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December 25th, 2023 (Permalink)

The Christmas Party

Every year, the Blancs throw a Christmas party for their extended family. This year, the guests threw their hats and heavy winter coats into a pile on the bed in the guest bedroom of the Blancs' house. One of the five guests, uncle Al, who had to hurriedly leave the party early, grabbed a hat and coat that did not belong to him from the heap. What's more, the two outer garments that Al went off with belonged to two different relatives. As a result, when the other guests began to leave later, there was so much confusion that none of them got their own hat and coat. In fact, each left with someone else's hat and a coat belonging to a different person.

The day after Christmas, Mrs. Blanc tried to clear up the confusion so that each guest could retrieve both missing garments as well as return the incorrect ones to their actual owners. Here are the facts that Mrs. Blanc was able to discover:

  1. Aunt Debby took the coat of the guest whose hat was taken by cousin Eric.
  2. The relative who took cousin Carl's hat also took aunt Debby's coat.
  3. Cousin Betty didn't take aunt Debby's coat, and Debby didn't take cousin Eric's hat.
  4. Aunt Debby took the hat that belonged to the owner of the coat that cousin Carl took.
  5. Cousin Eric took uncle Al's hat.

From the above clues, can you help Mrs. Blanc determine whose hat and coat was taken by each guest?

Poll Watch
December 21st, 2023 (Permalink)

A Bad Headline for a Bad Survey

Here's a recent headline from a news story reporting a survey:

Majority of Americans 18-24 think Israel should ‘be ended and given to Hamas’1

You may notice, if you read the article beneath the headline, that there's no reference to a margin of error (MoE), which is unusual since most major American newspapers will report the MoE of a poll even when the reporter has no clue what it means. All the article says about the poll's methodology is: "The Harvard-Harris poll was conducted between Dec 13-14 among 2,034 registered voters." This is not an oversight on the The New York Post's part, since the report put out by the pollster, Harvard-Harris, also provides no MoE. Here's all that the pollster itself says about its methodology:

This survey was conducted online within the United States from December 13-14 among 2,034 registered voters by The Harris Poll and HarrisX. Results were weighted for age within gender, region, race/ethnicity, marital status, household size, income, employment, education, political party, and political ideology where necessary to align them with their actual proportions in the population. Propensity score weighting was also used to adjust for respondents' propensity to be online.2

So, this appears to have been an online poll that didn't use a random probability sample, which is why there is no MoE. The report doesn't tell us exactly how the sample was taken, but it might be a panel recruited from internet users.

The problem with such samples is that the recruits may not be representative of the population, which is why the pollsters weight the samples to match population characteristics. However, there's no guarantee that weighting can make up for every bias in the sample. For instance, the "propensity score weighting" mentioned appears to be an attempt to make up for the fact that people who spend a lot of time online are more likely to be in the sample than those who don't, and those two groups may differ in other ways. However, only those who spend at least some time online will make it into the sample, and they may differ from those who spend no time online at all.

So, the methodology is a reason to be skeptical about these results but, as we saw in the previous entry3, they are similar to those of other surveys that did use probability sampling. However, there are additional reasons for caution.

If you read down in the article, the basis for the headline is in the following sentence: "The survey, conducted this week by Harvard-Harris polling, found 51% of Americans between the ages of 18 and 24 said they believed the long-term answer to the Israel-Palestinian conflict was for 'Israel to be ended and given to Hamas and the Palestinians.'" So, it's a "majority" by only one percentage point, with the remaining 49% supporting either a separate Palestinian state or other solution4.

