Class - Applied Statistics

The Danish Mask Study Shows Masks Aren’t Worth It

HUFFIN’, PUFFIN’ & BLUFFIN’

The blustery squid-stained panicked hersteric Nassim Nicholas Taleb—the man who called those who dared not run around screeching like teenage girls as he did at the start of the coronadoom panic “psychopaths“—a man who is a supreme 妈宝, a fact I include because Taleb likes language references—has claimed the Danish mask study which shows masks don’t work ackshually shows masks do work, because math.

He’s wrong.

Here is that study. They looked at two groups who stayed at least three hours outside their homes, with and without mask recommendations. The masked were supplied with “50 surgical masks and instructions for proper use.” Which makes that group more rigorous than masks in the common public.

Goal: “The primary outcome was SARS-CoV-2 infection in the mask wearer at 1 month by antibody testing, polymerase chain reaction (PCR), or hospital diagnosis.”

Outcome: “A total of 3030 participants were randomly assigned to the recommendation to wear masks, and 2994 were assigned to control; 4862 completed the study. Infection with SARS-CoV-2 occurred in 42 participants recommended masks (1.8%) and 53 control participants (2.1%).”

The completed numbers were 42/2392 mask infections vs. 53/2470 non-mask infections, where “infection” was defined generously, as you see.

Their conclusion: “The recommendation to wear surgical masks to supplement other public health measures did not reduce the SARS-CoV-2 infection rate among wearers by more than 50% in a community with modest infection rates, some degree of social distancing, and uncommon general mask use. The data were compatible with lesser degrees of self-protection.”

I conclude, given the study’s dictated rigorousness of mask usage (“good” ones supplied with proper instructions for use), and the generosity of noting an infection, and with all the other massive evidence we have about masks, that masks in the general public don’t provide any significant benefit, or even no benefit, and can even cause harm.

Therefore making masklessness a crime, as many localities do, is asinine, anti-evidence, unethical, and immoral.

That’s me. What about Taleb? Screams “Save me!” as usual. He starts his attack with these words:

Every study needs its own statistical tools, adapted to the specific problem, which is why it is a good practice to require that statisticians come from mathematical probability rather than some software-cookbook school. When one uses canned software statistics adapted to regular medicine (say, cardiology), one is bound to make severe mistakes when it comes to epidemiological problems in the tails or ones where there is a measurement error.

I am in near total agreement with this. Except for the very obvious caveat, which Taleb misses, that slavish adherence to math often leads to the Deadly Sin of Reification. Math misapplied is worse than no math, because it gives the false patina of “science.” That, as it turns out, will be Taleb’s mistake.

Now it should be obvious that the burden of proof is on Taleb and his Fearful Party and their petty tyrant instigators to show masks work. They are the ones insisting the masklessness is a crime.

It would therefore be an obvious and idiotic error to say that because this study says that masks don’t work (as they defined “work”) that therefore masks work because this study was incomplete. Right?

Taleb: “The study does not take into account the fact that masks might protect others.”

So? The study also doesn’t show that masks protects against gonorrhea in fleas. There are an infinite number of things the study doesn’t show. What it does show is that wearing masks don’t do much about protecting wearers from infection. If the other guy not wearing a mask is infected, you wearing one isn’t going to do it for you. And anyway, they burden of proof is still on the Fearful Party to prove all claims about masks.

It’s at this point Taleb launches into a blizzard of math, most of which is of no use, but which pleases the easily pleased. I will spare you (most of) the math, but assure you it is there and can be looked up.

THE EVIDENCE

There’s two ways to look at this. We can assume perfection in the tests, or we can assume there’s error in the form of both false positives and false negatives. Let’s start with no error.

No Error

There was some missings (people entering the study but never measured). According to the “intention to treat” principle, we still have to account for them. Since the burden of proof is on the Fearful Party, it follows we should accord these missings as non-infections. In the same way as you count a non-response in a new drug trial as the drug not working. Fair is fair. But, since that makes my job too easy, I’ll just ignore the missings, recalling that I’m then looking at a worst case scenario.

