The UK currently has 1,657,270 positive cases of COVID-19

[Yavin4]

Last edited Mon Jul 5, 2021, 08:19 PM - Edit history (1)

https://coronavirus.data.gov.uk/easy_read

According to the UK's official daily summary:

Between 28 June 2021 and 4 July 2021, there have been 7,163,729 tests.

Between 29 June 2021 and 5 July 2021, 178,128 people had a confirmed positive test result.

That works out to be a positive rate of 0.025. Using basic statistics, we can say that the positive rate for the entire population of the UK is (66,650,000 * 0.025) or 1,657,270 within a 99% confidence interval. We can say 99% because the total number of tests taken far exceeds the sample size required for a 99% confidence interval for the size of the UK population.

Currently, 1905 have been hospitalized or 0.00115 of the population total of positive cases (1905/1,657,270).

In the past month, there have been 448 deaths or 0.00027 of the population total of positive cases (448/1,657,270).

My math may be off. Please free to check and correct anything that I may have gotten wrong. However, this is what COVID zero looks like. It is not going to be zero cases. It can never be zero cases. Rather, it's the percentage of very negative outcomes to the percentage of total positive cases. In the UK, that's essentially zero. This is the results of their vaccine program and natural immunity to the virus. The same may be true for Israel, but I have not checked their numbers.

ON EDIT:

The UK tests over 7 million people a week. Just yesterday, they tested 1.276 million people. That's more than enough for a representative, random sample.

Read this page for more details about their testing:
https://coronavirus.data.gov.uk/details/testing

[RockRaven]

1. Correct me if I'm wrong, but they're not testing random samples of the population, are they?

Why are you assuming that the test positivity ratio is generalizable/applicable to the entire UK population? Aren't the people being tested a non-representative sample of UK residents?

[Yavin4]

3. They're doing over 7 million tests a week

That's more than enough for a representative sample for the entire population. Also, we can generalize a sample to the entire population when the sample size is of a sufficient size as is the case here.

[RockRaven]

5. The large size of the sample doesn't fix the selection bias problem.

How do you think they decide who to perform those tests on?

[Yavin4]

8. I don't have insight into who or how their tests are done.

But it's safe to assume that 7 million is large enough to be a representational sample for the entire population.

[RockRaven]

13. The opposite, actually.

[BannonsLiver]

16. No, I had it just right.

It’s not gloomy and doomy enough so the usual folks are trying to pick at it. Have seen this movie many many times before.

[RockRaven]

12. Not when the large sample is selected in a non-random manner. The size does not make it

inherently representational. Please read up on sampling bias.

[Yavin4]

18. I understand sampling bias.

The UK has conducted over 200 million tests. Yesterday, they did 1.2 million tests alone. There's only 66 million people in their country. Their testing is probably the most comprehensive in the world.

https://coronavirus.data.gov.uk/details/testing

[Ms. Toad]

31. Obviously, you don't.

Based on the numbers you are citing, you believe that quantity = representative. That is nonsense.

[Yavin4]

34. The UK has conducted over 200 million tests.

They've tested 3,190,695 per 1 million of its population (Citation: https://www.worldometers.info/coronavirus/)

If 7 million is not a representative sample, then all of the opinion polls showing Biden's approval rating should be thrown out as well. They only have sample sizes of 1000 or so. (Citation: https://projects.fivethirtyeight.com/biden-approval-rating/)

[Ms. Toad]

37. You are still missing the difference between size of sample,

and representation.

You keep focusing on quantity - and lots of tests does not make the tested group representative of the general population.

Let's make it concrete. Because the data isn't available, we'll need to make some reasonable assumptions:

Let's say:

half of the testing is done because people are symptomatic (40%) or were exposed (10%),
30% of the testing is due to travel (I think that's high - but just to put a concrete number to the reason you suggested is the reason people are testing), and
20% are people who have just randomly decided they needed a COVID 19 test for the heeck of it.

Further - of these groups:
those who have symptoms are most likely to be positive (let's say 5.9% - within the range of % positive tests I have been able to find for people who are testing because they are symptomatic),
and let's say roughly half as many positive tests (3%) for those who were exposed, but have no symptoms - they are likely to have a lower positive rate because they are not symptomatic - but higher the general population because they were exposed.
Those testing due to travel have probably been taking precautions - they are likely to be pretty low - let's say .42%, and those randomly testing probably haven't been taking precautions - so they are slightly higher - let's say .65%.