Since the survey has no MoE, we can't say that this difference was within the margin, but that doesn't mean that the results are perfectly precise. If the entire sample of over two-thousand had been a probability sample, the MoE would have been slightly over two percentage points plus or minus5. So, even if it were a probability sample, 51% would be a "majority" only by over-precision6. Moreover, there are two reasons why the actual error bars for this result are much greater:

  1. Since it's not a probability sample, there may be a systematic bias that weighting does not correct. If, as suggested above, there is a difference between people who spend at least some time online and those who spend no time online, there's no way to weight the results to correct the difference. In particular, people who do not use the internet at all are likely to be older and poorer than those who do7, and we've seen that there is a large age difference in attitudes towards Israel.
  2. Given that the headline result is for the 18-24 age group, it is based on only a fraction of the two-thousand respondents for the entire survey. The results were partitioned into six age groups4, so that the size of the subsample would be about one-sixth of the entire sample, that is, a little over three-hundred respondents. The MoE for such a small probability sample would be over five percentage points either way.

For these reasons, the headline claim is not supported by this survey, and a more accurate headline would have been: "Half of Americans 18-24 think Israel should 'be ended and given to Hamas'", but there are still more reasons for skepticism.

In the same survey, respondents were asked: "Should Hamas be allowed to continue to run Gaza or does Hamas need to be removed from running Gaza?8" 58% of the same age group responded that Hamas needs to be removed from running Gaza, which is inconsistent9 with the claim that 51% think that all of Israel should be given to Hamas.

The responses include other such inconsistencies, for instance, when asked: "Do you think Israel has a right to exist as the homeland of the Jewish people…?10", 69% of 18-24 year olds answered that Israel has such a right. How is this consistent with half of the same group thinking that it should be "ended" with Hamas taking over? There are additional inconsistencies, but that's enough to show that something is seriously wrong with these results.

I'm not sure what went wrong with this survey, but given the inconsistent results, convenience sampling, and the limited explanation by the pollsters of their methodology, I'm filing it in the round file.


  1. Jon Levine, "Majority of Americans 18-24 think Israel should ‘be ended and given to Hamas’", The New York Post, 12/16/2023.
  2. "Key Results-Harvard CAPS-Harris Poll: December 2023", Harvard CAPS-Harris Poll, p. 2.
  3. Does watching Republican debates make people 17% less likely to vote for Nikki Haley?, 12/15/2023.
  4. Harvard CAPS-Harris Poll, p. 69.
  5. All MoEs in this entry were calculated with the following calculator: "Margin of Error Calculator", Good Calculators, accessed: 12/20/2023.
  6. See: Overprecision, 8/27/2022.
  7. Andrew Perrin & Sara Atske, "7% of Americans don’t use the internet. Who are they?", Pew Research Center, 4/2/2021.
  8. Harvard CAPS-Harris Poll, p. 64.
  9. It's logically consistent that Hamas should be removed from running Gaza and given Israel, since these are separate territories, but its not psychologically consistent: if Hamas is not fit to run tiny Gaza, it's surely not fit to run a larger area.
  10. Harvard CAPS-Harris Poll, p. 57.

Debate Watch Debate Watch
December 14th, 2023 (Revised: 12/15/2023) (Permalink)

Does watching Republican debates make people 17% less likely to vote for Nikki Haley?

As I discussed during the summer1, I haven't been paying attention to the party political debates, unlike in past years, but I did hear about one claim from a debate that deserves attention. During the most recent Republican debate, Nikki Haley, the former governor of South Carolina and current candidate for the party's nomination for president, said: "For every 30 minutes that someone watches TikTok, every day, they become 17% more anti-Semitic, more pro-Hamas based on doing that.2"

"More than what?" This is the question you should always ask yourself when confronted by a dangling comparative3. There are two such comparatives in her statement: "more anti-Semitic" and "more pro-Hamas", but more than what?

Haley appears to be saying that an individual who watches TikTok for thirty minutes becomes 17% more anti-semitic and also more pro-Hamas―also 17%?―than when he or she started watching a half-hour before. It might be said that some people are more anti-semitic than others―for instance, those who want all Jews to be killed as opposed to those simply wanting to keep them out of their country club―but how in the world could this be quantified to a percentage? Is a neo-Nazi who supports genocide 17% more anti-semitic than a Christian who thinks that all Jews should be forcibly converted to Christianity?