Taleb’s binomial take is wrong in the sense that a better model exists, which, it turns out, regular readers met not that long ago. His binomial—and this will be hilarious for those who get the joke—is too small, too light in the tails! What a fun mistake.

We have evidence of 42/2392 mask infections vs. 53/2470 non-mask infections. We have to take that evidence as it is here assuming no error. And we want to extrapolate that information to Denmark as a whole.

We need only two assumptions: there are two states measured, infection or not, and a certain number of people measured. From that we deduce a beta-binomial predictive model (with deduced, i.e. know-with-certainty parameters) to extrapolate to those not yet measured (the math is all in here and in the many articles on the free stats class; all code is below at the bottom of this post). This is based on the prediction principle: I don’t need to predict data I already know!

There are about 5.8 million Danes. We want the probability any number of them get infected whether or not they wear masks in the way prescribed (surgical, with training). This is easy. That is, we can calculate the probability of each possible outcome (0 new Danes infected, 1 new Dane infected, …, 5.8 million new Danes infected) for both masks and no masks.

And then we can ask, given a person is infected, the chance they crap out. I don’t know what the infection fatality rate of the coronadoom is in Denmark. They are, however, in no crisis as this Google picture search for “Denmark coronavirus deaths” shows.

Worldometer says Denmark has 146 doom deaths per million. And Ioannidis estimated counties with rates like that have an IFR of about 0.2%.

Since there is a possibility, however small, everybody wearing a mask or not can become infected, and we are ignoring all previous infections (accounting for them would only reduce the 5.8 million to some smaller number), we have to pick a probability cutoff.

For instance, we want to be 99% sure the number of infected will x or less, and solve for x for both masks and no masks. We can’t use 100% certainty because that would give us 5.8 million for x for both groups (if you don’t follow this, stop and think).

In our model, there is a 99% chance 144,185 or fewer masked would be infected, and 169,623 or fewer non-masked, out of 5.8 million. This is a difference of 25,438, which is the real effect we’re looking for it the entire country mandated masks. This all assumes the model, data, full compliance, and so on.

Most people who get the doom have, at worst, mild symptoms. Therefore we want a more practical measure of its effect, such as deaths. This brings up the IFR. We assumed 0.2%. On average, given all our assumptions, we’d expect 0.002 * 25,438 = 51 (rounded up) lives would be “saved” by forcing all citizens to wear surgical masks with proper training. In our worst case scenario.

If we do intention to treat and realize most won’t wear the masks as rigorously as the study prescribed, and some people aren’t out of the house more than 3 hours a day, the real effect would be even smaller than 51 lives. Likely a lot smaller.

Error

Now let’s bring in some error. We can have tests with a certain false positive and false negative rate. Opinions vary on the rates, but we know what they are here to a certain bound. How? Easy. Gaze and wonder at these glorious graphics.

The cells are labeled to show that with the given marginal totals, we can solve for each cell value, as long as we know the error rates. We must accept the marginal totals, because that’s what was measured!

For instance, a = c * (1 – FNR) / FNR, and b = d * FPR / (1 – FPR). We also have the constraints that c + d = 2350 (or 23417), and a + b = 42 (or 53). The latter may be written c * (1-FNR)/FNR + d * FPR/(1-FPR) = 42 (or 53). Given FPR and FNR, we then have two equations with two unknowns that can be solved for.

Taleb uses a FPR = 1%, so let’s pick that with an equivalent FNR = 1%.

What we want is an estimate of the true infection rate. That would be ( a + c )/ n, with n = a + b + c + d = 2392 or 2370.

Plugging in 1% for both error rates gives (a + c) = 18 for masked, and 29 for unmasked. Notice these are smaller than the original 42 and 53 because of error: those 42 and 53 are positive tests, not actual infections if there’s error.

