Liverpool Thread - 2021/22

Status
Not open for further replies.
I know I made some rough estimated predications yesterday and earlier today about how unlikely multiple false positives on a Lateral Flow Test might be. Now I have finally/sadly crunched the numbers for real, it seems I actually over-estimated the likelihood of multiple falsely positive Lateral Flow Tests occurring at Liverpool recently.


I appreciate I've been banging on about this, but just so everyone is clear (those with lives look away now) here is my working:

The United Kingdom Health Security Agency (UKHSA) has made it clear that a positive indication on a lateral flow test is correct 9,997 times out of 10,000 (that is, subsequent PCR tests have proved them to be correct). In fact, they are so reliable (from a positive test point of view at least) that producing one has removed the need to take any further confirmatory test (e.g. a PCR) as was previously government policy.

The probability of suffering a false positive on a LFT is 3 in 10,000. I read today that the UKHSA are saying that, so far as the new Omicron version goes, getting a false positive for that strain is ten times even less likely than it was for Delta i.e. the probability, i.e. occurrence, of false positives on LFT's for Omicron is a vanishingly small 3 in 100,000.

For those that care, calculate the probability of Liverpool players encountering just three false positives in a row when taking an LFT from those in circulation in this country.

That is (3/10000)*(3/10000)*(3*10000)
i.e. (0.0003) x (0.0003) x (0.0003)
That comes to 2.7 times in 100 billion i.e. 2.7 times such a scenario would arise in 100,000,000,000 times of trying it.

To get 15 false positive lateral flow tests on the bounce you would multiple the chance of it occurring just the once i.e. 0.0003 and that happening on 14 subsequent occasions. You would multiple 0.0003 by the probability of producing another false positive LFT test which remains the same (i.e. 0.0003) and do so with the results of that sum a further 14 times. That is 0.0003 to the power of 15.

It produces such a small chance of probability (it has 54 0's after the decimal point before you get 1435) that it is the equivalent of every star in the universe (higher estimate to be 10^24 which is 1 with 24 zero's after it) being multiplied by the same number, and then the produce of that little lot multiplied a mere 10,000 further times for further good measure.

There is a 1.435 chance in 10 to the power 54 chance (a 1 with 54 zeros after it) of drawing out 15 false positive randomly selected Lateral Flow Tests on the bounce.

I appreciate that not all 15 had to be on the trot and that they could play 9 jokers (no false positive tests) in amongst those to make up the squad of 24. I will let a better man than me work out this precisely chances of encountering 15 false positive LFTs out of a squad of 24, it's clearly slightly less than I have indicated with the above illustration. It's a long time know since I did O' level maths. You did your best Mr Meakin!

So, if the batches of lateral flow tests did not prove to be faulty, Liverpool might simply have just been a little unlucky in this incidence. If it's often the case with them I hear.
 
Edward Deadwood said:
I know I made some rough estimated predications yesterday and earlier today about how unlikely multiple false positives on a Lateral Flow Test might be. Now I have finally/sadly crunched the numbers for real, it seems I actually over-estimated the likelihood of multiple falsely positive Lateral Flow Tests occurring at Liverpool recently.


I appreciate I've been banging on about this, but just so everyone is clear (those with lives look away now) here is my working:

The United Kingdom Health Security Agency (UKHSA) has made it clear that a positive indication on a lateral flow test is correct 9,997 times out of 10,000 (that is, subsequent PCR tests have proved them to be correct). In fact, they are so reliable (from a positive test point of view at least) that producing one has removed the need to take any further confirmatory test (e.g. a PCR) as was previously government policy.

The probability of suffering a false positive on a LFT is 3 in 10,000. I read today that the UKHSA are saying that, so far as the new Omicron version goes, getting a false positive for that strain is ten times even less likely than it was for Delta i.e. the probability, i.e. occurrence, of false positives on LFT's for Omicron is a vanishingly small 3 in 100,000.

For those that care, calculate the probability of Liverpool players encountering just three false positives in a row when taking an LFT from those in circulation in this country.

That is (3/10000)*(3/10000)*(3*10000)
i.e. (0.0003) x (0.0003) x (0.0003)
That comes to 2.7 times in 100 billion i.e. 2.7 times such a scenario would arise in 100,000,000,000 times of trying it.