If you calculate it out using the numbers from your first post, that mix gives you the overall 2.5% positivity rate you calculated.

Now - moving to the population as a whole:

most people who are symptomatic are going to get tested. Let's say 80% got tested. That means that there are an additional 20% in the general population who have symptoms, but didn't bother to get tested. They will be positive at roughly the same rate as those exposed and tested.

Probably considerably fewer of those who were merely exposed got tested - so let's say that's 50% got tested - the other 50% didn't bother (but will be positive at roughly the same rate as the tested group).

If you need to be tested for travel, you would have been tested, so no additional predicted positives there

Which leaves everyone else (62,409,072 or so) represented by the 20% of the tested population who just likes to take tests - and who will presumably be positive at about the same rate as the randomly tested population.

That gives us:

211,330 positive tests among those who had symptoms and either got tested (2,865,492) - or should have (716,373) @ a 6% rate

17,193 positive tests among those who were exposed and either got tested (286,549) or should have but didn't (286549) - @ a 3% rate)

361 positive tests among those who were tested for travel - @ .42% positive

405,659 positive tests among those who were randomly tested (17193) or weren't (62,409,072)

That's a total of 634,543 positives - or predicted positives (not 1,657,270) because the representation in the sample did not match the distribution in the population and because the sample was self-selected in a way that generates an artificially high positivity rate.



I have tried to make these numbers as realistic as possible, but I am not asserting they are the actual numbers. The mix I have created has the same positivity as you calculated - BUT - when extended to the population as a whole - generates a number of presumed positive individuals about 40% of the number you suggested. The point of this is to demonstrate a concept you seem unable to grasp.

The positivity rates in the 4 groups are within the ranges I have been able to find. And I'm pretty sure my assumptions about the split in the general population relative to the sample tested are realistic - largely that most of the untested population will be represented by a small portion of those tested who were not being tested for any particular reason - and are thus far more likely to be negative. Obviously there may be more reasons to be tested - each of which would have its own characteristic positivity rate.

But the big point is that the mix matters. If your sample - regardless of how large it is - does not match the mix in the actual population, you cannot, with any statistical validity, calculate an overall percentage for the tested group and extend it to the population as a whole.

Because you are asserting the extension is valid, it is your obligation to demonstrate that (1) positivity rate is the same regardless of the reason for testing or (2) the mix in the tested group mirrors the population as a whole.

As to sample sizes being accurate as to Biden's approval rating - they pay people big bucks to ensure that their small sample is representative, the step you are completely ignoring when you calculate an overall positivity rating and try to extend it to the population as a whole.

[Ms. Toad]

20. And that is precisely why you can't extrapolate.

In order to extrapolate from a sample to the whole, you need to know why their tests were drawn so you can adjust the positivity rate for each component population based on what portion of the population as a whole it comprises.

[BigmanPigman]

2. I have been tracking Russia and the UK

and they have been similar in increasing numbers of new cases. Then there is a huge difference. While the UK has very few deaths, Russia has a ton and is worse now than at any time since Covid began.

https://www.worldometers.info/coronavirus/country/russia/

https://www.worldometers.info/coronavirus/country/uk/

[Yavin4]

4. Yep.

More confirmation of the effectiveness of the vaccines.

[Shermann]

11. Except Sputnik V... nt

[ecstatic]

6. What about the US?

Are we near that here too?

[Ms. Toad]

7. People generally test when there is a reason to test.

So it is simply not statistically valid to extend the number of positives confirmed in a population which is predisposed ot be positve to the entire population.

[Yavin4]

10. 7 million people?

Given the UK's population, a representative sample would only need 10,000 people, and they're testing 7 million.

[Ms. Toad]

17. A representative sample must still proportionately mirror the population.

Testing is not a random process - it is heavly biased toward people who have some reason to believe they have COVID.

For example - if you went to the southern US states and surveyed 7 million people as to whether they spoke Spanish - would you really expect to be able to just multiply that ratio by the population of the US and accurately predict how many Spanish speakers there are in the entire country?