Even if there were some way to measure the degree of anti-semitism such that 17% more anti-semitic would make sense, is it plausible that only a half-hour's viewing would cause such a large change? I could more easily believe that watching TikTok for half an hour makes you 17% more stupid as measured by an IQ test.

Moreover, anti-semitism no doubt overlaps with being pro-Hamas, but they're not identical; for instance, a Christian anti-semite might well be appalled by Hamas' terrorism and strongly oppose the group. Given that these attitudes are not identical, it would be surprising if the supposed pro-Hamas effect of TikTok was also 17%. There's also the same measurement problem: How would you measure pro-Hamas beliefs? Is someone who supports Hamas terrorists raping Israeli women before killing them 17% more pro-Hamas than one who thinks that they should just kill them?

When Haley's campaign was asked about the source for her claim, it pointed to a news article in The New York Sun4, which reported as follows: "Spending a mere 30 minutes per day on TikTok led to an average 17 percent increase in a user’s 'antisemitic or anti-Israel views.'5" The newspaper was reporting an analysis of a survey that asked questions about Israel and Jews. The analysis compared people who use TikTok for at least thirty minutes a day to those who don't, so the results were at the group level, rather than the individual. I assume that the "30 minutes a day" distinction was a rather arbitrary attempt to divide people into those who were regular TikTok users, and those who either didn't use it at all or only did so casually. So, the results do not mean that an individual who uses TikTok for half-an-hour becomes 17% more anti-semitic, but that 17% more of the frequent TikTok users were judged to be anti-semitic than non-users or occasional users.

None of this means that TikTok use is causing an increase in anti-semitism or anti-Israel attitudes6. TikTok users tend to be younger than the general population7, and recent surveys indicate that younger Americans are more likely than older ones to subscribe to anti-semitic views8. For instance, 20% of those aged 18-29 agreed to some degree with the statement that the Holocaust is a myth, whereas the level of agreement among older respondents was in the single digits for each age group and 0% for those 65 and older9.

According to another survey, Americans aged 18-39 are ignorant about the Holocaust with, for instance, 22% thinking that it occurred during WWI and almost half unable to name any concentration camp or ghetto10. Some of this ignorance may be due to youth, but it's also evidence of the failure of our schools to teach history, especially about the Holocaust.

In addition, there have been complaints from users for years about anti-semitism on TikTok, which could repel both Jews and others who are not anti-semitic from using it11. So, the reported results may be due to a selection effect.

The survey, which was commissioned by a software entrepreneur, asked a large number of questions, the answers to some of which could be interpreted as anti-semitic or anti-Israel12. However, it was the entrepreneur himself who analyzed the results as showing a 17% difference between habitual TikTok users and casual or non-users. I'm not sure how this result was arrived at, but it's plausible for the reasons suggested above. However, it's only a correlation between TikTok usage and anti-semitic beliefs, and doesn't tell us what caused this difference.

This is not to say that TikTok itself is not the cause of at least some of this difference. Given their youth, inexperience, miseducation, and naiveté, TikTok's users may have little resistance to anti-semitic propaganda and conspiracy theories. So, it's not implausible that TikTok's content is contributing to anti-semitism and anti-Israel sentiment among the young.

I don't use TikTok myself, not because it causes anti-semitism, but because it's the crack cocaine of anti-social media: addictive and unhealthy for the mind.