We then repeat the same calculations as above, with 99% cutoffs. That gives a 99% chance no more than 73,930 infections in the masked group and 103,410 in the unmasked group. A difference of 29,480. Again, with an IFR of 0.2%, this is a difference of 59 bodies, rounded up.

So, as expected, the test error leads to more concern, but not much more. If we bump up the cutoff to 99.9%, we get a morgue count difference of 62. If we keep the 99% but double the FNR, in line with other estimates, we get a body count difference of 53 out of 5.8 million.

You can play with other plausible values, but the answers are all in the same ballpark. (There are some questions of limits of FPR and FNR with the given marginals, but we can ignore these here. You’ll see the concerns if you push the rates too far away from 1%.)

Recall, again, this is the worst case scenario! Meaning the real effect will be less, even in the face of test error. Don’t forget, beside all the other weakness, many have already been infected and won’t be easily infected again soon, so the real number to consider is less than 5.8 million.

All these things and more will make the 53 smaller. And not only smaller, but much smaller.

IF WE CAN SAVE EVEN ONE LIFE!

The argument will be we must do everything we can to save even one life! This is a dumb argument, too dumb to even answer.

I went into nauseating detail, not so much to mock Taleb, though there is pleasure in that, but to help students interested in these things.

I do not ask you to take my model any more seriously than you take Taleb’s. Because it has to be married to the great cache of evidence we already have about masks (link). It was clear before this study that there is no reason to mandate masks in the general public. With this study, it’s even clearer.

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CODE

I trust those who know how to play with code will figure this out.

newdbetabinom = function(x, n.new, k.old, n.old){
   # New observables for predictive distribution given:
   # k.old = observed "successes"
   # n.old = total old observations
   # x = vector of new totals, up to 0:n.new, or single x
   # n.new = number new observations expected
   # beta-binomial
   a = k.old+1
   b = n.old-k.old+1
   (ans = exp(lchoose(n.new,x)+lbeta(x+a,n.new-x+b)-lbeta(a,b)))
}

#############################
##
## NO ERROR
##

# masked and unmasked probabilities over 5.8 millions
s = 0:5.8e6 
m1e = newdbetabinom(s,max(s),   42,2392)
m0e = newdbetabinom(s,max(s),   53,2470)

# numbers of infected with probability cuttoff of 99%
# the "-1" is because the counts start at 0
(ni.1 = tail(which(cumsum(m1e) < 0.99),1)-1) # masked
(ni.0 = tail(which(cumsum(m0e) < 0.99),1)-1) # no masked

# different morgue counts with IFR = 0.002.

0.002 * (ni.0 - ni.1)

#############################
##
## ERROR
##

fpr = 0.01 # push this beyond 0.015 and watch the fur fly!
fnr = 0.01

a = c((1-fnr)/fnr, fpr/(1-fpr),
      1, 1)
a = matrix(a,nrow=2,byrow=T)

# masks
b = c(42, 2350)
r = solve(a,b)
(nti.1 = round(r[1]*(1 + (1-fnr)/fnr)))

# no masks
b = c(53, 2417)
r = solve(a,b)
(nti.0 = round(r[1]*(1 + (1-fnr)/fnr)))

s = 0:5.8e6
m1e = newdbetabinom(s,max(s),  nti.1,2392)
m0e = newdbetabinom(s,max(s),  nti.0,2470)
  
(ni.0 =  tail(which(cumsum(m0e) < 0.99),1)-1)
(ni.1 =  tail(which(cumsum(m1e) < 0.99),1)-1)
  
.002*(ni.0 - ni.1)

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61 replies »

  1. Sshhh, Briggs. The criminals LOVE the masks and can rape, pillage and plunder at will without fear of being caught. Are you trying to ruin a good thing?

    Are you sure Talib (and you) are not saying that statistics is wonderful because you can find some method to prove what you want? That’s what I heard, anyway.

