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February 16th, 2023 (Permalink)
The following headline appeared recently in a medical newsletter:
1 in 4 Docs Experiencing Clinical Depression1
This would be alarming news if true, but thankfully it's not. The article the headline linked to has a less alarming headline:
More Physicians Are Experiencing Burnout and Depression
Given recent events, that's not surprising. The article beneath the headline begins: "More than half of physicians reported feeling burned out this year and nearly 1 in 4 doctors reported feeling depressed…". However, "feeling depressed" is not the same thing as "clinical depression", and the newsletter headline dropped the word "nearly". A more accurate if less scary headline would be: Nearly 1 in 4 Docs Report Feeling Depressed.
Later in the article, we read: "Among the 23% of physicians who said they were depressed, about two thirds said they had 'colloquial depression' (sad, blue, feeling down) compared to about 1 in 4 who said they were clinically depressed." Obviously, the editor who wrote the headline for the newsletter saw the first sentence, then later read that "about 1 in 4…said they were clinically depressed", and then thought that these were the same 1 in 4. Instead, the latter is a fourth of the earlier fourth.
More precisely, we learn from a slideshow about the survey2 that of the 23% who said they were "feeling depressed" 24% said that they were "clinically depressed". This is only about 5.5% of the physicians surveyed, which is close to 1 in 18 rather than "1 in 4".
It's hard to know whether this statistic is worrisome without knowing what percentage of the general public is clinically depressed, which the article does not mention. According to the National Institute of Mental Health, in 2020 6% of American adults had a "major depressive episode with severe impairment"3―which seems to correspond to "clinical depression"4. If so, then it doesn't appear that the physicians surveyed were unusually depressed.
Since the article was reporting a survey, there are some questions that should always be asked, for instance: What was the size of the sample? According to the slideshow5, the sample size was 9,175―a very large sample compared to most public opinion polls, which usually have about a thousand respondents.
Another important question is: How was the sample acquired? According to the slideshow: "Physicians were invited to participate in a 10-minute online survey.5" How were the physicians "invited"? How were they chosen to receive an invitation? The slideshow doesn't say. If the "invitation" was by e-mail or by a notice on Medscape's website, and only those physicians who volunteered to answer the online survey did so, then this was not a "scientific survey"6. The slideshow claims a margin of sampling error of slightly more than one percentage point, yet the mathematical theory of sampling error is based on the assumption that the sample was selected randomly from the population7―in this case, physicians.
Without more information about who received an invitation and how the participants were selected, we can't be sure that this sample was representative of physicians in general. The physicians who were invited and accepted the invitation to participate in this survey may have differed from those who either were not invited or turned down an invitation. Perhaps those who were depressed were more likely to participate in such a survey, or maybe they were less likely to do so because they were too depressed.
For these reasons, it doesn't appear that this survey is anything to get depressed about.
- The headline, from an undated Medscape psychiatry newsletter, links to the following article: Christine Lehmann, "More Physicians Are Experiencing Burnout and Depression", Medscape, 2/1/2023. Thanks to Lawrence Mayes for calling the problem with the headline to my attention.
- Leslie Kane, "'I Cry but No One Cares': Physician Burnout & Depression Report 2023", Medscape, 1/27/2023, p. 21.
- "Major Depression", National Institute of Mental Health, 1/2022.
- Daniel K. Hall-Flavin, "Clinical depression: What does that mean?", Mayo Clinic, 5/13/2017.
- Leslie Kane, "'I Cry but No One Cares': Physician Burnout & Depression Report 2023", Medscape, 1/27/2023, p. 29.
- How to Read a Poll: Scientific Versus Self-Selected, 12/6/2022.
- Charles H. Backstrom & Gerald D. Hursh, Survey Research (1963), chapter 2. The reality is that no survey of human beings ever has a completely random sample since people can always refuse to participate, which is a problem currently bedeviling public opinion polling.
February 14th, 2023 (Permalink)
Who's My Baby?
The song "Everybody Loves My Baby", which will be one hundred years old next year, has been performed by everybody from Louis Armstrong to, oddly enough, Brigitte Bardot*. The song's lyrics tend to differ depending on the performer, but one thing that stays the same is the chorus:
Everybody loves my baby
But my baby don't love nobody but me
Nobody but me!
Everybody wants my baby
But my baby don't want nobody but me
That's plain to see!
Relying entirely on the above lyrics, can you figure out who my baby is? This is not a trivia puzzle, so looking up the rest of the lyrics would only lead you astray.
Assume nothing: take the lyrics literally.
Ignore the double negative: "don't love nobody but me" means "loves only me".
I'm my baby.
