9 ms·

Just a moment, 0.72% x 0.03% = 0.0002%, which is about 2 out every 1,000,000.

by ocfnash 7y ago

ChrisRR 7y ago
So even then, 600 people in the US should be both born blind and scizophrenic
- giancarlostoro 7y ago
  That isn't a guarantee that 600 people will be born with both.
  - ehsankia 7y ago
    Obviously there's no guarantee, and there's also the fact that we may not have every case documented, but if it is true that we have 0 case documented, that's pretty far from 600. Even if it's not "impossible", then at the very least it's less likely.
    - luc4sdreyer 7y ago
      It's a simple binomial probability calculation. The probability of one or more blind schizophrenic people born in the US, assuming they're independent variables, is 1-0,999998^330000000. I don't have a calculator on hand that can calculate that, but it's more than 1 - 10^-87. So the odds that there is no link between the two is close to the odds of guessing a specific bitcoin wallet's key in one try.
harryh 7y ago
Wowsers! That's quite the elementary math mistake in a journal article. I'm tempted to track down the authors and point this out to them.
- dooglius 7y ago
  Or the journal editor, you definitely should. This is the kind of thing that can easily get cited in future work on the matter.
  - glofish 7y ago
    it is probably not a math mistake since, when they applied the probability the 620 people is correct. Might be a typesetting (formatting) mistake. The 0.0002 is already a percent, but someone overlooked that and turned it again into percent. Still it should definitely be corrected as the 2 out of 10,000 is a value that sticks in the mind.
    - mennis16 7y ago
      They also used the 2 in 10,000 figure when picking out the comparison syndromes. I believe Retts is ~1 in 10,000. It's definitely not 1 in a million.
    - HourglassFR 7y ago
      My guess is the editor somehow messed up the per thousand sign ‱ https://en.wikipedia.org/wiki/Basis_point https://en.wikipedia.org/wiki/Basis_point edit: My bad. Correct character, incorrect description. It is indeed "ten thousand".
      - jfk13 7y ago
        Somewhat ironically, I think you're off by one character here. Unicode U+2031 ‱ is actually the per ten thousand sign (check its character name). Unicode U+2030 ‰ is the per thousand (or "per mille") sign.
        airstrike 7y ago
        The one thing worse than off-by-one errors are off-by-zero errors.
    - laszlokorte 7y ago
- Forgivenessizer 7y ago
  journalists really are a bit dumber than the average guy.
primo4444 7y ago
No, the .02 is correct. If you ignore the percentages part (since both left and right side use it), you're doing 0.72 x 0.03, which is indeed 0.02 If you do it as probabilities not expressed as percentages, it's 0.0072 x 0.0003, which is 0.0002, but that's 0.02%
- rlpb 7y ago
  You can't just ignore the percentage signs. 0.72% expressed as a decimal is 0.0072. 0.03% expressed as a decimal is 0.0003. 0.0072 x 0.0003 = 0.000002. Expressed back as a percentage, that's 0.0002%.
- gus_massa 7y ago
  > it's 0.0072 x 0.0003, which is 0.0002, but that's 0.02% No. 0.0072 x 0.0003 = 0.00000216‬ ~= 0.000002 = 0.0002%
  - primo4444 7y ago
    You're right. Not sure how I fell into that trap so easily.
    - injb 7y ago
      I wonder if it's better to treat percentage as a unit or variable. So a-percent x b-percent = c(percent-squared), or c divided by 100 twice.
      - deleted 7y ago
        [deleted]
      - petrogradphilos 7y ago
        You could also replace % with 10⁻² and use scientific notation: 0.72% ⋅ 0.03% = 0.72 ⋅ 10⁻² ⋅ 0.03 ⋅ 10⁻² = 7.2 ⋅ 10⁻³ ⋅ 3 ⋅ 10⁻⁴ = 7.2 ⋅ 3 ⋅ 10⁻³ ⋅ 10⁻⁴ = 21.6 ⋅ 10⁻⁷ = 2.16 ⋅ 10⁻⁶ ≈ 2 in 1 million
    - 7y ago
anordin95 7y ago
To be fair, it appears they fixed the math later, or at least roughly. (2 out of every 1M) x (the US population) [they cite ~311M]. That gives 622. Not far off the 620 they report in your quote.
- petrogradphilos 7y ago
  This is like having a weighted coin that comes up heads with probability 2⋅10⁻⁶, flipping it 311 million times, and seeing 0 heads. That's astronomically unlikely. To see this, observe that the number of heads follows a binomial distribution with n = 311 million and p = 2⋅10⁻⁶. This can be well approximated¹ by a normal distribution with mean μ = np = 622 and standard deviation σ = Sqrt[np(1 - p)] = 25. 99.7% of the time², when you sample from this distribution, the sampled value will be within 3 standard deviations of the mean, i.e., between μ - 3σ = 547 and μ + 3σ = 697. Results further from the mean are more unlikely. For example, seeing a value more than 7 standard deviations from the mean (i.e., less than 447 or more than 797) is about a 1 in 2 trillion event³. Since 0 is about 25 standard deviations from the mean, the probability of seeing 0 heads is on the order of 10⁻¹³⁸. [1] https://math.stackexchange.com/questions/2021801/conditions-needed-to-approximate-a-binomial-distribution-using-a-normal-distribu https://math.stackexchange.com/questions/2021801/conditions-... [2] https://en.wikipedia.org/wiki/68–95–99.7_rule https://en.wikipedia.org/wiki/68–95–99.7_rule [3] https://www.johndcook.com/blog/table-of-normal-tail-probabilities/ https://www.johndcook.com/blog/table-of-normal-tail-probabil...
  - paulmd 7y ago
    > This is like having a weighted coin Tangent: there is no such thing. You can weight a die, you cannot weight a coin. Intuitively this should make sense because even if you made one side of the coin from lead and the other from balsa wood, all you are doing is changing the center of gravity of the coin. The coin spins about its center of gravity, not the geometric center of the coin, so this makes no difference. https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf
    - 7y ago