    All of these tests are wrong anyway. You can’t pull mask wearing or social distancing or whatever out of a complex system and name it winner. Or else CO2 is the winner and you lose your fossil fuel. As long as we reduce complex systems to ONE factor, it’s stupid, unscientific and generally wrong. “Randomizing” life variables is impossible. You always end up with factors you never accounted for. Weasel lawyers buy more and more private islands based on that action. Science is really, really stupid when it pretends it can pull one factor out and measure its effect. The fictional Penny on “Big Bang” was actually more scientific than most scientists today, though I expect a large government grant would “cure” that. It’s disgusting and destructive, but it is what it is.

    Actually, “we must do everything we can to save even one life!” is a wonderful argument for 2AM with philosophy majors. Taken to the extreme, heads explode. Quite fun to watch, actually. Living under the dictatorship of the soon-to-be-exploded heads, not so much fun. Honestly, the government wants you dead, wants to control you and since you’ve been so very, very kind to volunteer your slavery and lives to the government, it’s all irrelevant anyway. You wear a mask “because I said so” from the government. Feel free to snicker and mock behind the government’s back, but never get caught. The penalty is severe. You just got grounded by Mom. Wait till the omnipotent dictatorship you live in and worship finds you mocking them. Have a nice little subservient day and wear those mask, OR ELSE. (And hide under your desk if you’re in school to protect yourself from Little Kim’s nuclear missile launch. It’s better than nothing and might save on life for an hour or so.)

  2. I have always found his attitude towards Covid19 very strange, given that he is fond of posing being an expert in risk management

  3. Facts don’t matter to the Covid Cultists. The Face Diaper is the badge to signal one’s status as a fully paid-up, Kool-Aid-drinking member of the Branch Covidians.

  4. “The blustery squid-stained panicked hersteric Nassim Nicholas Taleb.”

    Heh. He certainly has a talent for getting press.

    Taleb: “A correct computation of the odds ratio shows a massive risk reduction coming from masks.”

    He gets that from 42/2392 mask infections vs. 53/2470 non-mask infections. I guess it takes a genius to discover massive risk reduction in what looks plainly like no practical effect, but then, I’m not a genius. Taleb’s like a guy who tries to impress with his big fast car, shiny, bells & whistles, but he always drives it like a jerk. Well, he’s Greek — they all drive like that.

    “[Taleb] … is a supreme ??

    Google translate says that’s Chinese for “pixel”; likely not what you meant, but still pretty funny.

  5. Some good guy named Allan Stevo has penned an excellent book on masks and how to never wear one:

    Face Masks in One Lesson.

    $4.99 on Kindle. I got it, it’s good. His method is taking advantage of the exemptions every mask mandate has. Not in confrontational ways, but in effective negotiation to arrive easily at the desired outcome. Best thing I’ve seen yet on mask avoidance.

    Blurb:
    “Face mask orders and policies are called mandatory. The truth is millions are exempt from the face mask orders and don’t realize it. Face Masks in One Lesson provides the ultimate response to mandatory masking, and is an irreplaceable tool for those who will not go masked another day.”

  6. The mask is a political badge now, and as such, is also a religious symbol – analogous to wearing a cross or a religious medal around your neck.

    The religion of The Science, Safetyism and Holy Wokeness.

    Facts?

  7. When I just searched … ?? … got a youtube “11 signs he’s a momma’s boy

    From … Shenzhen Daily. Meaning: “?” means “mom,” “?” means “baby,” and “?” refers to a “man.” … the Chinese context, “mom’s baby boy” often refers to grown-up men dependent on their moms

  8. Mr. Briggs, when I was going over your post (I had already read the paper and were aware of the immediate, sometimes ridiculous backlash), I knew where it would eventually lead me, the (yes), “… dumb argument, too dumb to even answer”.

