Numbers: confusing and unreliable

The use of Numbers to demonstrate what's going on is both confusing and unreliable.


Excel snipThis snip on the right shows how false positives affect your actual chance of being infected as percentages vary.

It's easy to understand that if 100% of the population is infected the false positive rate doesn't matter, whether it's 99%, 10% or 0% the tested person IS infected.

Similarly, if 0% of the population is infected the false positive rate doesn't matter, whether it's 99%, 10% or 0% that person has IS NOT infected.

The problem comes in the middle and is easily seen on a spreadsheet. If 1% of the population has the virus and 99% do not, with an FPR of 5% it means that 5% of the 99% would appear to be positive whereas they're not. This means that, with those 1% actual and 5% FPR the chances that a person is truly infected is just 16.8%.

You can download the spreadsheet as xlsx and see for yourself how it works.

The implications for political decisions are huge. If the actual infection rate is low (say 0.8%) and false positives are 2.3% (interquartile range 0.8-4.0%)

the chances are that only 25% of reported infections are true.

But varying those figures to 0.5%/4% gives 11% and for 0.9%/1% gives 47%. From recent (2020-10-23) searches of ONS statistics those are reasonable assumptions. But for either extreme it means that the reported rise in cases (as reported infections by the government's own data) is probably between 10% and 50% of the true figure.

The real problem is that no one knows the actual infection rate - the number of people who are currently infected, which must NOT include those who have had the disease and are no longer infectious (who should therefore give a negative test result). Even the Infection Survey pilot fails to give a useful figure but they guess at 1 in 130 (0.8%).


Not only are the numbers confusing, they are unreliable. You can see above that a small error in genuine attempts to find the right figures is likely to lead to almost any conclusion you're seeking.

However, science has been subjugated to politics. You can safely ignore any politician saying "we're following the science". What they mean is they're promoting selected scientists to justify their policies. In fact, scientists all over the world are at odds with each other on the almost every aspect of the Covid-19. THERE IS NO SCIENTIFIC CONCENSUS.

And if that's not enough reason to doubt the statistics you should also be aware that leaders and governments have been known to cheat and even threaten the lives of statisticians if they tell the truth. Tim Harford (presenter of the Radio 4 programme "more or less"), in his book "How to make the world add up" has a chapter "Don't take statistical bedrock for granted" in which he gives many examples of politicians manipulating statisticians and statistics to suit themselves. But, of course, that couldn't happen here.

Below is an extract from a post by Dr Mike Yeadon on 4th November 2020 in which he urges MPs not to vote for a second lockdown.

Dear Sirs and Madams,

I am an independent scientist of over 30 years experience leading research into new medicines, operating up to Vice President and head of Respiratory Research at Pfizer, a US pharmaceutical company and founder and CEO of Ziarco Ltd a biotechnology company sold to Novartis in 2017.

As an independent I am less constrained than academics and commercial persons. However, I have applied the same rigour to analysing the pandemic since March as with any of my former projects.

The PCR testing machinery is, at best, greatly in error and completely misleading. I have good knowledge of mass testing systems. I have always been deeply worried about polymerase chain reaction (PCR) because of its power, not only to find one molecule as small as a broken fragment of viral RNA and amplify it, sometimes by two to the power of 40, through repeated cycling, but also because it can find something that is not there – it can yield a ‘positive’ result even though the virus is not present. The greater the amplification and the higher the number of tests being done each day day – and the lower the expertise of the staff doing it – the higher the probability of error. I was the person who, with a radio journalist, finally pressed Mr Hancock to disclose the false positive rate of the Pillar 2 test, when it was still measuring far fewer tests per day than now. Having established that false positives exist, it is important to know that the rate of these can be small yet, when the prevalence of the virus is low, many or even all the positive results are false. That’s a practical debate for another time.

