Critical Issues: Spot the Error

This one could be a WitCH or a PoSWW, except we’re withholding some information. So, consider it an analysis puzzle.

The following was posted to an Australia-NZ statistics list. The email was from an American statistician, referring to and quoting from this article (Update: link fixed), on a Texas hospital adopting critical care guidelines. See if you can identify the problem.

UPDATE (30/7)

A weird hint: we are not playing fair. (And, boy are people gonna be pissed.)

As we wrote in reply to a comment “There is the post, and the links to which the post refers. You can consider what ever issues you see.” So maybe list quickly, without elaboration, anything you see as an issue.

UPDATE (31/7)

OK, time to end this, and so a final hint. As indicated in the comments, the “problem” is with the poster’s line “Statistics is a bitch”. We’re very, very pleased that no one has hit upon the “problem” with this line.


Well, wasn’t that fun? Thanks to everyone for playing along.

As indicated above, the “problem” is with the line “Statistics is a bitch”. And what’s wrong with that line? Not a whole lot. It’s not a great line, since it can be read as treating the “statistics” as a from-nowhere reality, rather than the disastrous consequences of Republican screw-up. But no big deal.

So, why post on this as a problem? Because the stats email list to which the comment was posted thought it was a problem. A number of commenters took very serious issue with the poster’s use of the word “bitch”.

This began with an off-post email to the poster, indicating “the language used is not at all appropriate for [such] an email list” and a request: “I’d appreciate it if you could apologise for this choice of words.” (To whom?) The poster replied to the email list, with a long and unhelpful, but fundamentally reasonable, non-apology apology. In brief, the poster, who is in Texas, suggested that they had much, much bigger things to worry about. And then the bashing kicked in.

There were calls for the poster to “grow up”, to “stop using hurtful, offensive language”, suggestions that “the problem is the use of a term that is all too often directed at women in a derogatory way” (ignoring that this was not the case here), whining about “gendered name-calling”, and all manner of nitpicky and gratuitous complaint.

It was crazy and it was revolting, and all of it coming from proud and proper academics. Eventually there was some tepid defence of the poster, but way too little and way too late. No one stood up properly to these ridiculous, self-important language nazis.

Which is why we posted about it here. Of course this is the type of blog where those offended by strong language are unlikely to hang around. And, maybe some shyer types here agree with the poster’s critics. But, it was still very, very pleasing that no one who engaged here had a clue what we could have been on about.

71 Replies to “Critical Issues: Spot the Error”

  1. Indeed. Let’s say e.g. a death panel decides that blondes are more likely to succumb.

    Then, the statistics will reflect this as a “new fact”.

  2. The very definition of the survival rate required (for being allowed to continue hospital treatment) seems unclear. I suspect this is a relative of the Bertrand paradox, only that in this case we don’t even have a clear choice of probability spaces to choose from. It is also problematic that the decision on remaining in hospital or not will influence whatever survival rate is being used.

  3. There’s only one hospital for the whole county? Great job, American healthcare. (To say nothing of the fact that America’s let its side of the pandemic get this bad.)

    My gut feeling is that hospitals should be sending home the patients with the highest chances of recovery and focusing on rescuing those with the lowest chances, but I don’t know enough about medicine to say whether this will actually save more lives than the reverse.

    1. Hi, edder. Obviously, American health care is, even without the pandemic screw-up, a disaster. I have no idea what “county” means in this case, however, so it’s not obvious to me that having just one hospital is surprising or unreasonable.

      1. A U.S. county is the same thing as a Local Government Area in Australia so it’s not overly surprising a county might only have one.

  4. I give up Marty.
    Apart from the obvious point that patients sent home may transmit the virus, especially very ill patients. And the poor use of the word “alleviate”; and it should be something like “survival chances” not “survival rates”

    1. Thanks, tom. Yeah, those wordings are pretty sloppy, but that’s not the problem. I’m being deliberately hazy with this one. Maybe I’ll give a clue in a day or so.

      1. Hi Marty. I’m not honestly sure what it means to call statistics a bitch. But I take it the author means “oh jeeze, we’ve got these figures telling us our nation’s health system isn’t quite up to scratch, I suppose we have to go into damage control mode and only save certain people. If only the statistics were telling us something different.”

  5. Doctors choose which patients they “can save” is making a lot of assumptions.

    The definition of “likely” is also missing.

    But I suspect that is not the problem.

  6. One other problem – if people are really sick they are likely really contagious. Sending them home surely creates more problems than it solves in the long run.

    Again, I suspect I’m missing the problem.

    1. Yes, RF, that sounds like a crazy plan. I haven’t carefully read the guidelines (which are written in a general manner, not for COVID), so it’s not clear what is really intended. And yes, that’s not the problem.

  7. Well, they’re not just going to go home to die alone, are they. Someone will have to look after them, which means that person and their contacts are all at risk. And if those people get it, they’re more likely to be ‘ahem’ worth saving. In other words, sending the undeserving home to die is just going to come back and bite you on the ass.