    But as dumb as it is, that “even only one life is worth adopting drastic, permanent measures” is the automatic response EVERY single person with a similar mindset will give you when confronted by the danish paper. Probably they will also drop a pearl like “what if that one person is your mother?”…

    …which will lead us to that famous aphorism: “don´t argue with fools. You will not be able to raise their level, but they will dumb yours down, and once there, they will win the debate for a matter of experience”. Because to try to make them understand, you would see yourself trying to navigate the muddy waters of stupid examples of why that argument could be used to prevent people from doing…well, anything at all.

    Example: In Spain we have a remarkable number of internationally acclaimed scientific talent, and some of them have been saying the stupidest things one can conceive during the pandemics. I am talking about batshit (no pun intended) crazy stuff . One of them, the well known virologist named Margarita del Val, is all over the media since February. She is a total nutcase, but she is indeed a well respected professional, and the media will follow her claims like the Bible. Well, yesterday she precisely said that vaccines won´t work 100 % , so we won´t be able to stop using masks all the time “until every feeble person is protected”, insanity that of course has been covered and cheered by the media. Now try to go down enough stairs to get to her logical level and make her understand that weak, old, sick people has always existed and will always exist, so that would turn life into an impossibility. Try…

    These are some of the weirdest times ever. But there is something I enjoy: My daily life walking the streets feels like I am making the Red Sea miracle. Everybody is horrorized and gets the hell out of my way when they see me maskless.

  9. PS: I just viewed a picture of a college marching band that was wearing masks with holes designed into the front to accept wind instruments. So….even less effective than nothing at all, so to to speak….but still solidly virtue-signaling.

    That is all. Going to go hit my head with a hammer for awhile to ease the pain.

  10. “Now it should be obvious that the burden of proof is on Taleb and his Fearful Party and their petty tyrant instigators to show masks work.”

    Easy. Whatever the current state of matters with masking use, just assert they would have been much much worse without the masks; nobody can falsify this, and there are always enough other differences with non-masking countries that you can explain them away.

    Of all the things Aslan ever said in the Narnia stories, I never imagined that “No one is ever allowed to know what would have happened” would become the most relevant to my adult life.

  11. Enough already.. just for fun consider these pearls of wisdom from my alter ego: ( on winface.com, last july)

    Masks in the hands of untrained non medical personal can be very useful for robbing banks, but are worse than useless for protecting anyone from a virus.

    The gold standard for claims about the effectiveness or otherwise of anything medical is the randomized clinical trial. In 2014, and so well before the current insanity hit, a number of people with real Ph’ds in closely related specializations published a careful review of ten such trials: Wong VW, Cowling BJ, Aiello AE. Hand hygiene and risk of influenza virus infections in the community: a systematic review and meta-analysis. In May of 2020 a larger team including the original author reported revisiting the issue to include four more in the CDC’s Journal of Emerging Infectious Diseases as: Nonpharmaceutical Measures for Pandemic Influenza in Nonhealthcare Settings-Personal Protective and Environmental Measures.

    The key sentence from the summary for that report is:

    “Although mechanistic studies support the potential effect of hand hygiene or face masks, evidence from 14 randomized controlled trials of these measures did not support a substantial effect on transmission of laboratory-confirmed influenza.”

    That’s the science: 14 randomized clinial trials, all done before today’s double goodthink became mandatory, and no evidence that masks used in non medical settings reduce viral infections.

    The key reason masks are useless in non clinical settings is the combination of misuse with reuse.

    I rant on a bit (explaining why they don’t work) but any sane person can see that mask mandates are always and everywhere followed by exponential increases in “cases” – defined as some combination of intuition and a positive reading on a test of unknown sensitivity and untested selectivity.

    So why waste time arguing the case?

  12. Rogelio García: Thank you for your interesting and humorous report from Spain. Much appreciated.

  13. Even the “if it only saves one life” line is a crock. No one actually believes it, even the people who say that they do. The reason why is because everyone knows, either consciously or unconsciously, that it is impossible to simultaneously prevent all causes of death, at least not without stopping everyone from dying ever again.

