In a report you describe two "low-profile North Yorkshire social scientists" who wrote a book about the evils of income inequality, only to find themselves subject to "a wave of brutal attacks" by a "posse of rightwing institutes" staffed by "professional wreckers of ideas" (Spirited defence: how 'ideas wreckers' turned bestseller into political punchbag, 14 August). The victims of the "attacks" are Richard Wilkinson and Kate Pickett, their book is The Spirit Level, and we, apparently, are the "posse".

This depiction of Wilkinson and Pickett as hapless victims of a rightwing conspiracy is absurd. They are well-resourced academics with their own propagandising thinktank (The Equality Trust). We are two self-employed researchers who got interested in testing their claims.

We maintain that The Spirit Level is flawed, but we are not the only ones saying so. Although the authors repeatedly claim an academic consensus supports their book, they have been criticised by leading economists and social scientists, many of them on the left (Christopher Jencks, Andrew Leigh, Angus Deaton, John Kay, John Goldthorpe).

In their book, Wilkinson and Pickett are selective in their choice of countries, excluding unequal countries such as South Korea with strong social profiles that would have undermined their argument. They switch sources, dates and measures of inequality across different graphs to maximise the trends they want to find.

Furthermore, they are selective in their choice of indicators. Imprisonment gets in, but not crime (except homicides). Drugs are in, alcoholism is out. Murder is included, suicide excluded. Government aid is analysed, but charitable donations by individuals are not. Infant mortality is included, HIV infection rates are not. Teenage births are analysed, divorce rates are left out. Using different indicators, we could show (just as misleadingly) that social problems appear worse in more egalitarian countries.

Their graphs, too, are deceptive. They fit straight trend lines to plots heavily skewed by single outliers, producing hopelessly distorted results. They claim, for example, that UK murders would fall by 75% if income inequality were at Swedish levels, but our murder rate is actually lower than Sweden's!

Nor do they check whether their correlations hold across all the countries they look at. Scandinavia does better than us on things like women's rights and teenage births, but is this because of its more equal income distribution, or its different culture and history? When we check whether the same differences occur between other countries with varying levels of income inequality, we find in almost every case that the apparent effect of inequality disappears. Indeed, as your article notes, when one of us demonstrated that their US state data could be better explained by ethnic composition than income inequality, "Wilkinson branded Saunders's attack 'racist'".

Science is about testing empirical claims, which is what we've done. That doesn't make us "ideas wreckers", any more than it justifies comments by correspondents (Letters, 16 August) seeking to marginalise us as "mouthpieces of the rightwing wealthy classes rushing to defend their privileges". It simply means The Spirit Level is bad social science.