To get 15 false positive lateral flow tests on the bounce you would multiple the chance of it occurring just the once i.e. 0.0003 and that happening on 14 subsequent occasions. You would multiple 0.0003 by the probability of producing another false positive LFT test which remains the same (i.e. 0.0003) and do so with the results of that sum a further 14 times. That is 0.0003 to the power of 15.

It produces such a small chance of probability (it has 54 0's after the decimal point before you get 1435) that it is the equivalent of every star in the universe (higher estimate to be 10^24 which is 1 with 24 zero's after it) being multiplied by the same number, and then the produce of that little lot multiplied a mere 10,000 further times for further good measure.

There is a 1.435 chance in 10 to the power 54 chance (a 1 with 54 zeros after it) of drawing out 15 false positive randomly selected Lateral Flow Tests on the bounce.

I appreciate that not all 15 had to be on the trot and that they could play 9 jokers (no false positive tests) in amongst those to make up the squad of 24. I will let a better man than me work out this precisely chances of encountering 15 false positive LFTs out of a squad of 24, it's clearly slightly less than I have indicated with the above illustration. It's a long time know since I did O' level maths. You did your best Mr Meakin!

So, if the batches of lateral flow tests did not prove to be faulty, Liverpool might simply have just been a little unlucky in this incidence. If it's often the case with them I hear.
Click to expand...
I worked it out to be 0.000000000000000000000000000086% based on a 1% false positive rate, although I've probably f*cked up the maths
 
Trevor Morley's Tache said:
I worked it out to be 0.000000000000000000000000000086% based on a 1% false positive rate, although I've probably f*cked up the maths
Click to expand...
Your workings are good my friend, in terms of your taking the (same) percentage of the percentage probability of a false positive appearing on a lateral flow test.

You repeated that method 14 times to get to arrive at your assumed percentage chance of the unfortunate occurrence happening 15 times on the run to members of their squad.

eg if you toss one coin the chance of landing heads is 50%.

to land heads twice on the run is 50% of that ie 25%.

to land heads three times is 12.5%, then 6.25% for four, 3.125% for five etc etc.

For 10 heads on the run the chances would be 0.0977% ie there would be less than a one in one thousand chance of landing 10 heads in a row when flipping a coin. (a one in 1000 chance is the same as a 0.1% chance).

Back to false positives conundrum at Liverpool, you presumed a 1% false positive rate on LFTs, whereas extensive data collected by Track & Trace has led the UK Health Security Agency to conclude that 9997 out of every 10,000 positive indications on LFTs are correct - and that the false positives occur, unsurprisingly, only 3 times in 10,000 times.

The percentage probability of a false positive with an LFT is therefore (3/10000) x 100

namely 0.03% not the 1% you used, successfully I might add, for illustration purposes.

This is why we need an investigation or a simple confirmation that multiple batches of LFTs Liverpool used were faulty, or that club officials fucked up royally by making an honest procedural error we’ve not been made privy to and which we’d all like to avoid in the future.

I have just seen that the Liverpool version of events (as relayed by none other than the Liverpool Echo) states the club conducted simultaneous LFT and PCR tests just prior to the Arsenal game and which seemingly indicated this plethora of unexplained false positives.

A batch of faulty LFTs might have occurred (though we’ve not been told / reassured that was the case). For the PCR tests, which surely involve complex offsite lab analysis, to also to prove faulty (falsely positive) is shockingly bad luck.
 
Edward Deadwood said:
I know I made some rough estimated predications yesterday and earlier today about how unlikely multiple false positives on a Lateral Flow Test might be. Now I have finally/sadly crunched the numbers for real, it seems I actually over-estimated the likelihood of multiple falsely positive Lateral Flow Tests occurring at Liverpool recently.


I appreciate I've been banging on about this, but just so everyone is clear (those with lives look away now) here is my working:

The United Kingdom Health Security Agency (UKHSA) has made it clear that a positive indication on a lateral flow test is correct 9,997 times out of 10,000 (that is, subsequent PCR tests have proved them to be correct). In fact, they are so reliable (from a positive test point of view at least) that producing one has removed the need to take any further confirmatory test (e.g. a PCR) as was previously government policy.

