Re-examining Peter Townsend’s Controversial Poverty ‘Threshold’

This blog post is based on an article published in the Journal of Social Policy by Andrew Dunn.

Peter Townsend, best known for his work on poverty and for co-founding the Child Poverty Action Group, was one of the UK’s most celebrated social scientists. His 1968/69 survey is the most lauded UK poverty study of the last century, and its influence is clearly visible in poverty research today. That study pioneered the use of ‘deprivation indicators’, such as lacking a refrigerator, which Townsend formed into a ‘deprivation index’ that counted how many of a possible twelve respondents endured.

Yet controversy surrounded Townsend’s claim that his study established a meaningful poverty ‘threshold’ at an income level equivalent to 140% of means-tested state benefit rates, below which deprivation index scores increased more rapidly in relation to income. Townsend saw establishing this ‘objective’ poverty line as extremely important, as he felt it would put the study of poverty on a proper scientific footing. In support of his claim that his 1968/69 survey’s evidence pointed to the threshold’s existence, he presented what became one of social science’s most well-known graphs. It is recreated here as Figure 1; there is a definite ‘threshold’ effect, with the line steepening below a ‘log-income’ of about 2.1, which translates to about 130% of means-tested benefit rates. Townsend later claimed Meghnad Desai’s more sophisticated analysis of the same data confirmed the threshold’s existence at 150% of the same benefit rates – a claim disputed by some other senior academics.

Some of Townsend’s critics argued that there was no theoretical basis for expecting such a threshold to exist. Townsend did not give them a detailed response, and nor did he write about whether other variables might impact the relationship between income and deprivation. The main criticisms surrounding Townsend’s threshold graph were as follows:

1. It was inappropriate to standardise income for family size and type by measuring it as a percentage of what the family would be entitled to if it relied on means-tested benefit (which was Supplementary Benefit [SB] at the time), as those rates are determined by politicians.
2. Townsend ‘log-transformed’ his income variable (i.e. multiplied it by an algorithm) for his graph, without explaining why.
3. His ‘deprivation index’ included only twelve of his sixty deprivation indicators (Townsend later said it was a ‘pity’ he did not have time to include more).
4. He used ‘mode’ deprivation scores, not the more conventional ‘mean’ or ‘median’ ones. Even though Desai’s analysis used a mean measure, it did not in fact establish a ‘threshold’; it merely tested if the relationship between income and deprivation differed significantly either side of an arbitrary income level chosen by Desai.

My analysis of the 1968/69 data both replicated Townsend’s methods and included tests developed with his critics’ insights in mind. In addition, it measured deprivation levels in income ranges which, unlike Townsend’s, were of equal width. Even when all Townsend’s methods were replicated, including the use of his chosen income ranges, my findings differed from those he presented in Figure 1, as mode deprivation dipped as income fell to its lowest level. I discovered that Townsend’s famous graph was plotted inaccurately; findings presented elsewhere in the same book do not match his graph’s twelve points, while only four of those twelve were rounded/whole numbers, which ‘mode’ scores nearly always are. Nevertheless, my analysis suggested that the first three criticisms that surrounded Townsend’s threshold claim (listed above) appear to be red herrings. Tests using income adjusted for household type and size using the conventional OECD method (not benefit rate entitlement), tests using non-‘logged’ income data, and tests using various combinations of the sixty deprivation indicators all produced a similar pattern of findings to that produced by Townsend’s methods.   

However, my findings differed starkly from Townsend’s when I used income ranges of equal width, even when Townsend’s twelve-item deprivation index and his SB-based income measure were used. Figure 2 shows there is clearly no ‘threshold’, even for mode scores. Indeed, Figure 2 offers a clue about why Townsend’s use of mode scores was so unusual and hence controversial. The graph’s mode scores are easily the most erratic, as modes, unlike means and medians, are often dramatically affected by the presence or absence of just one or two cases.

Remarkably, even when Townsend’s twelve-item deprivation index was employed, mean deprivation decreased significantly in the income range immediately below his ‘threshold’ income level of 140% of SB rates, where he had insisted deprivation began increasing fast. Cohen’s ‘d’ statistical tests helped establish the income point below which deprivation did in fact increase most strongly, which was 119% of SB rates. However, this income level could not be described as a ‘threshold’ of the kind Townsend envisaged, as deprivation plateaued as income fell below it. Thus, my re-examination of the threshold controversy reminds us that, as Arthur Bowley, the prolific poverty researcher who authored the first statistics textbook in the English language, asserted over a century ago, all poverty lines are arbitrary.

Reference

Dunn, Andrew. 2026. “Townsend’s Poverty ‘Threshold’ Revisited: An Analysis That Utilises His Critics’ Insights and All 60 of His Deprivation Indicators.” Journal of Social Policy: 1–22. doi: 10.1017/S0047279426101640.

About the Author

Andrew Dunn is an Independent Scholar and former Senior Lecturer of Social Policy, University of Lincoln, UK.