### The Volokh Conspiracy

Mostly law professors | Sometimes contrarian | Often libertarian | Always independent

# Grocery Store Workers and Covid-19

## Basic statistics once again eludes mainstream journalism

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Given the contact many grocery store workers have with the public, they would seem to be potentially at special risk from Covid-19. And a headline in the Washington Post yesterday blared, Grocery workers are beginning to die of coronavirus.

But check the subheadline: "At least four people – who had worked at Walmart, Trader Joe's and Giant – have died from covid-19 in recent days." We learn in the body of the article that "a Trader Joe's worker in Scarsdale, N.Y., a greeter at a Giant store in Largo, Md., and two Walmart employees from the same Chicago-area store have died of covid-19." Do we know if they caught the virus at their place of work? The reporter doesn't say, and perhaps did not even ask.

Meanwhile, the reporter never stops to ask whether "at least four" is a sufficiently large number that grocery store workers should be worried. So here is some quick math. About 2.5 million Americans work in grocery stores. About one in every 30 thousand Americans has now died of Coronavirus. Taking the simplest route, you would expect approximately 83 grocery, or 2.5 million/30 thousand, grocery store workers to have died of the virus if they were of average risk.

If you were doing at least a semi-serious statistical analysis, you would then have to modify the 83 figure by age, preexisting conditions, etc., and almost certainly get a lower tally, somewhere in between 4 and 83. But the point is, despite the tenor of the article ("the rise of worker infections and deaths"), the fact that at least four grocery store workers have died of the virus doesn't give you any useful information about whether being a grocery store worker puts you at special risk.

I'm not saying there isn't an increased risk, and I do appreciate that the workers are coming to work every day and *potentially* putting themselves at higher risk. I am saying that reporting on "at least four deaths" out of 2.5 million grocery store workers isn't providing actionable information. Scare stories like this, that provide no context, with reporters who don't ask basic questions, are just irresponsible.

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1. the fact that at least four grocery store workers have died of the virus doesn’t give you any useful information about whether being a grocery store worker puts you at special risk.

Well, I agree it doesn’t give you much information, and the press could and should do a much better job with numbers. Journalists, like lawyers, are not very numerate.

But your “semi-serious” analysis is no better. The four came from three stores. How many grocery stores are there? How many employees do those four stores have? What is a sensible standard error to apply here (answer: very big).

1. You can add, which I thought of after I posted, that Walmarts aren’t grocery stores, though they do have grocery departments. So you’d have to know whether these workers worked exclusively in the grocery department, partly, or not at all.

2. Let’s just consider the two chicago area ones: how many people work at grocers in chicago? How do other covid-19 deaths in chicago divide up by employment type? And since they came from the same store – did they work together and thus did one likely infect the other? (So it would only be a single data point, not two). And so on.

I’m with Bernstein on this – the article was irresponsible and doesn’t even try to get a handle on what the danger level is for grocery employees. Journalists shouldn’t be making statistical arguments at all, much less by implication – they should get a data analyst to both do the analysis and explain it for them.

3. Actually, the number of stores and the average size of each store are irrelevant to the statistical analysis. The total number of people holding that job is sufficient to make (or rebut) the original journalist’s point.

I agree that a proper calculation of the confidence intervals of the calculation would be very useful to aid understanding. Running that calculation in this example would be non-trivial. Sadly, I must concede that it’s beyond the capabilities of the vast majority of journalists (and lawyers).

“Do we know if they caught the virus at their place of work? The reporter doesn’t say, and perhaps did not even ask.”

Perhaps because the answer is, almost by definition, unknowable in most cases.

The fact that four grocery store workers have died from COVID-19 that we know about suggests the real number is higher, as a significant number of deaths are not counted due to the lack of testing. It suggests the incidence of COVID-19 is much higher than 4 people in that population. And it suggests that there will be more such deaths in the future.

Personally, I’m terrified to go into a grocery store these days, even though I have to in order to get food. But then I’m not a law professor, so what do I know?

*Yes, you are quite right about the limitations of time and space. But if one limited themselves to scrutiny of Fox’s coverage, they wouldn’t get a full see of right-wing reporting and commentary. And that would be a shame because it has said so much about the “thinking” there.
*****

“Do we know if they caught the virus at their place of work? The reporter doesn’t say, and perhaps did not even ask.”
Perhaps because the answer is, almost by definition, unknowable in most cases.

*Damn, you jumped on that before I could. But it’s shockingly obvious, isn’t it.

[I assume health care providers won’t have trouble with workman comp claims, but I wonder how it will go for others will assert that they contract the infection in the course of their work.]

