Logical Reasoning

PT14 · S2 · Q25 A letter submitted to the editor

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A letter submitted to the editor of a national news magazine was written and signed by a Dr. Shirley Martin who, in the text of the letter, mentions being a professor at a major North American medical school.

Conclusion

The chances are better than 19 to 1 that letter was written by a man.

Evidence

The letter writer is a professor at a major North American medical school.

Fewer than 5% of the professors at such schools are women.

Evaluate

5% = 1/20, so if 5% (1/20) of the professors at such schools are women, 19/20 of the professors are men.

Thus, at these schools, the ratio of female to male professors is 1 : 19.

If we were to pick a random professor, we'd have a 1/20 chance of getting a woman and 19/20 chance of getting a man.

If fewer than 5% of these professors are women then the chances are worse than 1/20 that a random professor would be a woman and better than 19/20 (or better than 19 to 1) that a random professor would be a man.

So why is this flawed?

Because the Doctor's name is Shirley! That's typically a female name. It's certainly still possible that this is a male doctor named Shirley, but given how much more we hear the name Shirley as a female name than as a male name, it should drastically shift our sense of probability.

Goal

Basically, the editor's conclusion is basing probability purely on the underlying population of male / female professors, and it's failing to make use of the 2nd piece of information we know (the writer's name is Shirley) as a means of editing or re-thinking probability.

Let's look for an answer where the argument is estimating probability based only some background numerical fact while failing to consider some second fact that should probably shift their sense of probability.

25.

Which one of the following involves flawed reasoning most like that used by the editor?

  1. Since 19 out of 20

    Different Flaw

    At first, seeing the same 19 out of 20, we could be thinking, "Superficial similarity trap! They're just trying to bait me with the same fraction / ratio". But glancing down the answers, we see that all of the answer choices are still playing with the 5% / 95%, or 1/20 to 19/20 split. This argument is flawed because it interprets the 19 out of 20 too literally. It thinks that a past data point (we got the 1 word processing computer out of the 20) influences how the forthcoming data points will go. If we know that certain storms only occur once every 60 years, and we have that type of storm in 2020, we're not allowed to conclude that the next storm will be in 2080. That's interpreting an average rate too literally. The original argument wasn't guilty of interpreting an average rate too literally, based on some data point. It was guilty of ignoring a 2nd fact we had (female name) that might affect or supersede our other means of estimating probability (overall rate of females / males in that professional role).

    6% picked this

  2. Fewer than 1 in 20

    Different Flaw

    Just like (A), this argument is flawed because it interprets an average rate too literally. It thinks that if the rate of acceptance is less than 1 in 20, then there's no chance you get an accepted one until you get to at least 20 manuscripts. We can't accuse this argument, as we can with the original, of failing to consider how some known fact might supersede the probability statistic we're using.

    6% picked this

  3. Fewer than 5 percent of

    Bad Conclusion Match

    This conclusion is a conditional, and it also almost sounds causal. It sounds like it's saying, "If X had happened, it would have caused Y". That bears no resemblance to our actual conclusion, which is just saying, "There's a better than 19/20 probability that the letter was written by a man".

    5% picked this

  4. More than 95 percent of

    Different Flaw

    It's hard to even understand the argument this is trying to make, but let's use some specific numbers to try: UBC is an airliner. 4% of the planes they built last year were small. (So 96% of the planes they built were large) 96% of the planes they built met government standards. So, all of the large planes met government standards. The author is thinking since "more than 95%" matches the percent that met standards and "more than 95%" matches large planes, that those two things must be a perfect overlap. But the argument fails to consider that UBC may have had this breakdown: 4%, small + meets standards 92%, large + meets standards 4%, large + doesn't meet standards That would fit the evidence (96% meet standards) but not the conclusion (all the large ones meet standards). But this is not the same flaw as "ignoring a fact that should supersede your probability argument".

    12% picked this

  5. Correct

    Since more than 19 out

    Why this is right

    This replicates the "Shirley" flaw. If we were just going off population numbers, then, yes, the probability that what Emily saw was a mammal would be greater than 95%, because mammals are more than 19 out of 20. But the fact that the mammal was flying seems like it should shake up our default probability. That is a strong context clue that what she saw is probably a bird, just as Dr. Shirley Martin is a strong context clue that the person who wrote the letter is probably female.

    Skill tested: Parallel Flaw · how this choice captures the argument's function is the move to repeat next time.

    71% picked this

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