One with a large proportion of pupils from white working class backgrounds is not expected to improve its results as quickly as one with a similar number of Asian children.
Some heads are describing this situation, which has arisen under changes to the inspection regime introduced last term, as obscene.
However, a leading academic said schools were failing ethnic minority pupils if they adopted "colour blind" policies which effectively denied that, nationally, different racial groups performed differently.
The Performance and Assessment report, or Panda, which is sent to schools each autumn and provides data to support their Ofsted self-evaluation has been revised. Under the changes, inspection judgements now take into account not only the progress that pupils make between entering and leaving school, but their social backgrounds.
The thinking behind this "contextual value-added" (CVA) measure is that national figures show that pupils from poorer backgrounds make less progress than their more affluent counterparts.
But the measure also takes into account the varying exam performance of different ethnic minorities. For example, nationally Asian pupils from deprived backgrounds make more progress than deprived white pupils.
Therefore, schools with high proportions of Chinese, Bangladeshi and Indian pupils would be expected to show more progress, under CVA, than those with many white pupils from simliar backgrounds.
Kate Griffin, head of Greenford high in Ealing, west London, said: "The danger is that the new information will lead schools to set different targets for different ethnic groups.We have to bear in mind that different ethnic groups perform differently, nationally. But we cannot take that as something to aim for.
"There is the danger that this will depress expectations for certain groups, and nationally some groups will continue to be far ahead of others."
Roy Ashley is head of Wooton upper, in Bedfordshire, where 4 per cent of pupils are from Indian backgrounds and 6 per cent are from other ethnic minorities.
He said: "If you had two pupils with identical results at key stage 2, would you really be expected to make a different set of predictions for each child, based on their ethnicity? It's obscene."
But Professor David Gillborn, of London university's institute of education, said that "colour blind" approaches to tackling the different performance levels of ethnic groups had failed.
Any approach which recognised this fact was to be welcomed. However, placing too much emphasis on any one statistical approach should be avoided.
An Ofsted spokeswoman said that the changes came about because the inspectorate recognised that there was variation nationally on progress made by different groups of pupils. But schools should not set their pupils targets based on their ethnicity, she said.