    1. Hi, Damo. Yes, as others have noted, “send ’em home” is crazy, although it’s not clear whether that suggestion is a bad plan or poor reporting.

  8. Agreed, Damo. I suspect Marty has something a bit more fundamental in mind, but I can’t quite figure it out just yet.

    One suspicion is how they calculate “worth saving”. How do they weight the different factors such as age, underlying health conditions, insurance status…?

    Also, do these calculations change with the number of people in the hospital at any time? If so, the goalposts would be in a constant state of flux.

    For example, person X presents to a hospital today and there are N people already in the hospital. The panel calculates your “number” and sends you home. Overnight, M people in the hospital die, so person X comes back and this time is admitted…? Possible?

    1. RF, yes that kind of calculus is pretty weird. On the other hand, if they have to do it, they have to do it. Without getting into the kind of inhuman bean-counting that Gigi Foster has turned into an art form, it is not unreasonable for a hospital system to have some plan for when its facilities are overwhelmed. (Of course the fact that Texas is being overwhelmed now is pure Republican insanity.)

      But, the problem is different.

  9. So, just to be clear, it is a mathematical issue and not a health/logic one?

    If a patient were sick and was going to die in P days and another was sick and was going to die in P+10 days, surely they would send the second patient home since the first would tie up hospital resources for less time, but with the same outcome?

    Or, would they argue that with P+10 days to treat, there is a higher probability of recovery? Tough call.

    Horrible I know.

    1. There is the post, and the links to which the post refers. You can consider what ever issues you see.

      Just to clarify, although it doesn’t matter for the puzzle, the links are slightly confused. The poster quoted from a Guardian report but linked to a Texas newspaper. The Texas newspaper linked to the hospital’s decision, but not to the guidelines. I dug up the guidelines.

  10. Survival rate refers to a population, not to individuals in the population. The correct term is survival likelihood (chance of survival), or more precisely, mortality risk.

    1. I used to work in cancer statistics and got to know a bit about survival rates.

      One often hears statistics like this: The 5-year survival rate for women with breast cancer is 80%.

      One might think this means that, of 100 women who get breast cancer, 85 will survive for at least 5 years.

      Well it doesn’t.

      It turns out that “survival rate” is most often used for “relative survival rate” which is defined to be a ratio of probabilities. (No need for details here.) I thought that perhaps one could have a relative survival rate exceeding 100%. I discussed this with my pure-mathematical colleagues over coffee and sure enough we came up with an example where, conceivably, one could have a relative survival rate > 100%.

      The moral of the story is to go back to the definitions.

      1. I meant:

        One often hears statistics like this: The 5-year survival rate for women with breast cancer is 80%.

        One might think this means that, of 100 women who get breast cancer, 80 will survive for at least 5 years.

  11. Here are a few random thoughts from overnight:

    The survival rate is historical and since this is a new virus, can the “survival rate” of Texans be properly known?
    Its Texas, so could factors such as race be used in the calculations?
    Hospitals who only treat patients with greater chances of survival will naturally report higher success rates. This doesn’t mean they are any better (thinking Simpson’s paradox here) since the more sick patients will tend to go to the better hospitals simply because the better hospitals can succeed where others cannot or will not try.

    EDIT: Is it relevant that the guidelines to which the article refers are from January 2014?

    1. Hi, N8. Yes, the idea of evaluating “survival rate” for COVID is problematic. And, yes, any subjective standard is open to corruption. But what’s the alternative? Again, although the language of the reports is sloppy, and the nature of the guidelines is problematic, there is probably no choice. If you have N beds/whatevers and 3N people who need them, you gotta make choices. And if you have poor information for making those choices, you still gotta make choices.

    1. Yes, but they seem to be the correct guidelines. The point was to have a general plan for when a hospital is overwhelmed by some health crisis. It wasn’t a particular plan for a particular type of crisis.

  12. I’m pleased by this one, although it might end up with me being beaten up. Should I give a(nother) hint? Big or small?

  13. This sentence is problematic “…our doctors are going to have to decide who receives treatment, and who is sent home to die by their loved ones.”

    Something tells me though that the “statistics is a bitch” line is key here. An internet search for “when winning is losing” linked me up with an interesting article but I don’t think that was the point.

  14. Also, technically it is probability being used, not statistics.

    Statistics are what they become after they get the virus etc.

    1. A statistic is a characteristic of a sample. Data is data. It bugs me that the media confuse the two: The latest COVID-19 statistics are that 700 people were infected in the last 24 hours. No. The latest COVID-19 data is that 700 people were infected in the last 24 hours.

      Statistics isn’t the bitch. The data that gets crunched is the bitch.

  15. No statistics seem to have been quoted anywhere in the article.

    No mean, sample-mean, not even sample size (there were a few mentions, but nothing I would say confidently is the sample size)

    And, if we’re talking about grammar, data is plural. The singular is datum. Very few reporters seem to know the word though.

    1. Yep, (1) and (2) could be considered problems. Since the field of statistics is singular, I’m not sure the grammar is a problem, but in any case none of these are the problem.