1. Meh. If someone worked in the stockroom at Walmart, and also volunteered at a nursing home where half the residents tested o positive for the virus, we’d have a pretty good idea where he likely was exposed. just for example.

2. Is it possible that the reason you are “terrified” is because of irresponsible reporting rather than justifiable understanding of true risk? Does it not seem strange to you that a National coverage newspaper would highlight the deaths of four people in a country of 300M? It strikes me as sensationalism.

1. And: I love the WaPo. I think it’s America’s best paper.

1. That’s a horrible thing to say about journalism.

1. Disaffected people say horrible things about journalism all the time, but the Washington Post is as good as any newspaper in the United States, and serious, educated, informed people tend to recognize that point.

2. Name a better paper, then.

1. Charmin. There’s plenty of WaPo in the grocery stores. But everybody loves to buy Charmin so much, you can hardly find it at all.

1. Your refusal to even attempt a serious response is noted.

2. So can we expect that Twitter, WhatsApp, and other social media site will delete this article from the Washington Post as misinformation about the virus?

Yeah, I didn’t think so either.

1. Why would Twitter delete an article that reports true facts but is merely sensationalist? It’s not even “misinformation”. What point are you trying to make?

3. There are many Walmarts and they are huge. They are the largest private employer in the US. I would be surprised if there weren’t several stores with multiple deaths from the bell curve alone.

Anyway, watch as memes shift live before your eyes. The shutdown is about “flattening the curve”, so hospitals with limited resources aren’t overwhelmed, leading to even more deaths. But not anymore?

It’s not about flat-out stopping a horrible disease from flaming through the population. That won’t happen.

But the meme inevetably shifts and people now treat it like death sentences in a post-apocalyptic world.

1. Don’t forget that most of those who have died from COVID-19 were over retirement age, too ill to work, or both. Walmart’s customer-contact jobs are also more physically demanding than typical office jobs – standing all day and lifting boxes. So “able to work at Walmart” implies a group with few of the more vulnerable people.

Fox just lives rent free in every libs head. Wait til OAN gets bigger,

NBC broadcasts pure ChiCom propaganda but its just Fox.

1. You figure the OAN is the future of reasoned, informed, mainstream thought and journalism in America. Chanel Rion is your idea of a legitimate journalist?

These are your peeps, Prof. Volokh. Good luck with that.

1. To be fair, he didn’t say that. He just said it would bug the shit out of liberals. I’d never even heard of OAN until John Oliver’s hilarious workup last Sunday.

3. Well, the story is from the Washington Post, so we can fairly start in full skepticism mode. Nobody expects a WaPo employee to ask questions beyond “How many followers does this twit have?”.
And every category of worker, including those forced out of work, are starting to die.
And retirees are starting to die.
Some of those dying are dying of COVID-19 virus effects.
So what? We all die.

4. It’s even worse — a “greeter” is usually an employee who is physically unable to do anything else, it is largely an anti-shoplifting effort as the “greeter” is a pair of eyes who can see carts full of stuff going out the entrance and can call security if it happens.

A greeter is likely to be elderly, likely to be disabled, likely to be the type of person who loves having a job sitting in a chair because that is all the person is physically capable of.

It’s honorable work — all work is honorable — but if they said that a guy unloading trucks died, it would be a different issue because that person isn’t as likely to have multiple preexisting conditions….

5. It would be useful to have more information — that the reporter should have been able to get.

Such as, what positions did these workers hold? A worker doing overnight stocking is probably at considerably less risk (of infection) than a cashier who comes within a few feet of hundreds of customers per day. Even with masks, gloves, and plexiglass dividers, some cashier (or other) will have lots of proximity with lots of people, lots of recently touched items, and probably quite a bit of cash.

So, reading the WP article was highly unsatisfying and could have been better, but it wasn’t really irresponsible. I’m sure that there will be better stories about dead grocery workers to come.

Supermarkets are hiring like crazy now, so you could pick up some extra cash during the crisis. At least until you have some actionable information that convinces you that you shouldn’t.

6. How cute is that! Longtobefree says you can start by being skeptical anything from WaPo, which this article is, so it’s at least on point. bratschewurst doesn’t even pretend to be on point and immediately complains about Fox News.

Me, I’d have said you can be skeptical about all media reports, not just WaPo. So maybe bratschewurst is a counterbalance to Longtobefree, although an overbalance, methinks.

7. I never watch the “news” and don’t have cable, but when multiple friends share a certain clip replaying something I will give it a look. Here:

Tucker makes a number of good points, including that these broad lockdowns are useless, because now everyone is just going to the neighborhood grocery store, and given that, for the vast majority of people going to their jobs isn’t going to increase spread.

