BRITAIN’s public services present a conundrum. Internationally, they score highly on efficiency measures. Yet some important outcomes in health and education often lag behind other developed countries. In other words, Britain’s Leviathan provides major services at scale and rather cheaply, but struggles to attain reliably high standards and to match the improvement rate of fast-growing economies in Asia and eastern Europe.

Now a new “Efficiency Index” of education, compublished by the GEMS Education Solutions http://www.edefficiencyindex.com, involving British and Spanish university researchers, attempts to merge data about efficiency and effectiveness and test which countries are best at combining the two. Overall, the winners and losers are not so different to the conclusions of other major studies, like the OECD’s PISA tests and the TIMMS and PIRLS numeracy and literacy check-ups.

But the GEMS research adds a useful value-for-money perspective. The study ranks Britain 11th in the efficiency of its education system, higher than France or Germany (largely because these countries spend excessively on teacher salaries or allow them to a light teaching load). Unsurprisingly, Finland, Japan and South Korea, all regular stars PISA stars, scored highest for both efficiency and effectiveness (some Asian tigers such as Singapore were not included in the GEMS Index; nor was China.)

The most challenging reading for education ministers and the Treasury is the suggestion from comparative data that a similar level of results in Britain could have been achieved even if the pupil-teacher ratio were to rise, or if teacher salaries were to be reduced. Britain thus figures in a group of countries tagged “More efficient than effective”—those that have a good record on efficiency when it comes to using resources sensibly, but get mediocre results. In the same category are other mid-rank performers, including America, Sweden and France. Some countries in this category have more excuses than others. Hungary, Israel and the Czech Republic, for example, all have very low teacher salaries (Hungary decreased its salaries as an austerity measure to just under $15,000 (£9,000) after 2008). But Britain does not pay teachers at all badly. The average salary of $41,000 (£25.000) puts it ahead of other good performers on efficiency in the rich world, such as Norway, with an average teacher salary of $33,570 (just over £20,000).

And yet attainment levels remain depressing. British schools have had lacklustre results in the last two rounds of the OECD’s PISA tests. They were ranked 25th for reading, 28th for maths and 16th for science in 2008. By 2012 Britain remained among the average, middle-ranking countries, in 23rd place for reading, 28th for maths and slipping in science to 21st.

If class sizes compare favourably with other countries and teachers are relatively well paid, something else must be amiss. Countries that rank well on efficiency but not effectiveness should worry that investment in their education systems and sound management of resources is still not catapulting them into the super-league of global performers. The conclusion should not merely be a race to maximise efficiency—Britain could raise its ranking here simply by cutting teacher wages by around 10%, but that is hardly likely. Instead, it needs to work out more rigorously what teachers should be doing differently, apply the best practice more consistently and allow poorly performing schools to be taken over by better ones. The statistical deluge is enlightening. But the factor most likely to make a difference to outcomes is what happens at the chalk face.