Just a moment, 0.72% x 0.03% = 0.0002%, which is about 2 out every 1,000,000.

ChrisRR 7y ago

So even then, 600 people in the US should be both born blind and scizophrenic

giancarlostoro 7y ago
That isn't a guarantee that 600 people will be born with both.
- ehsankia 7y ago
  Obviously there's no guarantee, and there's also the fact that we may not have every case documented, but if it is true that we have 0 case documented, that's pretty far from 600. Even if it's not "impossible", then at the very least it's less likely.
  - luc4sdreyer 7y ago
    It's a simple binomial probability calculation. The probability of one or more blind schizophrenic people born in the US, assuming they're independent variables, is 1-0,999998^330000000. I don't have a calculator on hand that can calculate that, but it's more than 1 - 10^-87. So the odds that there is no link between the two is close to the odds of guessing a specific bitcoin wallet's key in one try.

harryh 7y ago

Wowsers! That's quite the elementary math mistake in a journal article. I'm tempted to track down the authors and point this out to them.

dooglius 7y ago
Or the journal editor, you definitely should. This is the kind of thing that can easily get cited in future work on the matter.
- glofish 7y ago
  it is probably not a math mistake since, when they applied the probability the 620 people is correct. Might be a typesetting (formatting) mistake. The 0.0002 is already a percent, but someone overlooked that and turned it again into percent. Still it should definitely be corrected as the 2 out of 10,000 is a value that sticks in the mind.
  - mennis16 7y ago
    They also used the 2 in 10,000 figure when picking out the comparison syndromes. I believe Retts is ~1 in 10,000. It's definitely not 1 in a million.
  - HourglassFR 7y ago
    My guess is the editor somehow messed up the per thousand sign ‱ https://en.wikipedia.org/wiki/Basis_point https://en.wikipedia.org/wiki/Basis_point edit: My bad. Correct character, incorrect description. It is indeed "ten thousand".
    - jfk13 7y ago
      Somewhat ironically, I think you're off by one character here. Unicode U+2031 ‱ is actually the per ten thousand sign (check its character name). Unicode U+2030 ‰ is the per thousand (or "per mille") sign.
      - airstrike 7y ago
        The one thing worse than off-by-one errors are off-by-zero errors.
  - laszlokorte 7y ago
Forgivenessizer 7y ago
journalists really are a bit dumber than the average guy.