Explanation: According to the first line of the first stanza, everybody loves my baby. My baby is, of course, included in "everybody". So, my baby loves my baby, naturally enough. However, the second line tells us that my baby loves only me. Therefore, my baby = me. I'm my own baby!
Of course, it may strike you that there's something weird about this conclusion. We would usually understand "everybody loves my baby" to mean "everybody else loves my baby", that is, everybody other than my baby loves my baby. But that's rather a mouthful, so we just leave "other than my baby" implicit.
Similarly, we understand "my baby don't love nobody but me" to mean that among other people my baby loves only me, ignoring the possibility of self-love. This is why I said to take the lyrics literally in Hint 1. If you don't do so, then there's no way to figure out who "my baby" is from the little information given in the chorus.
Technical Appendix: For those who know predicate logic, here's an analysis of the lyrics and a proof of the solution. The lyric "everybody loves my baby but my baby don't love nobody but me", is a conjunction consisting of two statements conjoined by "but", so I'll treat the conjuncts separately:
- "Everybody loves my baby.": Since the subject of these lyrics is people―me, my baby, and the people who love and are loved by me and my baby―we'll take people as our universe. In addition, let "b" stand for "my baby" and "Lxy" mean that "x loves y". Given those abbreviations, we can represent the statement as: ∀xLxb.
- "My baby don't love nobody but me.": Let "m" represent "me". The statement says that the only person my baby loves is me; in other words, if my baby loves a person then that person is me. So, the statement can be represented: ∀x(Lbx → x = m).
That completes the logical analysis of the lyrics. Now the proof that I'm my baby is easy:
- Lbb, from 1, by universal instantiation (UI), since b is a person.
- Lbb → b = m, from 2, by UI.
- b = m, from 3 and 4, by modus ponens (MP).
As mentioned above in the Explanation, "everybody loves my baby" is not usually taken so literally as to imply that my baby loves herself, but you had to do so in order to solve the puzzle. If we modify the above predicate logic representation of the two statements to interpret them more colloquially, we get:
- "Everybody loves my baby.": "Everybody" excludes "my baby", so we add a hypothetical clause to exclude "b": ∀x(x ≠ b → Lxb). Literally speaking, what this says is: everybody other than my baby loves my baby.
- "My baby don't love nobody but me.": Again, we need to exclude "b" from the universal quantifier, so we add an additional hypothetical clause: ∀x[(x ≠ b & Lbx) → x = m].
With those changes made, the proof that b = m no longer works since b ≠ b is false, thus blocking MP.
* You can check out B.B.'s surprisingly good performance here, though it's obvious that English is not her native tongue: "Brigitte Bardot―Everybody Loves My Baby" (1968), YouTube.
February 4th, 2023 (Permalink)
Guesstimate It, Part 2
Last month's guesstimation entry1 was a warm-up for this one. If you haven't already read that entry and tried to guesstimate the answer, you should do so before attempting this one since the solution to this month's problem will use what we learned last month. Here is this month's problem:
Guesstimate It: What is the percentage of women of child-bearing age in the United States who are currently pregnant?2
Extra Credit: How many American women are currently pregnant?
Use what you know. It's common knowledge that human pregnancy lasts about nine months. You should remember from last month that we estimated the child-bearing years as thirty years out of a woman's life.
How many children on average does an American woman have in her lifetime? You should be able to estimate this based on common knowledge.
Put together your estimates from the two previous hints to guesstimate the answer to the problem.
In the previous guesstimation, we estimated that the average number of child-bearing years is thirty. From common knowledge, we know that a pregnancy lasts about nine months. Also from common knowledge, we can estimate the average number of children that an American woman has. Clearly, it's not zero. Is it as high as ten? Surely not; while there may be some women who have as many as ten children, most currently have far fewer than that. Based on your own experience, you can estimate that the average is in single digits, and probably in the low single digits.
Is the population of the United States increasing? Yes, but if it weren't for immigration, the U.S. population would be close to stable. This means that the average American family is reproducing at about the replacement rate, that is, at a rate sufficient to replace the existing population. The replacement rate is somewhere between two and three children per family―it needs to be slighly greater than two since some people do not have children. So, let's guesstimate that the average woman has two-and-a-half successful pregnancies.
Finally, not all pregnancies go to term as there are both spontaneous and induced abortions. Exactly how many months of pregnancy are added to the average time spent in pregnancy is much harder to estimate than the previous numbers, but let's suppose it's an additional half of a full-term pregnancy. So, our final estimate would be that the average American woman experiences approximately three pregnancies, for a total of 27 months pregnant.
