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I have encountered American university students who did not understand how percentages work.

DanBC 9y ago
Most people don't understand how percentages work. Ask people these questions: 1) I'm going to sell you a TV. It's priced at $300. I'm going to give you a 10% discount. What will it cost after the discount? 2) I'm selling you a washing machine. You're paying me $500. It's already had a 10% discount. How much did it cost before the discount? Most people can get an answer for (1), but they do it by mashing buttons on their smartphone calculator app. They don't know the method; they would not be able to talk through the method on paper. Most people can't give you an answer for (2) even after some time mashing buttons on their calculator. People can't spot misuse of percentages (eg, the "politician's bridge" (also called the Mexican Bridge from How to Lie With Statistics)) This isn't just the general population. We find some scary lack of understanding of percentages in doctors. https://en.wikipedia.org/wiki/Confusion_of_the_inverse https://en.wikipedia.org/wiki/Confusion_of_the_inverse > In one study, physicians were asked to give the chances of malignancy with a 1% prior probability of occurring. A test can detect 80% of malignancies and has a 10% false positive rate. What is the probability of malignancy given a positive test result?[3] Approximately 95 out of 100 physicians responded the probability of malignancy would be about 75%, apparently because the physicians believed that the chances of malignancy given a positive test result were approximately the same as the chances of a positive test result given malignancy.[4] > The correct probability of malignancy given a positive test result as stated above is 7.5% Gerd Gigerenzer's book Reckoning with Risk has many examples of this.
- kutkloon7 9y ago
  Of course, these are well-known examples. Recently it was claimed in a Dutch newspaper that a soccer player paid over 100% in taxes (but still received money). The particular students I met did not understand the idea behind percentages and could not calculate 10% of a given price.
- llasram 9y ago
  I agree that innumeracy of various degrees is a widespread problem, but I do think the last example is because the term "false positive rate" sounds to many people like it should mean the false discovery rate. I'm sure there are some people who do have trouble reasoning from the correct definitions, but mis-identifying/remembering the semantics of the values provided leaves no chance for succesful calculation.
- pishpash 9y ago
  That's not a lack of understanding of percentages, but of Bayes' rule, which arguably is in a completely different realm of conceptual sophistication.
  - DanBC 9y ago
    Gigerenzer's point is that the same people who don't understand the example when given using percentages find it trivially easy to answer if you give natural numbers such as "1 in 1000 people".
WalterBright 9y ago
I took a brief course in accounting. The instructor was a former used car salesman. So we were talking about that business, and he said that the dealership didn't make money off of the cars, they made money off of the financing. And they made that money because the customers simply could not understand interest rates and payments. He said he'd repeatedly patiently explain the options to them, how the higher payment plan would save them money in aggregate. They'd eye him suspiciously, tell him they weren't going to be taken in by shenanigans, and always pick the lowest monthly payment plan, which was always the costliest to them. This is what happens when you dog learning arithmetic in school, wondering what use it possibly can be. Not understanding arithmetic will cost you real money, a lot of it, throughout your life.

Most people don't understand how percentages work. Ask people these questions: 1) I'm going to sell you a TV. It's priced at $300. I'm going to give you a 10% discount. What will it cost after the discount? 2) I'm selling you a washing machine. You're paying me $500. It's already had a 10% discount. How much did it cost before the discount? Most people can get an answer for (1), but they do it by mashing buttons on their smartphone calculator app. They don't know the method; they would not be able to talk through the method on paper. Most people can't give you an answer for (2) even after some time mashing buttons on their calculator. People can't spot misuse of percentages (eg, the "politician's bridge" (also called the Mexican Bridge from How to Lie With Statistics)) This isn't just the general population. We find some scary lack of understanding of percentages in doctors. https://en.wikipedia.org/wiki/Confusion_of_the_inverse https://en.wikipedia.org/wiki/Confusion_of_the_inverse > In one study, physicians were asked to give the chances of malignancy with a 1% prior probability of occurring. A test can detect 80% of malignancies and has a 10% false positive rate. What is the probability of malignancy given a positive test result?[3] Approximately 95 out of 100 physicians responded the probability of malignancy would be about 75%, apparently because the physicians believed that the chances of malignancy given a positive test result were approximately the same as the chances of a positive test result given malignancy.[4] > The correct probability of malignancy given a positive test result as stated above is 7.5% Gerd Gigerenzer's book Reckoning with Risk has many examples of this.

kutkloon7 9y ago
Of course, these are well-known examples. Recently it was claimed in a Dutch newspaper that a soccer player paid over 100% in taxes (but still received money). The particular students I met did not understand the idea behind percentages and could not calculate 10% of a given price.
llasram 9y ago
I agree that innumeracy of various degrees is a widespread problem, but I do think the last example is because the term "false positive rate" sounds to many people like it should mean the false discovery rate. I'm sure there are some people who do have trouble reasoning from the correct definitions, but mis-identifying/remembering the semantics of the values provided leaves no chance for succesful calculation.
pishpash 9y ago
That's not a lack of understanding of percentages, but of Bayes' rule, which arguably is in a completely different realm of conceptual sophistication.
- DanBC 9y ago
  Gigerenzer's point is that the same people who don't understand the example when given using percentages find it trivially easy to answer if you give natural numbers such as "1 in 1000 people".

WalterBright 9y ago

I took a brief course in accounting. The instructor was a former used car salesman. So we were talking about that business, and he said that the dealership didn't make money off of the cars, they made money off of the financing. And they made that money because the customers simply could not understand interest rates and payments. He said he'd repeatedly patiently explain the options to them, how the higher payment plan would save them money in aggregate. They'd eye him suspiciously, tell him they weren't going to be taken in by shenanigans, and always pick the lowest monthly payment plan, which was always the costliest to them. This is what happens when you dog learning arithmetic in school, wondering what use it possibly can be. Not understanding arithmetic will cost you real money, a lot of it, throughout your life.