  1. See: To Debate Or Not to Debate, That is the Question, 6/30/2023.
  2. "RNC Fourth Presidential Primary Debate 12/06/23 Transcript", Rev, 12/6/2023.
  3. See: Dangling Comparative, 10/16/2023.
  4. Em Steck, "Fact Check: Nikki Haley makes a misleading claim about TikTok leading to antisemitism", CNN, 12/8/2023.
  5. Maggie Hroncich, "Spending 30 Minutes on TikTok a Day Significantly Increases the Chances of Holding Antisemitic and Anti-Israeli Beliefs, Study Finds", The New York Sun, 12/1/2023.
  6. David Ingram, "Nikki Haley went after TikTok, but she may have flubbed her statistics", NBC News, 12/7/2023.
  7. Raymond Zhong & Sheera Frenkel, "A Third of TikTok’s U.S. Users May Be 14 or Under, Raising Safety Questions", The New York Times, 12/8/2020.
  8. Jordan Muchnick & Elaine Kamarck, "The generation gap in opinions toward Israel", The Brookings Institution, 11/9/2023.
  9. "The Economist/YouGov Poll", p. 103, 12/2-5/2023. The number of respondents in the youngest age group was only 207, so the margin of error is almost seven percentage points plus or minus.
  10. "Executive Summary", p. 10, survey conducted: 2/26/2020-3/28/2020.
  11. For instance: Kalhan Rosenblatt, "Jewish teens say life on TikTok comes with anti-Semitism", NBC News, 9/25/2020.
  12. "Generation Lab", survey conducted: 11/21-28/2023.

December 9th, 2023 (Permalink)

How to Lie with Photographs

A visitor to New England from the big city, noticing a flock of sheep in a field, said to a Yankee farmer: "It must be shearing time. Those sheep have just been shorn."

"Ayuh," replied the farmer, looking at the sheep, "on this side, at least."1

Late last month, the sports website Deadspin published an article about a young fan of the Kansas City Chiefs football team sporting an American Indian chief's feather headdress and with his face painted2, and much has been subsequently written about this incident and Deadspin's article3. It's not my intention to weigh in on the debate about whether it was appropriate for the boy to wear such a headdress to the game; instead, I want to address only the claim that he was wearing "Black face", as the publication calls it.

This is not a fact check, but the article's claim was false: the fan was not wearing black face. Instead, his face was painted half black and half red, the Chiefs' team colors. What attracted my attention to this controversy is the photograph of the fan at the top of the article. That profile photo shows only the right, black-painted side of the fan's face, whereas full face photos taken at the same game show both red and black halves of his face. I don't include any of the photos here, since they are likely copyrighted, and you can see them at the articles linked in the notes, below.

The article has since had an undated "Editor's Note" added at the top, its headline changed, and the offending photo deleted4. The original headline was:

The NFL needs to speak out against the Kansas City Chiefs fan in Black face, Native headdress

The current one reads:

The NFL Must Ban Native Headdress And Culturally Insensitive Face Paint in the Stands (UPDATED)

Some of the criticism of the original article focused on its accusation of racism against a nine-year old boy, and his parents subsequently threatened to sue5, so these changes were obviously intended to defuse the criticism and threat. The Editor's Note claims that the "black face" accusation was based on "the available photo", suggesting that the publication had access to only that one photograph. If so, then this saves the outlet from an accusation of intentionally choosing a misleading photo, but it doesn't save them from an accusation of carelessness.

It's hard to see how the author, editor, and photographic editor―for an online sports magazine, no less―could have failed to realize that the fan might have had his face painted with the team's colors. Not only sports fans, but even Seinfeld fans6, know about face painting. At the very least, someone should have checked to be sure that the unseen half of the boy's face was also painted black.

When you think of fake photography today, you probably think of Photoshop, or some other digital manipulation of a photograph in order to create a misleading image. Of course, in this case, there's no reason to think that the photo of the young Chiefs fan was manipulated in any such way, but there was no need to do so. The photo is not itself a false image, but one that tells only half of the story: it's the photographic equivalent of a half-truth.

