of results. The number of children per workless household is indeed lower than the number of children in working and mixed households, but the number of children per mixed household is higher than that in working households.

Actual childless

Hence, Perkins’ conclusions regarding the impact of benefits on reproduction are incorrect. The actual results suggest that there does not appear to be a systematic relationship between the employment status of a household and the number of children in that household. This goes to show how excluding certain groups from a dataset can introduce bias in any results obtained from analysing that dataset.

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