That's one of the reasons that using land lines for political surveys is generally not considered valid. The population which still relies on land lines is not represesntative of the population as a whole. It skews older, and likely more conservative.

To extend from a representative sample ot the general population, the sample has to be truly representative - it is not just quantity that matters. The distribution must match the population as a whole as to the relevant variable.

Good statisticians can adjust for some of that - but to do so you need to know what the mix is, and how it compares to the population as a whole. You have made no attempt to do that - and I would be incredibly surprised if that data is even compiled anyplace publically available.

[NickB79]

19. It's like extrapolating STD positivity rates to the general population

You'll come to believe almost every adult in the country has some type of STD.

The reason this doesn't work is that people generally don't ask for an STD test unless they have a reasonable worry they may have an STD, whether it's from actual symptoms or exposure.

The same applies to Covid testing. People choose to get tested, and not for fun.

[Ms. Toad]

22. Perfect example.

There are other times people get COVID tests (e.g. prior to surgery) - but the general principle holds. Most of the people getting tested have symptoms or have reason to believe they have been exposed.

[Yavin4]

29. You are correct, but it's not the same as extrapolating STD positivity rates.

If over a million STD tests were being done on a daily basis, then yes, you can extrapolate to the general population.

[Yavin4]

21. They test over 1 million people a day.

They get tested for variety of reasons, travel abroad being the most common. But with 7 million people a week, that's a pretty representative sample.

On this page, they tested 1.276 million NEW test just yesterday.

https://coronavirus.data.gov.uk/details/testing

[Ms. Toad]

25. Quantity means next to NOTHING

Representative is NOT quantity - representative means it represents the population. People who get COVID tests are far more likely to be positive because they are testing for a reason. They have symptoms or believe they have been exposed.

This is part of the math illiteracy I've been fighting as to the COVID data out there. As someone suggested earlier, do some research on sample bias. You don't understand what you are talking about if you truly beieve you can overcome sample bias just by having a large enough quantity.

[Yavin4]

28. You are making assumptions without any evidence or facts.

You assume that the tests are not representative. Where is your evidence to support your assumption? If over 200 million tests in the UK are not "representative" for a country of 66 million, then you need to provide evidence that it's not. You have provided none.

You assume that only people who are sick get tested for covid in the UK. That's also not true. Many people get tested because it's a travel requirement.

Just because my opinion does not concur with yours, that does not make it "math illiteracy". Far from it, you have confirmation bias in that you only want to believe data that supports your position, and you don't have any counter evidence for positions that contradict your bias.

[Ms. Toad]

30. You are the one asserting a number that cannot be supported

unless the sample is representative.

Its on you to justify that the sample is not only large enough, but representative.

It is math illiteracy, at its most basic, to pretend that you can just multiply the ratio of positive tests in a self-selected sample times the population at large. And since I have two math degrees, and taught math for 11 years, I'm well-suited to recognize math illiteracy. Identifying it as such has nothing to do with confirmation bias. I follow the math where it leads me. Not vice versa.

The most basic question you have to ask yourself when trying to justify extrapolating from a very small sample to a population as a whole, is to identify whether the populations are similar enough to justify it.

You have not justified why your sample, whether 10,000 or 7 million is representative of the population of the UK as a whole as to infection with COVID 19.

[Tribetime]

32. When you talk about 7 million and not 700

I agree with yavin

[Ms. Toad]

33. Quantity only alters the need for representation

if the sample is random.

This is a non-random self-selected sample, which will be biased because one of the main reasons for testing is because of symptoms or exposure. That means it will skew towards higher positivity than the population as a whole.

[Yavin4]

35. The UK leads all of Europe in the number of tests done.

It's well over 200 million. Their population is only 68 million. What are you talking about? They test for travel. They test for attendance at Wimbeldon:

Do I need to test before attending?
As part of the ERP, every spectator at the championships will be required to prove their Covid status on arrival, with stewards checking and then handing out wristbands.

https://inews.co.uk/sport/tennis/wimbledon-2021-tickets-how-get-buy-centre-court-capacity-covid-restrictions-explained-1087190

[Ms. Toad]

38. Completely irrelevant -

You are still fixated on quantity - and quantity, alone, does not guarantee that those tested represent the population as a whole. See the lengthy explanation above.

