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The UK’s statistics watchdog has warned Matt Hancock that government figures used on Covid-19 testing are neither “complete” nor “comprehensible”.

In a fresh rebuke to the health secretary, the UK Statistics Authority has written to him to express a raft of concerns about “misleading” data presentation.

It singles out the heavily criticised decision of the government to classify tests posted out as the equivalent to tests actually carried out.

The move, seen as a dodge by critics, meant that Hancock was able to meet his 100,000 daily testing target by the end of April.

HuffPost UK revealed last week that the UK Statistics Authority had remaining concerns despite a letter from Hancock attempting to respond to a previous warning about his use of statistics.

Now its chairman Sir David Norgrove has written again directly to the health secretary to make plain his continuing worries about the use of statistics.

In his letter released on Tuesday, Norgrove said “the figures are still far from complete and comprehensible” despite attempts by Hancock to address his concerns.

“The testing statistics still fall well short of its expectations. It is not surprising that given their inadequacy, data on testing are so widely criticised and often mistrusted,” Norgrove said.

He said the current statistics on testing fail to help the public understand the pandemic properly or to help manage the new NHS Test and Trace system. Statistics on testing perhaps serve two main purposes.

“The aim seems to be to show the largest possible number of tests, even at the expense of understanding. It is also hard to believe the statistics work to support the testing programme itself. The statistics and analysis serve neither purpose well,” he said.

Among the raft of issues he raises are the controversial decision to classify test swabs sent in the post as tests actually completed.

The most recent figures show that of the 115,725 tests counted as done, some 42,139 were in fact merely swabs put in the post.

“The headline total of tests adds together tests carried out with tests posted out. This distinction is too often elided during the presentation at the daily press conference, where the relevant figure may misleadingly be described simply as the number of tests carried out,” Norgrove writes.

“There are no data on how many of the tests posted out are in fact then successfully completed. The slides used in the daily press conference do not show the date when the tests were carried out.”

Norgrove had already told Hancock on May 11 that he had concerns about the “trustworthiness” of the way the government was presenting and counting its numbers of tests for the virus.

Letters to ministers from the watchdog are extremely rare and to have two within a few weeks underlines how seriously it takes the issue.

In the latest missive, Norgrove further says it is “not clear from the published data how often” people are tested more than once for the virus. “More generally the testing figures are presented in a way that is difficult to understand,” he writes.

He also advises that test results should have a breakdown of various characteristics of those tested.

That should “include key types of employment (e.g. medical staff, care staff), age, sex and location (by geography and place, such as care homes). How many people in what circumstances are infected? Where do they live?”

With the government relying on its new NHS Test and Trace scheme as a way out of the lockdown measures, the watchdog is scathing about the figures being relied upon

“For Test and Trace it is important that a statement of the key metrics to measure its success should be developed systematically, and published, to avoid the situation that has arisen in relation to the testing programme.

“The statistics will need to be capable of being related to the wider testing data and readily understood by the public, through for example population adjusted maps of hotspots.”

Shadow health secretary Jonathan Ashworth said: “Following the Cummings scandal it’s vital ministers rebuild trust in their strategy especially as we want the public to adhere to social distancing to keep everyone safe.

 “This intervention from the UK statistics authority is damning. For test and trace to be effective we all need confidence in the data.”

Liberal Democrat MP Layla Moran pounced on the watchdog’s latest letter, saying it highlighted a “shocking misuse and spinning of statistics”.

“The number of tests posted out is not the same as the number of people actually tested. Everyone sees through this and all it does, in the end, is erode trust in politics and politicians.”

A Department of Health and Social Care spokesperson said: “The Secretary of State has spoken to Sir David and reiterated the Department’s commitment to continuing to work closely with the UKSA to address their concerns.

“We have sought to work closely with the UKSA throughout our response to coronavirus to ensure statistics, which are prepared in very challenging circumstances, are presented in the best way possible.

“Our approach throughout has been to increase transparency around the government’s response to coronavirus.”