  16. OK, you can delete my comments then, unless you or others will think they are amusing.

    I’m sure you are quite amused at our collective struggle here, which means it is going to be something quite obvious once we all find it…?

    1. Thanks, I’ll leave them for now, just in case others are getting an incorrect “comments are closed” message. I must have done something dumb, but I don’t know what.

  17. I’m thinking you’ve cut something off the original post that was written under the “statistics is a bitch” line and if we saw that part it would all be clear.

  18. Final guess and then I’m waiting for the post (hopefully coming…) about the SACs teachers have submitted.

    To answer your question to Craig: “Statistics is a bitch” implies that somehow the statistics are the reason certain people will be refused treatment. It is not the statistics making the decisions, it is doctors, and statistics can be used to justify many, many things depending on which statistics are used and which are ignored. (Or which statistics are given greater weight in the decision).

    A British scientist claimed in the early 2000s that increased sales of frozen confectionary over time was proof of global warming as an example.

    1. Thanks, RF. Your answer to Craig is (almost) a very good point. The intention of the poster is unclear from the post, but the colourless pointing to “statistics” distracts from the people applying these statistics. Also, and I think this is more important, it distracts from the circumstances that created these statistics, and the reasons for those circumstances. It’s telling that “death panels”, which was a vicious Republican slur against Obama, may now become a reality as a consequence of Republican lunacy.

      But, that’s not the “problem”. I’ll post a final hint in a minute. (And SAC post is coming.)

      1. I’m not sure that statistics plays any part in any of the decisions that lead up to someone being sent home. The guidelines apply once the governor declares a pandemic respiratory crisis – maybe this decision will be influenced by data and statistics, but it is not the only consideration. Once they do come into affect, the decision to send someone home is based on exclusion criteria and the MSOFA score – a score which is determined by assigning a number to a variety of measurements and observations. These numbers are added together to get a final number, which determines if you stay or go. So statistics may be a bitch, but it’s getting a bit of an unfair whack here – this is about a series of personal judgement calls informed by what appears to be a fairly arbitrary ‘score’. Still, I doubt this is ‘the problem’ that Marty is thinking of. Smug bastard.

        1. Not “the problem”. The “problem”.

          I don’t think the poster is serious about whacking statistics, or is attempting to be precise in any such manner. Perhaps it should be interpreted as “bloodless determination is a bitch”, but even then it’s unlikely they’re whacking the bloodless calculation.

          In any case, that’s not the “problem”.

  19. I’m a little unsettled by your insistence on the “problem” as opposed to “the problem”. Also by your insistence on “productive struggle”. I’m beginning to think – in light of your previous post WitCH 40: The Primary Struggle – this post is intended as a ‘prompt’, where we all struggle (or not, as the case clearly is) our way to a deeper understanding of Mathematics or something through a vague, open-ended ‘challenging question’. Surely it’s not intended as a ruse to highlight the inadequacies of such an approach? No, you wouldn’t do that. Would you? I’m going to bed to sleep restlessly and get up in the morning feeling emotionally and mentally crushed.

    Is the “problem” “How or why is statistics a bitch?”? No, it’s not. Why am I still here? That’s a problem.

    1. Well, there’s irony. Sorry, Damo, “productive struggle” was just a joke. But misinterpreting the joke meant you were struggling in just about as productive a way as primary kids inflicted with that nonsense.

      “Problem” is in scare quotes.

  20. This is almost certainly wrong since you’ve now said it concerns the last line, but I just thought of something. Maybe the “problem” is this.

    The first paragraph sounds like the openening to a VCE hypothesis testing problem, like one such as “a factory manager has set up a testing machine to see which products are fit for sale and which ones are defective.” Then maybe an “answer” to the “problem” is the last line.

  21. I’m going to stick with my guess that the problem is the word “Bitch” since the author of the original article and everyone quoted (including the nurse at the hospital) is a “he”.

    I’m constantly haunted by the thought that the problem has to be Mathematical in nature though…

    1. RF wins. The problem, or “problem”, is the word “bitch”. We’ll update with an explanation soon.

  22. Thanks for the clear wrap up. Indeed, kinda interesting no commenter was concerned about this word.
    A quick story – I’m a secondary teacher, and one day fell into a conversation with a kid about not much, and he reckoned he was pretty good at spinning a basketball on his finger, and I reckoned the same of me, so we went to the gym after school, found two basketballs, and had a one-shot winner takes all ($2! we made a bet!) competition, which I have on video out there somewhere. I won (natch) and it’s a highlight that at the end of the video, I turn to the kid and say, “so where’s my two bucks? … bitch.” And he laughed, and I laughed. Not that frightening a word.

    1. Jerry, that’s a hilarious story, and a perfect story. It demonstrates exactly why the statisticians’ take is so awful. Of course words can be offensive, and of course one must gauge the audience and choose words with the audience in mind. But this endless bad-faith game, this determined effort to seek and to maximise offence wherever possible, is poisonous. They’re assholes. And academia is full of them.

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