10 ms·

As always, it's important to remember that even in the absence of environmental factors, the probability of a particular town of this size having cancer rates t

As always, it's important to remember that even in the absence of environmental factors, the probability of a particular town of this size having cancer rates this high might be very low, but the probability of there existing such a town in the U.S. might actually be high. This is simply due to variance.

hammock 7y ago
"Variance" does not give people cancer. But pollution does. The nuance is lost in your comment, and what you might more accurately say is "statistics/variance predicts that there is a high probability that somewhere in the US there is a town that has enough pollution (or other cause) to create cancer rates this high. It happens to be Waycross, GA"
- gowld 7y ago
  Genetics also gives people a chance. There is some probability that somewhere in the US there is a town that has enough people with cancer-prone genetics to create cancer rates this high.
  - deleted 7y ago
    [deleted]
  - DoctorOetker 7y ago
    they would be getting the same set of rare cancers
- DangerousPie 7y ago
  No, that's not what "statistics/variance predicts". What statistics predicts is that even if there was no pollution whatsoever in the entire country we would still see some towns with increased cancer rates. That said, I didn't do the math and it's entirely possible that the rates in Waycross are way above what one might expect by chance.
  - deleted 7y ago
    [deleted]
  - wtvanhest 7y ago
    Your original comment was still valuable though because it makes people consider another, and important angle. Someone will probably do the math and show that even after considering statistical variance, this is still an outlier, but I feel like I have a more complete view with your comment.
wjnc 7y ago
Four one in a million events in 15k inhabitants. Yes in any ranked list of stochastic outcomes there must be a highest scorer and a lowest scorer, but in case of Wayland GA it's still off the charts. With these diseases for any given town in the US you'd expect 0 or 1, hardly ever 2, if independently distributed.
- nkurz 7y ago
  Your conclusion is probably correct, but you also need to know how many classes of events you looked at. The particular form of cancer wasn't set in advance, it arose out of the data, so you need to multiply the number of towns by the number of types "rare cancer". There seem to be about 1500 towns in the US with populations between 10000 and 25000: https://www.statista.com/statistics/241695/number-of-us-cities-towns-villages-by-population-size/ https://www.statista.com/statistics/241695/number-of-us-citi... There seem to be about 200 defined types of "rare cancer" (where rare is defined as affecting less than 1 in 100000 people[3]): https://www.macmillan.org.uk/information-and-support/audience/rare-cancers/what-is-rare-cancer.html https://www.macmillan.org.uk/information-and-support/audienc... My programming is better than my math[1], so I brute forced it as a simulation. Using 2000 towns, each with a population of 10000, and testing for 200 different types of cancer with a prevalence of 1 in 100000, I got this distribution: 1: 36393 2: 1831 3: 63 4: 1 That is to say, in the single simulation I ran[2], with a higher prevalence of 1 in 100000 vs 1 in 1000000, but a lower population of 10000 rather than 15000, I found that 1 in 2000 towns had 4 incidences of one of the 200 types of cancer I considered. This proves nothing directly, and environment probably played a role in the town in the story, but it does imply to me that it's not absurd that a small town might have 4 incidences of a rare cancer merely by chance. [1] What's the right way to calculate this mathematically? [2] My slow Perl code took about 10 minutes to run while I was writing this, and I committed to showing the numbers generated regardless of what they came out as. [3] Oops, reading more closely I now see that the linked article is distinguishing between "rare" and "very rare".
  - hervature 7y ago