primo4444 7y ago

No, the .02 is correct. If you ignore the percentages part (since both left and right side use it), you're doing 0.72 x 0.03, which is indeed 0.02 If you do it as probabilities not expressed as percentages, it's 0.0072 x 0.0003, which is 0.0002, but that's 0.02%

rlpb 7y ago
You can't just ignore the percentage signs. 0.72% expressed as a decimal is 0.0072. 0.03% expressed as a decimal is 0.0003. 0.0072 x 0.0003 = 0.000002. Expressed back as a percentage, that's 0.0002%.
gus_massa 7y ago
> it's 0.0072 x 0.0003, which is 0.0002, but that's 0.02% No. 0.0072 x 0.0003 = 0.00000216‬ ~= 0.000002 = 0.0002%
- primo4444 7y ago
  You're right. Not sure how I fell into that trap so easily.
  - injb 7y ago
    I wonder if it's better to treat percentage as a unit or variable. So a-percent x b-percent = c(percent-squared), or c divided by 100 twice.
    - deleted 7y ago
      [deleted]
    - petrogradphilos 7y ago
      You could also replace % with 10⁻² and use scientific notation: 0.72% ⋅ 0.03% = 0.72 ⋅ 10⁻² ⋅ 0.03 ⋅ 10⁻² = 7.2 ⋅ 10⁻³ ⋅ 3 ⋅ 10⁻⁴ = 7.2 ⋅ 3 ⋅ 10⁻³ ⋅ 10⁻⁴ = 21.6 ⋅ 10⁻⁷ = 2.16 ⋅ 10⁻⁶ ≈ 2 in 1 million
  - 7y ago

anordin95 7y ago

To be fair, it appears they fixed the math later, or at least roughly. (2 out of every 1M) x (the US population) [they cite ~311M]. That gives 622. Not far off the 620 they report in your quote.

petrogradphilos 7y ago
This is like having a weighted coin that comes up heads with probability 2⋅10⁻⁶, flipping it 311 million times, and seeing 0 heads. That's astronomically unlikely. To see this, observe that the number of heads follows a binomial distribution with n = 311 million and p = 2⋅10⁻⁶. This can be well approximated¹ by a normal distribution with mean μ = np = 622 and standard deviation σ = Sqrt[np(1 - p)] = 25. 99.7% of the time², when you sample from this distribution, the sampled value will be within 3 standard deviations of the mean, i.e., between μ - 3σ = 547 and μ + 3σ = 697. Results further from the mean are more unlikely. For example, seeing a value more than 7 standard deviations from the mean (i.e., less than 447 or more than 797) is about a 1 in 2 trillion event³. Since 0 is about 25 standard deviations from the mean, the probability of seeing 0 heads is on the order of 10⁻¹³⁸. [1] https://math.stackexchange.com/questions/2021801/conditions-needed-to-approximate-a-binomial-distribution-using-a-normal-distribu https://math.stackexchange.com/questions/2021801/conditions-... [2] https://en.wikipedia.org/wiki/68–95–99.7_rule https://en.wikipedia.org/wiki/68–95–99.7_rule [3] https://www.johndcook.com/blog/table-of-normal-tail-probabilities/ https://www.johndcook.com/blog/table-of-normal-tail-probabil...
- paulmd 7y ago
  > This is like having a weighted coin Tangent: there is no such thing. You can weight a die, you cannot weight a coin. Intuitively this should make sense because even if you made one side of the coin from lead and the other from balsa wood, all you are doing is changing the center of gravity of the coin. The coin spins about its center of gravity, not the geometric center of the coin, so this makes no difference. https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf
  - 7y ago