The probability of suffering a false positive on a LFT is 3 in 10,000. I read today that the UKHSA are saying that, so far as the new Omicron version goes, getting a false positive for that strain is ten times even less likely than it was for Delta i.e. the probability, i.e. occurrence, of false positives on LFT's for Omicron is a vanishingly small 3 in 100,000.

For those that care, calculate the probability of Liverpool players encountering just three false positives in a row when taking an LFT from those in circulation in this country.

That is (3/10000)*(3/10000)*(3*10000)
i.e. (0.0003) x (0.0003) x (0.0003)
That comes to 2.7 times in 100 billion i.e. 2.7 times such a scenario would arise in 100,000,000,000 times of trying it.

To get 15 false positive lateral flow tests on the bounce you would multiple the chance of it occurring just the once i.e. 0.0003 and that happening on 14 subsequent occasions. You would multiple 0.0003 by the probability of producing another false positive LFT test which remains the same (i.e. 0.0003) and do so with the results of that sum a further 14 times. That is 0.0003 to the power of 15.

It produces such a small chance of probability (it has 54 0's after the decimal point before you get 1435) that it is the equivalent of every star in the universe (higher estimate to be 10^24 which is 1 with 24 zero's after it) being multiplied by the same number, and then the produce of that little lot multiplied a mere 10,000 further times for further good measure.

There is a 1.435 chance in 10 to the power 54 chance (a 1 with 54 zeros after it) of drawing out 15 false positive randomly selected Lateral Flow Tests on the bounce.

I appreciate that not all 15 had to be on the trot and that they could play 9 jokers (no false positive tests) in amongst those to make up the squad of 24. I will let a better man than me work out this precisely chances of encountering 15 false positive LFTs out of a squad of 24, it's clearly slightly less than I have indicated with the above illustration. It's a long time know since I did O' level maths. You did your best Mr Meakin!

So, if the batches of lateral flow tests did not prove to be faulty, Liverpool might simply have just been a little unlucky in this incidence. If it's often the case with them I hear.
Click to expand...

Have you got the lottery numbers for Saturday please?
 
Edward Deadwood said:
Your workings are good my friend, in terms of your taking the (same) percentage of the percentage probability of a false positive appearing on a lateral flow test.

You repeated that method 14 times to get to arrive at your assumed percentage chance of the unfortunate occurrence happening 15 times on the run to members of their squad.

eg if you toss one coin the chance of landing heads is 50%.

to land heads twice on the run is 50% of that ie 25%.

to land heads three times is 12.5%, then 6.25% for four, 3.125% for five etc etc.

For 10 heads on the run the chances would be 0.0977% ie there would be less than a one in one thousand chance of landing 10 heads in a row when flipping a coin. (a one in 1000 chance is the same as a 0.1% chance).

Back to false positives conundrum at Liverpool, you presumed a 1% false positive rate on LFTs, whereas extensive data collected by Track & Trace has led the UK Health Security Agency to conclude that 9997 out of every 10,000 positive indications on LFTs are correct - and that the false positives occur, unsurprisingly, only 3 times in 10,000 times.

The percentage probability of a false positive with an LFT is therefore (3/10000) x 100

namely 0.03% not the 1% you used, successfully I might add, for illustration purposes.

This is why we need an investigation or a simple confirmation that multiple batches of LFTs Liverpool used were faulty, or that club officials fucked up royally by making an honest procedural error we’ve not been made privy to and which we’d all like to avoid in the future.

I have just seen that the Liverpool version of events (as relayed by none other than the Liverpool Echo) states the club conducted simultaneous LFT and PCR tests just prior to the Arsenal game and which seemingly indicated this plethora of unexplained false positives.

A batch of faulty LFTs might have occurred (though we’ve not been told / reassured that was the case). For the PCR tests, which surely involve complex offsite lab analysis, to also to prove faulty (falsely positive) is shockingly bad luck.
Click to expand...
You can, apparently, get a positive reading with some acidic drink ( orange juice)
Maybe you can get a positive with an asthma inhaler…
 
Status
Not open for further replies.
Unread Posts

Don't have an account? Register now and see fewer ads!

SIGN UP
Back
Top
✖
  AdBlock Detected
Bluemoon relies on advertising to pay our hosting fees. Please support the site by disabling your ad blocking software to help keep the forum sustainable. Thanks.