    Probability of 1 town of 10^5 people having 4 people disease with 1 in 10^-6: (10^5 choose 4)x(10^-6)^4x(1-10^-6)^9996 ~= 3.77x10^-6 Assuming independence between diseases and towns (not a terrible assumption but definitely not true) we have: 2000x200x3.77x10^-6 ~= 1.5 Which agrees with your simulation [1]. [1] My slow brain and calculator took 2 minutes to calculate this ;) EDIT: Changed asterisks to x to avoid formatting. EDIT 2: Here are the numbers for all the cases you have: 0: 361934.8 1: 36913.8 2: 1809.5 3: 60.3 4: 1.5
gowld 7y ago
> This is simply due to variance. "This" == "a possibility", not "this" == "Waycross cancer rate". What matters is what the probabilities/frequencies are.
magicalhippo 7y ago
Related: https://en.wikipedia.org/wiki/Multiple_comparisons_problem https://en.wikipedia.org/wiki/Multiple_comparisons_problem http://cms.web.cern.ch/news/should-you-get-excited-your-data-let-look-elsewhere-effect-decide http://cms.web.cern.ch/news/should-you-get-excited-your-data... https://xkcd.com/882/ https://xkcd.com/882/
- mcguire 7y ago
  "The more inferences are made, the more likely erroneous inferences are to occur." Whoa. :-)
draw_down 7y ago
Ah yes, it must be statistics that is giving people cancer.
francisofascii 7y ago
I think you are referring to the Law of Large numbers. "with a large enough number of samples, any outrageous thing is likely to be observed" https://en.wikipedia.org/wiki/Law_of_truly_large_numbers https://en.wikipedia.org/wiki/Law_of_truly_large_numbers
peteradio 7y ago
What a stupid reckless comment, do you have evidence this is in the realm of statistical variance if no then jeez what a pointless general reckless dismissal of a well researched article.
- sctb 7y ago
  Could you please review the guidelines and stop breaking them? https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
  - peteradio 7y ago
    Apologies. Will be more thoughtful.
mcguire 7y ago
Some quick Googling and bad math (let me know where I screw up): 36,000 people in Ware County, GA. 3 cases of RMS, 1 of Ewing's. 327,000,000 people in the US. 400-500 cases of RMS in the US per year. Chance of a case: 0.0000015 Chance of 4 cases: 5.5e-24 ...in Ware County: 2.0e-19 ...in any Ware County-sized population: 1.8e-15 [edit; I'm an idiot] [think I was right the first time] Bonus: number of cases in US based on Ware Cty: 36,000 (weird, eh?) or about 73× more common.
- DangerousPie 7y ago
  Wait, how can the chance of 4 cases in any population be lower than the chance of 4 cases in a specific population? That can't be right can it?
  - mcguire 7y ago
    Yep, it can't.
crimsonalucard 7y ago
Your logic has some flaws. Allow me to elucidate: The probability of you randomly selecting a sample of people who happen to have a high rate of cancer is very low. The probability of you EVENTUALLY selecting a sample of people who have a high rate of cancer after selecting many samples is actually very high. The probability of you eventually selecting a sample of people who happen to have a high rate of cancer AND happen to live in the same town AND happen to have cancers that are classified as rare is very very low. There is no doubt this is an anomaly by every logical measure and not a statistical quirk. This is an example of where your gut notion of a cancer cluster actually trumps the statistical logic. While logic is always correct and the logic you were using was technically wrong, this is a good example of how your intuitive gut feeling of what a cluster is, trumps your logical mind. Don't ignore your gut feelings, don't ignore your intuitions. The logical part of the human mind is just as flawed as your intuitions and it can build an incorrect scaffold of compositions that support an incorrect conclusion. When your logic collides with your intuitions, do not automatically assume that logic trumps all. Evaluate both.
- psychometry 7y ago
  Your reliance on "logic" and not statistical training (it appears you don't have much) has lead you astray. Read the other replies to my comment to understand why you haven't understood.
  - crimsonalucard 7y ago
    I read it and it appears to me you are still wrong. You are better served to explain to me explicitly why you think you are not wrong then for me to read your mind. There are events that contain so much information that the probability of the event occurring due to entropy are basically impossible. The event fitting those 3 conditions I mentioned is one example. Let me add one more conditional to the cancer-cluster event: Happening within the same time-frame.

