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There has been widespread concern about the fairness of the 'calculated' results
A-level grades awarded in sixth form colleges this year fell below the average of the last three years in England, new analysis suggests.
The Sixth Form Colleges Association said its research is evidence that students in larger institutions have been failed by this year's system.
Almost 40% of A-level grades awarded on Thursday in England were lower than teachers' predictions.
The government has defended the approach it used to determine grades.
Students, who were not able to sit exams this year because of the coronavirus pandemic, had 280,000 A-level results downgraded.
Exam regulator Ofqual has faced criticism over the statistical model it used to decide the grades.
Many students are expected to appeal, although there has been confusion over the appeals process after Ofqual withdrew its guidance for challenging results within hours of publishing it on Saturday.
New guidelines are still being drawn up by Ofqual, the Department for Education said on Sunday evening.
Hundreds of students held a demonstration in central London on Sunday to demand clarity over the appeals procedure.
Prime Minister Boris Johnson has been told by Labour leader Sir Keir Starmer that he needs to take "personal responsibility" and "fix" the situation.
The Sixth Form Colleges Association (SFCA) said it looked at 65,000 exam entries in 41 subjects from sixth form colleges and found that grades were 20% lower than historic performances for similar students in those colleges.
It said that this equated to "12,048 missing grades" in those colleges alone.
For example, in Biology, it found that 24% of sixth form college students were awarded a grade lower than similar students in recent years.
The SFCA said its analysis of 41 subjects had not found a single one where the results were above the three-year average.
Ofqual states that its objective for A-level results this year was to ensure "national results are broadly similar to previous years".
SFCA said its research showed that Ofqual had "failed" to meet that "fundamental objective" and the model it used had "not only failed to produce broadly similar results, but has in fact produced worse results in every single subject".
Bill Watkin, chief executive of the SFCA, said Ofqual should "immediately recalibrate and rerun the model to provide all students with an accurate grade".
"Should this still fail to produce results that are broadly similar to previous years, students should be awarded the grades predicted by teachers (known as centre assessed grades)," he said.
Dr Mark Fenton, chief executive of the Grammar School Heads Association, said the results had also been unfair to some of its students.
He told the BBC that "a great injustice has been done" with "utterly baffling" results for some students.
He said the "only fair outcome" available would be to revert to the grade predicted by teachers and for the limit of 5% extra university places in England to be lifted.
The cap on increasing student numbers for each university was put in place by ministers to prevent academically selective universities recruiting heavily to make up for a fall in international students.
"Natural justice must surely now trump the understandable desire to maintain national standards in this, the most exceptional of years," Dr Fenton added.
Three of Oxford University's colleges - Worcester, Wadham and, as of Sunday evening, St Edmund Hall - have confirmed that all places offered to UK students will be secured irrespective of their A-level results.
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After exams were cancelled due to the coronavirus pandemic, grades were awarded using a controversial modelling system, with the key factors being the ranking order of pupils and the previous exam results of schools and colleges.
Ahead of GCSE results due to be released on Thursday, former Conservative Education Secretary Lord Kenneth Baker urged the government to delay the publication of grades until the situation surrounding A-levels had been resolved.
"If you are in a hole, stop digging," Lord Baker said.
The statistical model used by Ofqual faces two legal challenges, with students arguing they were unfairly judged on the school they attend.
Before results were released, the Department for Education announced a "triple-lock", which meant that students could accept the grade calculated by Ofqual, appeal to receive a "valid mock result" or sit autumn exams.
The government announced on Friday that schools would not have to pay to appeal against exam grades.
In England, 36% of entries had grades lower than their teachers predicted and 3% were down two grades. A similar situation in Scotland saw a U-turn by the government, which agreed to accept teacher estimates of scores.
