Ofsted explains in detail how the CVA score works
England's education inspectorate has said that government tables of "top performing" schools are "meaningless".
Ofsted says contextual value added (CVA) scores - taking into account external factors such as poverty - are the best measure of education quality.
But it adds that absolute CVA values or rankings using them have no meaning because of the way they are calculated.
The Department for Children, Schools and Families produces tables of the schools with the highest CVA values.
The CVA scores take into account factors known to affect children's attainment but which are outside a school's control - such as poverty and ethnicity.
So they are regarded as fairer than raw exam results alone.
Each actual CVA figure - based around 1,000 in secondary schools (100 in primaries) - is accompanied by what statisticians call upper and lower confidence intervals, related to how many pupils it has.
So in an example Ofsted gives it may appear that a school with a CVA of 1,009 is doing better than another with a CVA of 992.
"However, that would be incorrect," it says in new guidance to schools about the use of data.
"In both cases, the range between the upper and lower confidence limits includes 1,000, so both schools are achieving average outcomes; their performance is about as expected."
The guidance adds: "No meaning can be attached to an absolute CVA value, and any ranking of schools by their CVA values is meaningless."
The Department for Children, Schools and Families says it does not produce "league tables" because its main "achievement and attainment" tables do not rank schools.
Scores above 1,000 represent schools where students on average made more progress than similar students nationally, while scores below 1,000 represent schools where students made less progress
DCSF: School achievement and attainment tables
It leaves the rankings to the news media.
But it issues news releases with two tables which do rank schools - one on the basis of sustained improvement, the other showing "the top 100 schools using the contextual value added measure".
And in detailed information accompanying the attainment tables, the DCSF says:
"Scores above 1,000 represent schools where students on average made more progress than similar students nationally, while scores below 1,000 represent schools where students made less progress.
It also says: " ... a measure of 1,006 means that on average each of the school's students achieved the equivalent of one GCSE grade higher in one subject than the average attained by similar students."
And: "Conversely, a score of 994 means that the school's students achieved one grade lower in one subject on average, while a score of 952 means that students achieved on average one grade lower in each of their best eight subjects."
It does say that a school CVA measure "must always be interpreted alongside the confidence interval" - but does not publish the confidence intervals in its "top performing" table.
A spokeswoman for the DCSF said: "We do occasionally release lists of the 'most improved' maintained schools in the country. This simply gives credit to schools which are often working in challenging circumstances and which may not have great raw results, but do very well for the pupils they have, and it gives them a chance to have their hard work recognised.''
A spokeswoman for Ofsted said: "The DCSF's table recognised the impact of the cohort size as it was constrained to schools where 30 or more pupils were included in the calculation.
"It also includes a column alongside the CVA value, giving the number of pupils at the end of Key Stage 4. The CVA value in the final column should be interpreted, taking this into account."
In its guidance, Ofsted says school test results will always be questioned because they are "imperfect".
It says: "The data are only as good as the process that produce them, and only reflect attainment as measured by specific exercises undertaken on a specific day.
"Objections will always be possible. It may be argued that assessment is flawed or the exercises test only certain kinds of attainment in certain ways."
But it adds: "Imperfect as they inevitably are, these assessments have been developed and honed over time and their reliability is high."
In a foreword to the report, chief inspector Christine Gilbert says data are valuable but only measure what has been tested.
"And people often only test what they feel they can measure.
"The challenge for schools, and for inspectors, is to understand the data available and get behind the figures to explore the strengths and weaknesses they indicate."