Yesterday, in response to a written question, the Government disclosed that while attempts had apparently been made to determine the operational false positive rate, it still doesn’t know it. As an experienced lab scientist, I know that when testing capacity is boosted substantially and the staff recruited have less and less lab experiences, there is only one outcome: errors of handling and of procedure. These in turn destroy the integrity of the testing system. The entire response of the UK depends upon the reliability of these tests. I have to tell you quite firmly: at present, it is practically, logically and legally impossible for anyone to be able to tell you what fraction of the positive tests recently obtained are real and which are not. For a range of reasons related to strong evidence that this virus cannot just hover around as it has been suggested and viruses certainly do not perform waves ever, the most secure conclusion is that these results are not to be trusted and are not reliable in any way.

So what I am saying is this. Despite warnings from all sides over months about this test it has continued to be used with increasing ferocity. It’s a medical diagnostic test. On no occasion would such a diagnostic be put into mass testing – in the NHS, for example – without knowing in advance how reliable it is. In terms of proper characterisation, it has NEVER been measured, despite the war-like impact of the test results on the nation and its people. At a minimum, the charge is reckless endangerment. Given all this information, it is literally impossible to guess whether the FPR is 1% or 10%. If even near the latter, there are no “cases” et seq. And there are other reasons to be very concerned about mass testing which I cannot go into today.

In my view, community mass testing is the pathology in the country now – not the virus. It must cease today. Without the ‘cover’ of mass testing, there is no evidence at all that the health of the nation is under any threat whatsoever. That event occurred in spring and our responses to it have been exaggerated and – what is worse – extraordinarily persistent, even when all the evidence says the pandemic has concluded.

I have a colleague who has a half a dozen sets of data all related to the pandemic. These show clear relationships between the data in the spring, all of which illustrated the impact of the virus. However, time after time, these relationships have broken down. The explanation for this is that at least one of the measurements are wrong, and the culprit is the PCR test. This has happened before. In New Hampshire in the USA there was a hospital that was convinced it had a huge outbreak of whooping cough. Physicians, patients and parents were all very worried about the expected deaths. Eventually, an older physician examined some of the patients and did not agree with the diagnosis. Asking the staff why they were so sure it was whooping cough, the answer was it had been diagnosed by the PCR test, the sole diagnostic tool. A review was ordered and this led to culture of the organism from the suspected patients. There was not a single person who actually had whopping cough. No infectious organism was found. What had happened was a now infamous case of a “PCR False Positive Pseudo-epidemic”. That is what I believe we have now in UK and in many other countries using similar technology.

And here's a piece, also presented on 4th November 2020 from someone employed at a PCR testing site in Salisbury (UK).

Forgive the intrusion but I was given your contact details courtesy of a mutual friend. I realise the gravity of making this information public and genuinely feel that you are best placed to air my concerns about the fundamentally flawed service provided at testing sites. To be specific, the site operating in Salisbury which has been awarded/allocated without tender or public scrutiny to the unlikely coalition of Mitie and Deloitte.

I was accepted for work instantly after applying online at 01.00 in the morning. I filled out a mere two pages of information – no reference checks, no criminal record check, no photographic ID – and started work the following Monday at 08:00. I was deployed into the car park to essentially point and wave at cars for my first two shifts. I was told that we could read books, use our phones and use tablets in our non-customer-facing time. In a 12-hour shift that time could easily be upwards of eight to nine hours. After proving myself with my enthusiastic waving and gesturing to genuinely bemused looking members of the public I was promoted after three days to the PPE team. At this point, I still hadn’t had any non automated contact with the agency which had placed me.

The PPE team as it turned out was indeed a promotion. Along with ensuring the continuous supply of plastic gloves and surgical face masks to staff on site, we were tasked with assembling the MT PCR testing kits. This entailed putting the vials, swabs and instruction leaflets in foil bags. Some bags were sealed if they were for RTS use (mobile units) and others unsealed if for use on the static site. The static site being a special site donated free of charge by Wiltshire Council as it was now redundant as a park-and-ride site. Redundant thanks to lockdown.

It became apparent to me frighteningly quickly how unstructured and chaotic the processes on the site were across the board. I completed two-and-a-half years of a mental heath nursing degree back in 2013 and I realised, thanks to my prior training, we were preparing these tests in a totally non-sterile environment. A bloody shipping container to be precise! I questioned the practice with site management only to be told that they had no formal written policies in place and so procedures were “fluffy”.