To take your assmption to the extreme - that 7 million testing sample could have managed to catch every single positive case in the UK. If so, there would be a grand total of 178,128 cases in the UK, not roughly 10 times that many, as you claim.

Until you know the mix of people tested (why they were tested, and the positive rate for sub-groups of people tested for that reason), you simply cannot, with statistical validity, use a large sample as a representative one simply because it is large.

You have numerous people in this thread telling you exactly the same thing. You might want to do some research on how to construct a valid sample group, rather than just searching for larger and larger testing quantities.

[Yavin4]

43. Numerous people in this thread simply do not understand basic statistics.

The 7 million tested is on a weekly basis. So, are you telling me that 7 million people suspect that they're ill every single week? It's absurd.

[muriel_volestrangler]

45. No; schools do a lot of regular tests, and so do care homes and hospitals

People who have been in contact with known cases are tested far more than the general population.

You keep claiming this is about "basic statistics". Your argument is not. You think that there is a country where the only tests conducted are random ones. There's nowhere in the world that's doing that. Why would they? Why would you think that they would? What actually would be absurd is someone saying "I've got symptoms, I need a test" or "I need proof I haven't got covid, since I need to travel" and the state replying "no, only people chosen at random can be tested - all tests that have a reason are forbidden".

You are conflating "lots of tests" with "test subjects chosen at random". That would be an awful mistake to make in any form of statistics, because it's a mistake at a more fundamental level than statistics.

[Yavin4]

48. Schools, care homes, people attending Wimbeldon, people traveling abroad, people coming home

from abroad, mobile tests in the streets, etc. etc.

That looks like a pretty representational sample to me.

And if we're throwing this sample out, then every single Biden approval poll needs to be discarded as well, right?

[muriel_volestrangler]

54. Wrong. I think you are now winding us up, but it isn't funny.

Your OP is still on DU, giving false information. You may be enjoying pissing around, claiming that throwing out a few categories is "a pretty representational sample", but when you've been telling other people they don't understand statistics, you can't play dumb just for comic effect.

You need to delete your OP. It's a disgrace.

[Ms. Toad]

46. You are the one who does not understand basic statistics,

And you obviously didn't even bother to review the example I gave you of a mix.

Further - You are the one proclaiming that extending the sample to the entire population is statistically valid. The onus of proving it is a valid assumption is on you. Put up (by demonstrating the mix is equivalent) or shut up.

[Yavin4]

47. You need to show me where the bias is in the sample.

You still have not done so. You've used conjecture and group think to prove your point which is not proof. It's you that needs to re-learn inferential statistics, not me. I've seen no evidence that the tests they're doing is biased or unrepresentative in any way. They test a variety of people in a variety of ways. It's not just the ones that are sick.

If we're going to throw out the UK's testing data, then we'd have to throw out ALL testing data.

[Ms. Toad]

50. A sample is presumed to be biased,

unless it is carefully constructed to avoid bias. That is statistics 101. You, so far, have not demonstrated that the tested population was carefully constructed to avoid bias.

No one is suggesting they don't test "a variety of people in a variety of ways." That isn't what matters to create a representative sample. What matters is that the mix in your sample matches the mix in the population. If it doesn't, you can't just just calculate the positivity rate of the whole by simple multiplication. It is always up to the person insisting that is possibl to demonstrate that the mix is truly representative.

No one, not a single person in this thread, is suggesting throwing out testing data. What we are telling you is that until you prove the sample was representative of the population of the UK, it is statistically invalid to suggest that all you have to do is to multiply the ratio of positive to testec by the population of the UK to determine how many people are currently positive.

You obviously are clueless as to sample bias, and are unwilling to take basic educational steps to find a clue.

We have nothing more to discuss until you - the proponent of a simple proportionality calculation - demonstrate such an extension is valid by providing the mix of those being tested demonstrate it matches the mix of the population as a whole.

[BGBD]

36. There's a historic example for this

The 1936 "Literary Digest" poll surveys 2.5 million people, in an election with just over 40 million votes, and managed to predict that Landon would beat FDR 57-43.....FDR of course went on to win 62-38. That's missing the prediction by 38 points. The size of the sample doesn't matter unless it was randomly selected and then the results weighted to match the population.