1. How do you become informed about public affairs?

1. I read Mother Jones and posts by AK on VC comment threads.

1. I guess the remainder of the culture war is going to be even easier than I expected.

8. Not terribly surprised at irresponsible reporting.

Consider a story last week whose headline boldly announced a 19yo had tested positive for covid-19 and died. That claim is right up top in the article, which then quickly concedes he had other medical conditions. There’s several paragraphs about family and covid-19 context for the UK (which is where this person died). Then, in the very last paragraph, it reveals he died of something else, not covid-19. It was a gigantic bait-and-switch, and that was hugely irresponsible.

9. Walmart has 1.5 million employees in the United States alone. Trader Joe’s is smaller with 503 stores employing some 10,000 persons. And Giant is part of the Dutch conglomerate Ahold Delhaize, which employs 375,000 people at 6,500 stores in 11 countries.

While tragic, four deaths amongst the couple million people who work in American grocery stores is statistically irrelevant.

Hence not only do we not know if they even caught it on the job, nor how many underlying medical conditions they had, nor even if this even was what what actually killed them (all we know is that they tested positive for it) — but it is a statistically irrelevant number of people in the first place.

I mean, like, there probably are four grocery store workers who believe that Elvis is still alive — when you are dealing with numbers this large, probably more than four.

Which goes to why did the WaPo write this story in the first place — why are they irresponsibly contributing to the mass hysteria which is currently gripping this country. Is it that their basic math skills are so lacking that they can’t estimate how many grocery store employees there are — and hence how small a percentage of that four would be? Or is it more malicious and part of the larger “Orangeman Bad” campaign?

And why are we, as a formerly free people, putting up with the obtuse (and frankly bullshyte) regulations that we are? And why are we doing it on purported “science” that is almost as close to Alchemy as the Global Cooling/Global Warming./Climate Change diatribe….

I say again, we neither know how many people have the Wuhan Virus nor how many have already recovered from it. If, hypothetically, 90% of the people with it are never sick enough to need medical care (i.e. hospitalization), then not only do we move the decimal point one place to the left on all the dire counts and percentages, but we could already at peak infection.

Already — and in spite of all the bullshyte…..

1. why are [wapo] irresponsibly contributing to the mass hysteria which is currently gripping this country

Tbh very big stories are the tree of life to news orgs. The first Gulf War made CNN as you need 24 hour news to check up on things continuing to happen right now. Before this it was the 3-day power collapse. Before that, 9/11. Hurricanes are little burbles in this realm.

10. Yay, more of the same folks generalizing to say the lockdown is bad because their model and facts are better than the experts.

Truly the main victim of this pandemic is Trump.

1. The lockdown is very, very bad. The question is is it worse? For now, no. On retrospect…?

We don’t know if they will be hyperinflation at some point from all this unprecedented overspending and borrowing, wiping out life savings. We were spending at WWII per-capita rates before this, in good times.

And that’s just the beginning of the utilitarian arguments. There are larger ones we won’t know the results from for decadss to come, like how easy government overreach in taking away liberties might grease its use in the future. Perhaps more unsavory use.

1. It is another Citizens Compliance exercise, maybe the last one.

1. Why do you guys hate America?

Is it the Civil Rights Act? Women getting to vote? Students no longer subjected to religious indoctrination in public schools? Women admitted to graduate schools? Too much education, tolerance, science, progress, and reason?

2. It won’t take hyperinflation to wipe out life savings — memory is that the “Stagflation” of the Jimmy Carter era did a pretty good job of doing that to the generation that had fought in WW-I.

Back then it was the consequence of Lyndon Johnson wishing to have both Guns *and* Butter — his borrowing to fund both Vietnam and the Great Society, the latter of which was (and largely still is) purported to be a social good.

But I wonder how the Baby Boomers will feel when their retirements evaporate in a few years as the direct result of what well may have been a giant hoax. Yes, hoax — and don’t think that there aren’t a lot of people getting very rich off of this….

1. ” what well may have been a giant hoax. Yes, hoax ”

These are your followers, Conspirators. Still think you have a chance to turn the tide of the culture war in conservatives’ favor?

2. Truly the main victim of this pandemic is Trump.

At the very least — I would not be surprised if some seek to make the pandemic appear worse than it actually is so as to harm his re-election efforts. The country truly *is* that partisan today, and heaven help the next Democratic President because the same tactics will be employed against him, her, or it.

Andrew Cuomo may think that he can walk this into the Presidency, and maybe he can, but I hope people aren’t expecting him to be treated any more civilly than another New Yorker is currently being treated.