Unlike some of my other colleagues, I decided to read the storage instructions that accompanied the containers of the vials. To my horror, it emerged that the formula needed to be stored at between zero and eight degrees Celsius after a sample is taken and then transported to one of the three testing labs in Milton Keynes, all run by Lighthouse. I have photographic evidence of the temperature in one of the unsanitary shipping containers that the tests were stored in prior to collection – it was not between zero and eight. Furthermore, the instructions stated that the sample must be stored and transported upright. Yet at the Salisbury site, the completed tests were put into medex containers on their side with up to 100 samples crammed in. The aforementioned containers were then collected and transported to Milton Keynes by a combination of Royal Mail vans and privately unmarked and undocumented couriers using their own family saloon cars.

I reported my concerns to management but was told that if I had a problem I should contact the CEO of Mitie. Not unsurprisingly, I declined for fear of the retribution that would almost certainly follow. The testing facility itself never had less than 34 staff on site. That’s one thing Mitie had insisted upon and it was strictly adhered to. Not a single staff member involved at any level had any medical training. Not one! The closest to it was an ex-army nurse who no longer held her pin and was allocated to supervise the car park traffic. The Site Lead and the Deputy Site Manager were an ex-para trooper and a DJ from Ibiza. No disrespect to either DJs or para-troopers as they have been part of some of my best nights out ever. They are not, however, the people I want deciding how we store and handle possible COVID-19 samples on a testing site with “fluffy” procedures. From Dido Harding at the top to the unvetted, poorly-educated minions implementing policy at the coal face, not one of these people is remotely qualified for the task in hand.

I was also added to a WhatsApp group for the PPE team which was rather unorthodoxly sent to our private phones. I remained part of the group for weeks after I left the site. I have a record of exactly how many tests were performed each day from the July 29th until October 14th. During this time we were told to limit the amount of tests undertaken each day to 145, despite there being ample capacity and stock. The previous daily record of tests undertaken on our site was 459. No reason was given as to why we should limit testing in this way. Without doubt the highlight of the WhatsApp stream is an email shared between G4S and Mitie about a gentlemen in a white van who appeared at the MTU 179 in Lewisham trying to collect tests with a van covered in graffiti that was full of rubbish and contained a large dog. Incredibly, he appeared to have a medex box from another site that he’d already picked up and was taking to a lab when he was turned away from Lewisham.

In Parliament on 4th November 2020 Mrs Theresa May criticised Labour's call for a short, "circuit breaker" lockdown as impractical - but accused Mr Johnson of choosing data to fit his coronavirus policies.

The lockdown decision was "to some extent based on the prediction of 4,000 deaths a day," said the former PM, but that figure had already been proved "wrong".

"For many people it looks as if the figures are chosen to support the policy, rather than the policy being based on the figures. We need these proper analyses. We need to know the details behind these models."

To quote Abraham Lincoln: "You can fool all the people some of the time and some of the people all the time, but you cannot fool all the people all the time."

I'll admit I was fooled at the beginning of this fiasco but given the amount of information and knowledge gained since March 2020 I am utterly sceptical about the current government policies. Sadly, also concerned for those who remain fooled. I see the emperor has no clothes. Wikpedia explains:

Two swindlers arrive at the capital city of an emperor who spends lavishly on clothing at the expense of state matters. Posing as weavers, they offer to supply him with magnificent clothes that are invisible to those who are stupid or incompetent. The emperor hires them, and they set up looms and go to work. A succession of officials, and then the emperor himself, visit them to check their progress. Each sees that the looms are empty but pretends otherwise to avoid being thought a fool. Finally, the weavers report that the emperor's suit is finished. They mime dressing him and he sets off in a procession before the whole city. The townsfolk uncomfortably go along with the pretense, not wanting to appear inept or stupid, until a child blurts out that the emperor is wearing nothing at all. The people then realize that everyone has been fooled. Although startled, the emperor continues the procession, walking more proudly than ever.

And the two swindlers are...?