The Royal Statistical Society has described Ofqual’s defence of the gagging clause that it asked statisticians, offering help on its grading algorithm, to sign as “desperate”.

The RSS also said the “allegations” that Ofqual had made against it in response to the society’s concerns about the non-disclosure agreement were “baseless”.

Asked what he thought about Ofqual’s line of defence that its confidentiality agreement was not precluding anyone from commenting on the model, Stian Westlake, chief executive of the RSS, said: “Frankly, this is pretty desperate stuff from Ofqual at this stage. The confidentiality agreement that they asked our expert statisticians to sign before they would consider their help was what one lawyer I showed it to called ‘very widely drafted’.”

Exams crisis: Ofqual hits back at stats society claims

GCSEs and A levels: Stats watchdog to probe algorithm

A-level and GCSE grades U-turn: How did we get here?

Speaking on BBC radio, Mr Westlake explained that the agreement would have prevented the statisticians from commenting on any information that was discussed in private with Ofqual and that the regulator choose not to publish.

GCSE and A-level results: Ofqual in row over non-disclosure agreement

He said: “In the end, they published the methodology document [about the algorithm] but the decisions that went into it, decisions about like trade-offs, key issues like grade inflation versus individual accounts, that would have been up to Ofqual whether we could have discussed that.”

Mr Westlake said that when the statisticians were asked to sign the agreement, they had no way of knowing what Ofqual would have chosen to publish and that now a “lively discussion” was taking place, information about how the model was chosen should be made public. He noted that had the RSS’ statisticians signed the confidentiality agreement, they wouldn’t be able to discuss it now.

He said: “As you have seen, there is a lot of information about how the model was chosen that is still not in the public domain. The minutes of those discussions are not in the public domain and, had our experts signed that agreement, these people who have professional reputations and professional integrity would, if they were honouring that agreement, be bound by that, not be able to have an open discussion even now.”

Commenting on the letter that Ofqual sent on Friday, which suggested the society had created “widespread misunderstanding and suspicion of Ofqual’s process”, Mr Westlake said: “I was surprised by the response. I imagined Ofqual were busy with other things at the moment.

“I would say that we are very happy to enter into a dialogue with them. We are very happy if they find it useful to publish our interactions with them.

“I would note that Ofqual are much prompter in responding to our email than they were in responding to our initial concern, where we got a partial response to our questions after 51 days, and they seem a lot quicker on the mark now.”

He added: “I think the allegations they made against us in the letter are baseless.”

Ofqual said it did not wish to comment beyond what it had said in Friday’s letter.