[Ms. Toad]

39. Yup. But that point isn't getting across, for some reason. n/t

[Yavin4]

42. Election sampling is completely different

because you don't know the population of the final electorate. Also, how the Literary Digest conducted its poll is unknown. We know how the UK conducts its testing every week.

[Ms. Toad]

51. Then explain the mix -

If you know, then provide the data and demonstrate that it matches the population as a whole. It's as simple as that.

[ismnotwasm]

14. In the well vaccinated Seattle area, cases are dropping

And It’s glorious. My hospital was so full we went in divert—this was last week WITHOUT a covid crises.

What I and others personally am expecting is a smaller, fifth wave of unvaccinated individuals as summer gatherings heat up.


I am not enthusiastic about this, but we will care for everyone, no matter how poor their choices are

[Dave says]

15. Probably already said

You can’t simply extrapolate from the positivity rates. The numbers have bias. The tests weren’t random (my guess), so they’re somewhat ‘self-selected’. I don’t know to what degree they’re biased, but the overall infections is some number less than 1,657,270.

[IbogaProject]

23. Many sick are getting tested

I doubt you can extrapolate like that, as many won't need to be tested, if they are w/o symptoms or a reason to get tested, like travel.

[Yavin4]

26. People in the UK get tested for a variety of reasons.

For example, it's a travel requirement. It's not just the sick.

[NickB79]

24. At that rate, the entire nation would be infected in 40 days

Which is statistically impossible, given almost 18 months of prior spread (providing a degree of natural immunity to many millions) and widespread vaccinations.

There literally aren't enough susceptible people in the nation to sustain such a spread.

[Yavin4]

27. Not quite.

That would be true if the positivity rate from the daily tests grew each day.

[muriel_volestrangler]

40. From the Office for National Statistics, it's about 257,000 at 26th June

As many have pointed out, a large number (in fact, most) of the tests are not 'random', so your calculations in the OP do not produce a meaningful figure. However, the Office for National Statistics does use its expertise and knowledge of how the tests are done to produce a proper figure. The latest result is here:

https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/2july2021

There is also a study that does sample people in England truly at random - 'REACT' (I took part in this a few months ago, and didn't have covid). This reports every month, and its last one was for samples taken from 20th May to 7th June.

https://www.imperial.ac.uk/news/224113/coronavirus-infections-rising-exponentially-england-react/

The rate for England then was 1 in 670; that's about 85,000, and might be 100,000 for the whole of the UK. The ONS figures are for up to 26th June. New cases went from about 5,000 to 12,000 from 7th to 26th June, so the increase from 100,000 to 257,000 in the same time looks about right. The latest new cases figure is 25,000, and if that rate of growth applied to the total, then about 535,000 in the UK have covid at the moment.

[Yavin4]

41. Please show me evidence that the 7 million tests per week were NOT at random.

Everyone making a claim WITHOUT proof is NOT proof. It's absurd, group-think to say that a sample size of 7 million tests in a week is not representative of a population of 66 million. That is just getting basic statistics wrong.

There is also a study that does sample people in England truly at random - 'REACT' (I took part in this a few months ago, and didn't have covid). This reports every month, and its last one was for samples taken from 20th May to 7th June.

And that study IS NOT current as it pre-dates the Delta outbreak.

[muriel_volestrangler]

44. Sure, though everyone has already explained that tests are mostly done for a purpose

such as extensive testing at schools, or for people who have been in contact with a positive result, or those that show symptoms. Of course, the point of me linking to the actual statistics was to give you the proof of what the UK statistics actually are; the ONS has credibility, while a DU OP does not.