    To see this try to convince people who use that argument that lockdowns should never be used. People have definitely committed suicide due to despair from the lockdowns. People have definitely died due to not getting regular and preventative medical care due to the lockdowns. So if we end them we would certainly save “at least one life.” Try making that argument. You might get into a discussion of whether they have a net effect of saving lives, which already destroys all the effectiveness of the “if it only saves one life” argument. But more likely you will find that the deaths from the lockdowns are dismissed. They don’t count. Only deaths from COVID count.

    It is the same as how pointing to known risks of constant mask usage (ex. wearing one for eight hours in a hot warehouse or restaurant) is considered conspiracy talk. But it is considered rational to imagine that someone might get infected by walking into a room hours after someone without a mask was there, due to the virus lingering in the air. What makes something “rational” or not has nothing to do with observations or logic, but only with what makes the Wuhan flu look the most dire.

  14. Proof that mask mandates don’t work, and mask don’t prevent a contagious person from spreading the virus.

    All across rural Pennsylvania, in county after county, COVID-19 is devastating nursing homes. If were just a few, then one could say that they were following protocols strictly enough, but it is the opposite, only a luck few nursing homes have not experienced an alarming increase in real cases and deaths.

    For example, one local nursing home stopped visitation on Sep-25 when they had zero patients or staff testing positive, but the local community was experiencing a spike in positive test results. Two weeks later, they had a couple staff test positive. Another two weeks later they had about 5 patients test positive. Another two weeks 45 patients, 23 staff.

    The Nursing home reported on Monday of this week, over 85% of residents have positive test results, over 25% of staff tested positive, and over 15% of the patient population died in the last two weeks.

    If Face Diaper mandates don’t work in a small closed setting where the consequences of non-compliance could result in financial ruin, then they can’t possibly work in the general population.

  15. Spud Jr 60:

    Reminds me of the New Jersey guy who upon hearing they were going to co-locate post-Covid patients in nursing homes, removed his 90 year old grandfather who later succumbed to the Covid after all. Virus be like damned if you do damned if you don’t

  16. I have a question that I wish someone would answer: for those individuals wearing masks in the Denmark study that were infected with Covid-19, how many people did they infect among those whom they came into contact? And a second question: If we assume that we don’t know the answer to the first question, how is it possible to say of wearing masks that it is worthless when it is possible they protect against spreading the disease?

  17. The main problem, Martin Dillon, is precisely what we have been saying all the way: your reasoning could be applied to any other infectious desease, turning the horrendous measures applied to “avoid the spread of Sars-Cov2 infection” into the life standard we should have taken since the world exists and until it stops spinning around the sun.

    You say, “how is it possible to say of wearing masks that it is worthless when it is possible they protect against spreading the disease?” Well, how do you know that you haven´t infected, say, 150 people with the flus you have suffered during your whole life? Is it possible to know how many of them were old, feeble people who died from it? So, why don´t give it a try and wear masks all the time, forever, so we “save” people from contagious pneumonias (3/4 million yearly deceased people by it), flus (500 000/700 000), tuberculosis (a pair of millions more), and so on? Well, because it is blatantly obvious that that would be as crazy a solution as it gets, because it would totally destroy what we understand as a life worth living…

    …but we have done it with this coronovirus, and once you open the door to insanity, and we have, you have to swallow all the craziness. It does not come in manageable packages: it comes like a tsunami.

  18. Dr. Briggs,

    I was confused by two sentences that you quoted from the study: “The recommendation to wear surgical masks to supplement other public health measures did not reduce the SARS-CoV-2 infection rate among wearers by more than 50% in a community with modest infection rates, some degree of social distancing, and uncommon general mask use. The data were compatible with lesser degrees of self-protection.”