Even before the advent of digital photography, it wasn't always necessary to use sophisticated means to create misleading photographs; instead, cruder techniques were used including double exposures7and airbrushing8. For instance, the infamous Cottingley fairy photos, produced by two young sisters, were just cutout figures propped up in the weeds9. Despite being produced by primitive means, the photos fooled such smart people as Arthur Conan Doyle.

So, keep in mind: "While photographs may not lie, liars may photograph.10"


  1. A traditional joke: I don't remember when or where I heard it.
  2. Carron J. Phillips, "The NFL needs to speak out against the Kansas City Chiefs fan in Black face, Native headdress", Deadspin, 11/27/2023. This is the archived page from the Internet Archive's Wayback Machine showing how the page originally appeared.
  3. For instance: Nick Mordowanec, "NFL Fan's 'Blackface' at Game Sparks Fight", Newsweek, 11/28/2023.
  4. Carron J. Phillips, "The NFL Must Ban Native Headdress And Culturally Insensitive Face Paint in the Stands (UPDATED)", Deadspin, 11/27/2023.
  5. See: Andrew Rodriguez, "Parents Threaten Lawsuit After Deadspin Accuses 9-Year-Old Of ‘Blackface’", State of the Union, 12/6/2023.
  6. See: "'You Gotta Support The Team!' | The Face Painter", Seinfeld, accessed: 12/5/2023.
  7. See: Robert T. Carroll, "Psychic Photography (Spirit Photography)", The Skeptic's Dictionary, 10/27/2015.
  8. See: Amos Chapple, "Fake Views: The Good, The Bad, And The Ugly Of Soviet Photoshopping", Radio Free Europe/Radio Liberty, 7/13/2018.
  9. See: Fairy Tale, 2/6/2013 and Robert T. Carroll, "Fairy", The Skeptic's Dictionary, 10/24/2015.
  10. Paul Vallely, "Lies, damned lies and photography: how the camera can distort the truth", The Independent, 2/18/2004.

December 3rd, 2023 (Permalink)

Guesstimate It, Too

At the start of the year, I asked you to guesstimate how many American women are of childbearing age1, that is, I asked you to not just guess, but to use what you know to estimate a number that you don't know.

Here's a follow-up question: How many American women are currently pregnant?2

This is the kind of question that you might well think you'd have to research to get an answer that isn't just a wild guess. However, I'm asking only that you guesstimate it, which means that I'm not expecting a precise number. Rather, the goal is to use what you know to come up with an estimate that's in the ballpark.

You're probably not especially interested in the answer to this question―neither am I!―but the purpose of this exercise is to develop your guesstimation ability. Like any other skill, it improves with practice. Guesstimation is a very useful critical thinking tool, and it will help to tune your internal credibility detector so that you can detect incredible numerical claims.

To get the most out of this exercise, make your own guesstimate before clicking on the "Guesstimate" button, below, to see mine. If you have no idea how to get started, try clicking on the first hint button, below. Click on as many hints as you need to make your guesstimate, but no more than necessary. So, let's get started!

Extra Credit: What percentage of American women of childbearing age are currently pregnant?


  1. Guesstimate It, 1/13/2023.
  2. This problem was suggested by one from: Saul X. Levmore & Elizabeth Early Cook, Super Strategies for Puzzles and Games (1981), pp. 57-58.
  3. "What is the current lifespan in the United States?", Wolfram Alpha, accessed: 11/21/2023.
  4. "Births and Natality", National Center for Health Statistics, 6/8/2023.
  5. "Births", The March of Dimes, 1/2022.

Recommended Reading
December 1st, 2023 (Permalink)

The New(s) Guardians & The Same Old Beeb


  1. See: Thomas Adamo & Josiah Joner, "Stanford's Dark Hand in Twitter Censorship", The Stanford Review, 3/24/2023.
  2. "Israeli forces carrying out operation in Gaza's Al Shifa hospital -military", Reuters, 11/14/2023.

Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In abridging them, I have sometimes changed the paragraphing and rearranged the order of the excerpts in order to emphasize points.

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