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March 21st, 2023 (Permalink)
The Independence Fallacy, that's what!
March 8th, 2023 (Permalink)
Little Big MOE
Cartoonist Scott Adams got himself into trouble recently1. I think everything sensible that can be said about it has already been said, together with a lot of things that aren't sensible, so I don't have anything to add. Instead, I want to comment on the poll results that seem to have set Adams off on his rant. So, after this paragraph I will say no more about Adams.
The poll, which was conducted by the Rasmussen polling organization, asked the following question among others: "Do you agree or disagree with this statement: 'It's OK to be white.'"2 Of the black respondents to the poll, 53% either "strongly agreed" (42%) or "somewhat agreed" (11%)―whatever that means―with the statement. Of the remaining 47% of black respondents, 18% "strongly disagreed" with the statement, and 8% "somewhat disagreed", whereas the remaining 21% answered "not sure".3
The entire sample was supposedly of a thousand American adults, which means that blacks were a subsample. However, according to a video put out by Rasmussen, the actual sample size was 1,182 respondents of whom only 117 were black. What is the margin of error (MOE) for a sample of that size? Approximately nine percentage points, which means that the 95% confidence interval for those blacks who agreed with the statement is 44%-62%, and similarly for all the other results for this subsample.4
So, this is another example of the statistical fact I've been emphasizing over the last few months5: subsamples have larger MOEs than full samples, and very small samples have very large MOEs. The Rasmussen poll had such a small sample of black respondents that the results are extremely imprecise and, as a consequence, generalizing from such a small sample to all black American adults is problematic.
Unsurprisingly, the news media did their usually poor job of interpreting the poll results for their readers. For example, a Newsweek article reported: "The poll was conducted on February 13-15 and had a margin of error of +/- 3 percentage points." Then, in the next sentence: "[Mark] Mitchell [head pollster at Rasmussen] told Newsweek that the percentage of Black respondents in the poll correspond with the Black population in the United States, which is around 13 percent."1 The article does not mention the MoE of the subsample, nor even the fact that it will be larger than ±3 percentage points. By juxtaposing these two sentences, most readers will think that the MoE mentioned applies to the "Black" subsample.
Mitchell deserves credit for giving the MoE for the subsample in the video previously referred to, but less that 1,500 people have seen it. Inconsistently, he goes on to say that Rasmussen refuses to do national polls with samples of less than 750, yet he defends the results for a subsample of only 117! In addition, he claims that other pollsters do as bad or even worse polling. He's probably right about that, but "if you think our product is bad, our competitors' products are just as bad or even worse" is not a very strong defense. Moreover, he tries to shift the burden of proof onto the poll's critics, challenging us to prove the results wrong. However, it's not our job to prove the poll wrong; it's Rasmussen's job to show that it's probably right.
- Jon Jackson, "A Poll Involving Black People Has Set the Internet on Fire", Newsweek, 2/27/2023.
- "Questions - Okay To Be White - February 13-15, 2023", Rasmussen Reports, accessed: 3/8/2023.
- The percentages in this paragraph are based on the following "tweet": "National Survey of 1,000 American Adults", Rasmussen Reports, 2/26/2023.
- "Rasmussen Polls: We Answer Your Questions About our Jaw-Dropping Racism Poll", Rasmussen Reports, 2/28/2023.
- MOE-mentum, 10/22/2022
- How to Read a Poll: Samples, Sub-Samples, and the MoE, 12/6/2022
March 4th, 2023 (Permalink)
Inflict or Afflict?
A book that I was reading last year inflicted the following sentence on me: "The main reason that they [cancer rates] are increasing is that we are not dying of the other diseases that have inflicted man throughout his existence."1 Can you see what's wrong with it?
"Afflict" and "inflict" are obviously sibling words that differ only in their prefixes since they both have the same stem, "-flict". That stem comes from the Latin verb "fligere", to beat, strike, or dash, which is also found in "conflict" and, surprisingly, "profligate"2. The difference in meaning among these words comes from their different prefixes: "con-" means "with" or "together", so that "conflict" means to fight with. The prefix of "inflict" is obviously "in-", which means much the same as the English word "in", so that "inflict" is to strike into; whereas, the prefix of "afflict", "af-", is a form of "ad-", "to" or "upon", so that to afflict is to strike upon3.
The distinction in meaning between "afflict" and "inflict" is subtle, so it's no surprise that Adrian Room writes that "[t]he two are quite often confused."4 Both mean to be struck with something bad, but infliction is typically done by people, whereas affliction is usually a natural occurrence. To return to the example sentence, the other diseases afflicted "man throughout his existence", but were not inflicted upon him.
I tried the example sentence in several online spelling or grammar checkers and only one flagged "inflicted" as a possible mistake, but it suggested "affected" rather that "afflicted" as a correction―close, but no cigar! So, it's unlikely that your spell-checking program, assuming that you use one, will catch such an error. File the distinction in your mental spell-checker, and don't inflict this confusion on others.
- John Brignell, Sorry, Wrong Number!: The Abuse of Measurement (2000), p. 202.
- John Ayto, Dictionary of Word Origins (1991).
- Joseph T. Shipley, Dictionary of Word Origins (1945).
- Adrian Room, The Penguin Dictionary of Confusibles (1980), under "inflicted/afflicted".
March 1st, 2023 (Permalink)
Coffee, Tea, or Both?
I love coffee, I love tea
I love the java jive and it loves me
Coffee and tea and the java and me
A cup, a cup, a cup, a cup, a cup!*
A restaurant that I frequent conducted a survey of its customers and it showed that 75% like coffee and 60% like tea. Knowing that I'm a logician, the owner approached me one day and showed me the results of the survey.
"What I'd really like to know is what percentage of my customers like both tea and coffee," she told me, "but I didn't think to ask. Can you figure that out?"
"I'm sorry," I replied, "but there's not enough information here to do that. However, I could tell you what the minimum and maximum percentages are."
"I'm not sure I understand that."
"The minimum is the lowest possible percentage, based on your survey data, that like both tea and coffee, and the maximum is the highest possible percentage that like both. The actual percentage that likes both will be between those two extremes."
"I see! That might help."
Can you help the restaurant owner? What are the minimum and maximum possible percentages of customers who like both coffee and tea?
Extra Credit: Assuming the maximum possible percentage of customers like both coffee and tea, what percentage likes neither? What about if the minimum likes both?
It's easy to see that the maximum percentage of customers who like both tea and coffee is 60%, since that would be the case if everyone who liked tea also liked coffee. The minimum overlap is the result of adding together the two percentages and then subtracting 100%―that is: 75% + 60% - 100% = 35%―which represents the minimum percentage that the two subsets of customers must overlap.
Extra Credit Solution: If 60% of customers like both tea and coffee, then an additional 15% like only coffee, which leaves 25% who like neither. If only 35% of customers like both, then 40% like just coffee and 25% enjoy only tea, so that 100% like one or the other, leaving 0% that like neither.
Disclaimer: This puzzle is fictitious. The main part of the puzzle is based on a problem that was used as an interview question by Google†―I just changed the numbers so that you couldn't "google" the answer.
† William Poundstone, Are You Smart Enough to Work at Google? (2012), pp. 88 & 265-268
*Milton Drake & Ben Oakland, "Java Jive". You can hear the Manhattan Transfer's rendition of this song here: "The Manhattan Transfer―Java Jive" (1975), YouTube