    Grammatically and semantically, the phrase “did not reduce the rate more than 50%” is horribly vague and ambiguous by itself. What were they trying to say?

    The difference in rates between mask and non-mask wearers in the study was clear — so I’m baffled by this couple of sentences.

    Thank you for any insight you can share.

    Excellent work, as always! (I’ve really enjoyed your book, BTW.)

  19. I think, Rick C., that the phrase about the 50 % protection alludes to previous (flawed) claims from medical authorities about masks protecting the user by that 50 % aproximately. I may be wrong, but I think that is the case.

    And yes, if the whole point of the study is to show a specific figure (0,3 %) that contradicts the official narrative, that ambiguous “data were compatible with lesser degrees of self-protection” is completely unnecessary. It gives the critics a 49,7 % margin.

  20. If masks did not reduce the rate by more than 50% and if reducing the rate by more than 50% is what we mean by ‘works’ then masks do not work. But, if masks reduce the rate by, say, 40%, then they do work to that extent, even if not to a greater extent. So, talk of ‘working’ and ‘not working’ seems too vague. But, at some point, if, say, a mask only reduces the risk by 1%, we would be comfortable saying masks do not work even without qualifying the matter further because the relative effectiveness is nearly zero. In this situation, I am not sure the relative effectiveness is close to zero, though I am also pretty sure it is not close to 100% either.

  21. But in this study it appears that there is virtually no difference in those wearing or not wearing masks.

  22. We are so detached from the truth of the facts that a schism between “science” and “reality” has been created, as if they were opposite forces in a boxing competition.

    In the “mask fight”, people have largely chosen to believe official science´s version although it absolutely contradicts the reality they face everyday: “In the blue corner, weighing in at one billion one-sided media reports , we got the undisputed world official version. In the red corner, weighing in at a dozen of internet websites and 100 mostly censured scientists, we got…reality.”

    As I said before, I am from Spain, the epicenter of mask religion, and one of the countries with worse infection figures. Here it is blatantly obvious that people get infected while wearing masks. You don´t need hard science to understand that if there is time correlation between the date masks got compulsory and the skyrocketing increase in infections, well, masks probably don´t work! The next step would be thinking “well, if we hadn´t used them, the results would be so much worse”. But it does not happen that way. Actually when you compare our figures with those with relaxed laws on masks, it is the other way round. So, what is there left to keep masking compulsory? Media avoidance of “countries data comparison”. Keep people away from historical and present context. Keep people focused not on reality, but on the unending data discharged.

  23. I don’t disagree with your argument but it seems to me that the differences between the straight up binomial model and the beta-binomial are negligible. You say that there is a 99% chance 144,185 or fewer masked would be infected, and 169,623 or fewer non-masked, out of 5.8 million.

    Assuming no error, the simple binomial model (using p-values, which I know you hate, corresponding to 99%) gives 140635 or fewer for masked and 166721 or fewer for masks. Assuming a 0.2% IFR this translates into a difference (unmasked – masked) of 38 and 52 deaths, respectively, out of 5.8 millions.

    Again, you say, “We then repeat the same calculations as above, with 99% cutoffs. That gives a 99% chance no more than 73,930 infections in the masked group and 103,410 in the unmasked group. A difference of 29,480. Again, with an IFR of 0.2%, this is a difference of 59 bodies, rounded up.”

    The corresponding numbers for the simple binomial model lead to 70318 for the masked group and 100972 in the unmasked group. The corresponding difference is 30654 infections which, at an IFR of 0.2% leads to 61 deaths.

    Admittedly the simple binomial model underestimates (because of smaller tails) and so gives a less rigorous upper bound, but they are still in the same ballpark and the basic conclusions would be unchanged. So I ask, strictly from the perspective of one willing to be instructed, why I should use the beta-binomial?

    Finally, you have provided a very good exercise in the analysis of data; something which is never done in the media outlets! Thanks!

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