Here's something explaining how testing is concentrated in certain situations:

This statistical publication provides information on rapid testing for people without
COVID-19 symptoms in England. This includes:
• the number of LFD tests and confirmatory PCR tests conducted by test result
• the number of LFD tests conducted linked to education settings
• the number of LFD and PCR tests conducted in care homes
• the number of LFD tests conducted by NHS staff
• the number of LFD tests conducted in private sector workplaces
This publication focuses on rapid testing using lateral flow device (LFD) tests,
however polymerase chain reaction (PCR) tests are included where appropriate,
either for comparison or where regular asymptomatic PCR testing is used. All data
used in the report can be found in the ‘Tests conducted’ data tables on the weekly
collection page. This includes information on both LFD and PCR tests at lower tier
local authority level.
The data in this release can be used to:
• determine the effectiveness of NHS Test and Trace in the expansion of rapid
asymptomatic testing
• monitor the levels of testing and positive test results amongst various settings
such as in education, care homes and by NHS staff
This data should not be used to:
• calculate the prevalence of COVID-19 in the wider population
• calculate case positivity rates, the reasons for which are explained in the
About this data section
• assess the effectiveness of the testing types used in England
• compare the mass testing programmes across nations

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/998266/Rapid_testing_210701.pdf

The point is that the REACT study is unusual in that it truly is random - they contact people at random saying "will you take part?". You are accusing other people of "getting basic statistics wrong" when that's you - you think that a lot of tests mean they must have been selected at random. That's just illogical - I'm not sure you understand what "random" means. But I understand you're guessing how the system in the UK works - I'm here, so I can tell you. Or you can look it up on the internet, rather than assuming you know and telling other people they're wrong, without evidence.

And the Delta variant was the predominant variant in the UK by the week ending 23rd May - see Figure 3 here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/997418/Variants_of_Concern_VOC_Technical_Briefing_17.pdf and the underlying data here: https://www.gov.uk/government/publications/investigation-of-novel-sars-cov-2-variant-variant-of-concern-20201201

[Yavin4]

49. Again, I'm using your governments official daily reports which when they support the groupthink here

everybody uses to scare people.

If those numbers are wrong and cannot be trusted, then everything needs to be thrown out. Your REACT study may be accurate, but I am using CURRENT reporting statistics on a sample size of over 7 million people per week. You can link all of the other studies that you want. That still does not change the basic fact that 7 million people per week are tested in the UK with over 200 million people tested to date. The UK has tested 3x their entire population.

That gives me more than enough of a sample size to make a basic inference. I can link statistical tutorials if you need them.

Also, every day we make inferences from samples much smaller than 7 million. For example, Joe Biden's approval ratings are based on sample sizes of 1,000 people or so who are called. Should we throw those surveys out as well?

[muriel_volestrangler]

53. The point is that you are making an unjustified assumption that all the people tested

in the whole country were selected at random, or selected to be a representative sample. Neither of those is true, and of course it's not true - have you not read the news in the past 18 months?

People get tested when they have symptoms. They get tested when they're told that they have been in close contact with someone who has tested positive. This has been in the news, day after day, since March 2020. Have you not seen this? Even if you hadn't, all you have to do is read the links I gave you - it explains how certain situations are getting tested. And as I said above, what you are claiming is that no one in the UK is allowed to ask for a test, even if they have symptoms, or a health care provider cannot decide to do a test on a patient - that the entire testing in the UK is only that done for a survey.

That means that the total group of people who have been tested are not, by definition, a representative sample of the whole country. Please, don't pretend you know anything about statistics. Find a person you know and trust who has taken a statistics course, and get them to explain to you what you're doing wrong.

If you heard that one in five pregnancy tests come up positive, would you assume that one in five people in a country are pregnant?

When inferences are made from samples for polls, they are from samples that are carefully selected to be a representative sample. You cannot, for instance, take a DU poll, even if it has 1000 votes, and say it's representative of the USA as a whole. The group that is tested in any week, whether in the UK or in any country, is never representative of the whole country. No-one, before you, has ever even imagined that it is. Your wrong assumption is, I think, entirely original. So, in a sense, congratulations on your creativity.

[Ms. Toad]

52. I got pretty darn close just estimating the testing mix and estimated positivity within the groups

I ended up with 600,000 some thousand.

Thank you!

[Yavin4]

55. Fine. I will use your estimate of 600K positive cases

2140 hospitalized
448 deaths in a month

hospitalized / positive cases = 2140/600000 = 0.003566667
deaths / positive cases = 485/600000 = 0.000746667

The rate of negative outcomes to positive cases is essentially zero. This is what covid zero looks like. It's never going to be zero cases and zero negative outcomes which you, and others, keep falsely promoting that we can reach if we all wear masks and shutter ourselves in our homes.


Source: https://coronavirus.data.gov.uk/easy_read