The usual litany of damning headlines greeted the first annual report from Christine Gilbert, Ofsted’s boss. “Fail, fail, fail”. “One in ten schools let kids down”. “Ofsted speaks: not good enough”. Many teachers must have wondered if the dark days of Chris Woodhead’s name and shame era had returned.

Although the Chief Inspector’s findings were softened with praise for the many schools doing well, the central figures appeared stark, and incontrovertible. One in eight secondary schools were “inadequate”, Ofsted’s figures said.

A further 38 per cent were considered satisfactory. And Ms Gilbert said satisfactory was no longer good enough. Among primaries, 7 per cent were inadequate, while 40 per cent were “less than good” or satisfactory.

Several newspapers cited the report as evidence that Labour was not delivering on the record investment flowing schools’ way.

How justified are these claims? To critics, they are astonishingly unfair.

Headteachers’ leaders say there are serious flaws in using inspection judgments on individual schools to make statements about the quality of all schools.

Close analysis of the way in which inspectors are now judging schools suggests the heads are right. Ofsted verdicts now place great weight on statistical judgments about how good a school’s test and exam results are.

The TES has seen copies of inspection packs in which inspectors are asked to use statistical tools in reaching a verdict on how high standards are in a school.

Each of these tools is framed in the same way: a comparison is made as to how good the school’s results are, compared to the national average. This can be plotted graphically, with the national average represented as a line in the middle. Those schools which finish well above the line are likely to be “outstanding” for standards.

Those slightly above the national norm will be “good”; those in line or slightly below will be “satisfactory”, and those well below the national average will be “inadequate”. What does this allow us to say about standards overall? Virtually nothing, according to the sceptics. For “inadequate” could simply be translated as “below average”, while “satisfactory”, in a system defined such as this, simply means “average”.

It is not surprising, in a regime constructed like this, that many schools will be average, and many will be below average, since by definition all schools cannot be above average. Yet Ofsted and the media appears to be saying it is unacceptable that more schools are not above average. Given how this measurement system worked, how could it be any other way?

To put it another way, if standards improved so that England’s schools were acknowledged as the best in the world, a system which adjudged below average performers as “inadequate” would still generate negative headlines.

Yet “average” schools, by English standards, could be better than those elsewhere. Ofsted’s system offers no comparisons with other countries, or even any sense of how standards have changed.

To use an analogy, one could imagine plotting the heights of everyone in England on a graph. Those below average would then be defined as short, and those above it, tall. It is clear that, on this measure, millions would be classed as tall and millions short.

But is England a nation of short people, or tall? The figures by themselves will not tell us. We can only make such a judgment from a comparison which looks further.

The logical leap that Ofsted and much of the media are asking people to make is to say that because many schools are around or below average, England’s schools system is somehow failing.

“This does not make sense because the statistical measures allow no one to say whether the “average” is any good. All we are told is that “average” is not good enough, that too many schools are in this position, and that they must improve.

Brian Rossiter is head of Valley School, Worksop, said: “If you have a system like this, then you will get outcomes which say some are above average and some below. We cannot all be above.”

Ruth Winterson is head of Neston high, Cheshire, classed as excellent by Ofsted just as Ms Gilbert’s report was published. She said: “In the reporting, both from Ofsted and by the media, it is so important to reflect the balance of what is good and bad. We would never dream of only reporting to parents on the negative aspects of a pupil’s work.”

So is it true that “satisfactory” actually means “average”?

Ofsted said inspectors took into account other aspects of school performance as well comparing them to other institutions. However, it also cited its advice to inspectors on how to categorise schools, which appears to define quality according to whether they are better or worse than others.

With statistical measures now central to everything that goes on in schools, it surely is incumbent on the inspectorate to be clear about its evidence base when making these pronouncements.

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