30 years consists of 360 months, so the fraction of her child-bearing years a woman spends pregnant would be 27 out of 360 or 7.5%. So, our final guesstimate is that around seven to eight percent of American women of child-bearing age are currently pregnant.
Extra Credit Answer: To answer this question, all we have to do is put together the above guesstimate with our previous guesstimate of the number of women of child-bearing age, namely, 62 million. 7.5% of 62 million is 4,650,000. So, four or five million American women are currently pregnant.
In the previous guesstimation entry, I may not have emphasized enough that I made the estimate before doing any research on the question. I can't prove this, of course, so you'll have to take my word for it. Similarly, I made the above estimate without researching any of the facts related to answering it, relying instead on common knowledge and my own experience. Part of the point of doing these guesstimation exercises is to emphasize that you don't need to research to make a good estimate. For this Fact Check, I'll do the research to check my work. By doing so, we'll also be able to see where any errors in estimation were introduced.
Let's start with the question in Hint 2: How many children on average does an American woman have in her lifetime? According to the most recent data I could find*, the current average is slightly below the replacement rate―which is about 2.1―at 1.73. This is less than I estimated, which would tend to make the final estimate too high, everything else being even.
Exactly how many American women are pregnant at a given time seems to be a hard statistic to find. However, since most women will not be pregnant more than once a year, we can use the number of babies born in a given year as a proxy for the number of pregnant women. 3.6 million babies were born in the U.S. in 2020†, the most recent year for which I could find data. This is a million lower than my guesstimate, but I slightly overestimated the average number of children per woman, so this is to be expected. Also, I included in that estimate women whose pregnancies did not result in live births, for which I've not found any statistics.
This exercise shows again that it's possible to make surprisingly accurate guesstimates quickly using only common knowledge and simple mathematics. Such guesstimates are useful for checking the plausibility of statistical claims made by advertisers, politicians, and the news media.
*"QuickStats: Expected Number of Births over a Woman’s Lifetime—National Vital Statistics System, United States, 1940–2018", Centers for Disease Control and Prevention, 1/10/2020
†"US birth rate falls 4% to its lowest point ever", BBC, 5/6/2021
- Guesstimate It, 1/13/2023.
- Like last month's problem, this one was suggested by one from Saul X. Levmore & Elizabeth Early Cook's Super Strategies for Puzzles and Games (1981), pp. 57-58.
February 2nd, 2023 (Permalink)
Evoke or Invoke?
The Introduction to a book that I've been reading includes a description of a seemingly ghostly experience the author had, ending with the following passage:
…I don't believe in ghosts. While the experience was very compelling, I thought that my mind was just playing tricks on me. … [M]y experience can easily be explained by what we know from scientific research on human perception (and misperception)―without the need to evoke supernatural phenomena.1"
"To evoke" is a verb meaning to call forth something, often a memory or a feeling2, but sometimes a spirit or other supernatural entity. The related adjective "evocative" describes something that evokes memories or emotions. The stem of both words comes from the Latin verb "vocare" which means "to call", and the prefix "e-", a variant of "ex-", meaning "out of" or "from". So, based on its etymology, "to evoke" is "to call out". So, "to evoke supernatural phenomena" would seem to mean to call forth such phenomena, that is, to summon spooks or raise demons. However, given the larger context of the word, it's clear that's not what the author meant.
"Vocare" is the source of many other English words, including "vocal" and "vocabulary", all having to do with speaking or words. Another is "invoke", which differs from "evoke" in having the opposite prefix "in-", meaning, unsurprisingly, "in". Thus, "to invoke" is, by its etymology, "to call something in", and in English means calling in something that explains or supports3. So, what the author was trying to say was that his ghost story can be explained by the science of perception without invoking the help of the supernatural.
Given that both "evoke" and "invoke" are English verbs, it's unlikely that a spelling or grammar checking program would catch the substitution of one for the other. I tried the quoted text in several spelling and grammar checking programs and not a single one objected to "evoke", though a couple seemed to think there was something wrong with "misperception"―a misperception4, indeed.
Only one of my reference books includes an entry on the confusion of these two words5, which may evoke the response that confusing the two words must therefore be uncommon. In response, allow me to invoke the fact that your spell-checker will not prevent your doing so. Moreover, it's worth appreciating the difference in meaning between these two closely-related words.
- Thomas Kida, Don't Believe Everything You Think: The 6 Basic Mistakes We Make in Thinking (2006), p. 12
- "Evoke", Cambridge Dictionary, accessed: 2/2/2023
- "Invoke", Cambridge Dictionary, accessed: 2/2/2023
- "Misperception", Cambridge Dictionary, accessed: 2/2/2023
- Harry Shaw, Dictionary of Problem Words and Expressions (Revised edition, 1987)