That said, the problem I have is that the purported experts are failing to follow basic statistical methods, something that no graduate student would ever get away with doing. They neither know what percentage of the people with the Wuhan Virus are going to get sick enough to seek hospitalization nor what percentage are immune from it because they’ve already had it.

Their curve model is legitimate based on the two aforementioned numbers, which they neither know nor are willing to admit that they don’t know….

This is like designing a city’s water tower without knowing either how much water it needs to hold nor how quickly you need to water out of it at peak usage. Do you see how not knowing those two things would be problematic?

I’m not challenging their models, instead I’m saying that the Emperor is stark naked…

1. “make the pandemic appear worse than it actually is so as to harm his re-election efforts”

The lib media is openly rooting for Plaquinel to not work because Trump is boosting it.

Did you know he owns 15,000 worth of a mutual fund which includes a French drug maker that sold the US rights years ago? He stands to make dozens of dollars.

2. At the very least, you’re willing to speculate about the bad faith of Democrats, but Trump is always the best.

If you don’t like the numbers because real life data gets janky (as though that’s a new an unexpected thing), why are you substituting your own take as though it has any more validity?

11. The public and Americans are largely innumerate.

Innumeracy: Mathematical Illiteracy and its Consequences (Hill and Wang, 1988) John Allen Paulous

Given the legal profession’s difficulties with Bayesian Inference, they are not excepted.

1. Nor are journalists.

Advertisers, on the other hand, have a pretty good handle on this stuff.

12. Amazingly, some things can be presumed to be true without requiring a rigorous statistical analysis.

Maybe come down from that horse once in a while and live among the regular citizens.

1. You can make that presumption. You will be wrong. To the example above, the original article claimed that grocery workers are at increased risk of infection. Statistical analysis showed that statement to be untrue. And it didn’t even require any great rigor. It was a pretty rudimentary analysis and still more than sufficient to disprove the article’s key thesis.

As that great scholar Barbie once said, “Math is hard.” That’s no reason to glory in your ignorance, though.

1. I suppose you could make the case that the rudimentary statistical analysis showed that the article didn’t prove its assertion. It certainly did not show that grocery workers are not at increased risk. Unless you are aware of some reported statistics that haven’t been included in this discussion.

2. Way to miss Jason’s point. Of course grocery store workers are at an increased risk of infection. Anyone who has more direct contact with others is at an increased risk of catching a respiratory virus.

1. Way to miss the point of the article. The data contradicts that hypothesis.

Another data point contradicting your (and Jason’s) hypothesis is the comparison of disease trends across jurisdictions with different lockdown rules. Sweden, for example, has not implemented the harsh social isolation rules of other countries yet their cases per capita are trending right in the middle of countries with much stricter rules. Right now, South Korea is the only outlier to the trends. The conclusion from looking at the actual data is that more or less direct contact does not, in fact, do all that much to your chances of catching this respiratory virus. That seems counter-intuitive – but that’s why we had to invent statistics. Human intuition is frequently unreliable.

1. No, there is no data in the article that contradicts the hypothesis that anyone with more direct contact with others is at an increased risk of catching a respiratory virus, including this one. We don’t have data to measure how many grocery store employees have caught Covid-19 or died from it. (I assure you that it is more than four.) We’re not even testing most sick people.

I am not sure what all Sweden is doing, but their deaths/1 mm population is higher than the U.S.’s. And they aren’t testing at the same rate as other countries, so their total cases/1 mm population may be skewed. There is an article about this on time.com today.

But I am sure that all the epidemiologists and infectious disease specialists are wrong here. Apparently, this respiratory disease spreads in some mysterious way. Feel free to walk around a the Covid-19 floors at an NYC hospital. I am sure you’ll be fine.

13. Surprised that nobody has mentioned (except Bernstein, in passing) the demographics of grocery store workers. Don’t those skew pretty young? If the people who died happened to be young, and thus members of a patient population which almost never dies of this illness, then even 4 of them, or 3, or 2, might be the tip of a quite large iceberg of grocery store infections. If their deaths were indicative of infections numbering in the thousands, would a claim of statistical insignificance still apply?

1. the demographics of grocery store workers. Don’t those skew pretty young?

There is a dual mode — 16-18 and 55-75, it’s who is interested in a part-time job, basically high school students and retirees. This is true for a variety of reasons including the fact that the high school students (a) in school weekdays and (b) are subject to state laws as to how late and how many hours they can work. They also can’t work around dangerous equipment (i.e. in a deli) nor sell alcohol in stores that sell it. Probably a few other things due to state laws.

So you have a lot of older people working during the day, and high school kids at night.

14. Morons!

Birx says government is classifying all deaths of patients with coronavirus as ‘COVID-19’ deaths, regardless of cause

15. Any update on this?