Leading statisticians have cast serious doubt on Jeremy Hunt’s claim that in only 10% of hospitals are patients seen by a senior doctor within 14 hours of being admitted at a weekend, and described it as unfair, misleading and a gross underestimation.

NHS England has also distanced itself from the health secretary’s claim saying the evidence it has collected on hospitals’ performance in this area does not vindicate his interpretation.

The controversy over the accuracy of Hunt’s statement, which he made in parliament, is the second time in recent weeks that questions have been raised about a key plank of his justification for imposing a new contract on junior doctors and turning the NHS into a seven-day service. The row comes as the result of the ballot for strike action by junior doctors emerges on Thursday.

Doctors recently complained to the Cabinet Office that Hunt has also misrepresented key research on how many patients admitted to hospital at the weekend die because too few senior doctors are on duty, and the British Medical Journal, which published the findings, has accused him of misrepresenting them.

The new row is over Hunt’s assertion to MPs, on 28 October, that “currently, across all key specialties, in only 10% of our hospitals are patients seen by a consultant within 14 hours of being admitted at the weekend”.

Three experts in statistics, who at the Guardian’s request reviewed the NHS data on which Hunt based his claim, said that the average percentage of patients assessed by a senior doctor within 14 hours – across all hospitals, specialties and the whole week – is around 79%.

ProfDavid Spiegelhalter, one of Britain’s leading statisticians, said the evidence did not support Hunt’s claim. “The data from NHS England don’t seem to match up with the minister’s statement in the Commons. The average across all hospitals and specialties is 79% seeing a consultant within 14 hours. This gives a somewhat different picture, and more representative of the patient experience.”

Hunt told MPs that the 10% figure was a fact. But Spiegelhalter, Winton professor for the public understanding of risk in the statistical laboratory of Cambridge University, said Hunt’s statement was flawed for two key reasons. “First, the available data are only for emergency admissions. Second, they cover the whole week and not just the weekend.”

NHS England also made clear that “the data does not allow for separate analysis of weekday and weekend performance for this question. Hospitals answer on the basis of the full week. Therefore it is not possible to cut the data by weekday/weekend.”

Dr David Craven, a Royal Society research fellow in Birmingham University’s school of mathematics, said it was simply impossible to arrive at Hunt’s conclusion based on the data. NHS England’s statistics are not a reliable measure of how many patients were seen within 14 hours because the sample sizes are too small, he said.

“The question itself seems to be chosen specifically to make the NHS look bad, and it is not a useful measurement if you want to know what the NHS is really like if you turn up as an emergency, whether on a Monday or a Sunday.”

Craven added: “With regards to extracting weekend data from this, that is simply impossible, using this dataset at least. It only gives averages for the week. That’s like me telling you I had sandwiches three times this week, and you working out if I had one on a Thursday; it simply can’t be done.” On Hunt’s figure, he added: “Prof Spiegelhalter is closer with the figure of four-fifths than one tenth is.”

In the Commons debate, Hunt said: “Let us look at some of the facts. What is the most important thing for people admitted to hospital at the weekend? It is that they are seen quickly by a consultant.” He then made his contentious claim that such patients were seen by a consultant within 14 hours at only 10% of hospitals.

Junior doctors protest against proposed new contracts. Photograph: Paul Stringer/Demotix/Corbis

The dispute is over Hunt’s representation of data collated by NHS England that seeks to capture how many patients admitted to hospital as an emergency, across 11 specialties including cardiology and paediatrics, were seen by a consultant within 14 hours across seven days.

It expects all hospitals to be doing that with at least 90% of patients in every specialty except psychiatry. However, its survey advised hospitals that they can decide to audit10 sets of case notes per specialty to help inform their answer, despite there being many more admissions and thus such reviews representing only a small fraction of the overall number. Overall, 57% of hospitals based their answer on clinical knowledge and the other 43% used samples of 10 case notes, despite concerns that that approach includes so few patients as to be an unreliable indicator of performance.

“It is true that only just over 10% of hospitals can claim that the proportion of patients assessed by a consultant within 14 hours is at least 90% on all specialties. Nevertheless, the average across all hospitals and specialties of the proportions of patients seen by a consultant within 14 hours is around 80%”, said Richard Samworth, professor of statistics at Cambridge University. “While this figure does not take into account the number of patients in each hospital or specialty, it is more representative of emergency admission waiting times from a patient’s perspective.”

Dr Mark Porter, BMA council chair, accused Hunt of cherry-picking statistics.

Heidi Alexander, the shadow health secretary, said Hunt was giving a skewed picture of what the figures show. “As health secretary Jeremy Hunt has a responsibility to present an accurate interpretation of data about the NHS.

“Unfortunately, this isn’t the first time that he has failed to do so. If Jeremy Hunt has made a mistake he ought to apologise and correct the record, but if he has wilfully misled MPs then that is a more serious matter. He needs to urgently clarify his comments.”

Responding to questions about Hunt’s statement, the Department of Health said his 10% figure related to the entire week, even though Hunt specifically said it was for weekend-admitted patients only.

“The health secretary has rightly pointed out that only 10% of hospitals consistently provide the crucial consultant care patients deserve across the week,” a spokeswoman said.

“Without this, patients could be denied important treatment which should always be available to ensure the best clinical outcomes. Far more must be done and we make no apology for highlighting this issue in order to tackle it.”

• This article was updated on 19 November. Hunt claimed that in only 10% of hospitals were patients seen by a consultant at weekends. The article originally stated that he had said 10% of patients went without prompt treatment.