hammock 7y ago

"Variance" does not give people cancer. But pollution does. The nuance is lost in your comment, and what you might more accurately say is "statistics/variance predicts that there is a high probability that somewhere in the US there is a town that has enough pollution (or other cause) to create cancer rates this high. It happens to be Waycross, GA"

gowld 7y ago
Genetics also gives people a chance. There is some probability that somewhere in the US there is a town that has enough people with cancer-prone genetics to create cancer rates this high.
- deleted 7y ago
  [deleted]
- DoctorOetker 7y ago
  they would be getting the same set of rare cancers
DangerousPie 7y ago
No, that's not what "statistics/variance predicts". What statistics predicts is that even if there was no pollution whatsoever in the entire country we would still see some towns with increased cancer rates. That said, I didn't do the math and it's entirely possible that the rates in Waycross are way above what one might expect by chance.
- deleted 7y ago
  [deleted]
- wtvanhest 7y ago
  Your original comment was still valuable though because it makes people consider another, and important angle. Someone will probably do the math and show that even after considering statistical variance, this is still an outlier, but I feel like I have a more complete view with your comment.

wjnc 7y ago

Four one in a million events in 15k inhabitants. Yes in any ranked list of stochastic outcomes there must be a highest scorer and a lowest scorer, but in case of Wayland GA it's still off the charts. With these diseases for any given town in the US you'd expect 0 or 1, hardly ever 2, if independently distributed.

nkurz 7y ago
Your conclusion is probably correct, but you also need to know how many classes of events you looked at. The particular form of cancer wasn't set in advance, it arose out of the data, so you need to multiply the number of towns by the number of types "rare cancer". There seem to be about 1500 towns in the US with populations between 10000 and 25000: https://www.statista.com/statistics/241695/number-of-us-cities-towns-villages-by-population-size/ https://www.statista.com/statistics/241695/number-of-us-citi... There seem to be about 200 defined types of "rare cancer" (where rare is defined as affecting less than 1 in 100000 people[3]): https://www.macmillan.org.uk/information-and-support/audience/rare-cancers/what-is-rare-cancer.html https://www.macmillan.org.uk/information-and-support/audienc... My programming is better than my math[1], so I brute forced it as a simulation. Using 2000 towns, each with a population of 10000, and testing for 200 different types of cancer with a prevalence of 1 in 100000, I got this distribution: 1: 36393 2: 1831 3: 63 4: 1 That is to say, in the single simulation I ran[2], with a higher prevalence of 1 in 100000 vs 1 in 1000000, but a lower population of 10000 rather than 15000, I found that 1 in 2000 towns had 4 incidences of one of the 200 types of cancer I considered. This proves nothing directly, and environment probably played a role in the town in the story, but it does imply to me that it's not absurd that a small town might have 4 incidences of a rare cancer merely by chance. [1] What's the right way to calculate this mathematically? [2] My slow Perl code took about 10 minutes to run while I was writing this, and I committed to showing the numbers generated regardless of what they came out as. [3] Oops, reading more closely I now see that the linked article is distinguishing between "rare" and "very rare".
- hervature 7y ago
  Probability of 1 town of 10^5 people having 4 people disease with 1 in 10^-6: (10^5 choose 4)x(10^-6)^4x(1-10^-6)^9996 ~= 3.77x10^-6 Assuming independence between diseases and towns (not a terrible assumption but definitely not true) we have: 2000x200x3.77x10^-6 ~= 1.5 Which agrees with your simulation [1]. [1] My slow brain and calculator took 2 minutes to calculate this ;) EDIT: Changed asterisks to x to avoid formatting. EDIT 2: Here are the numbers for all the cases you have: 0: 361934.8 1: 36913.8 2: 1809.5 3: 60.3 4: 1.5

gowld 7y ago

> This is simply due to variance. "This" == "a possibility", not "this" == "Waycross cancer rate". What matters is what the probabilities/frequencies are.

magicalhippo 7y ago

Related: https://en.wikipedia.org/wiki/Multiple_comparisons_problem https://en.wikipedia.org/wiki/Multiple_comparisons_problem http://cms.web.cern.ch/news/should-you-get-excited-your-data-let-look-elsewhere-effect-decide http://cms.web.cern.ch/news/should-you-get-excited-your-data... https://xkcd.com/882/ https://xkcd.com/882/

mcguire 7y ago
"The more inferences are made, the more likely erroneous inferences are to occur." Whoa. :-)

draw_down 7y ago

Ah yes, it must be statistics that is giving people cancer.

francisofascii 7y ago

I think you are referring to the Law of Large numbers. "with a large enough number of samples, any outrageous thing is likely to be observed" https://en.wikipedia.org/wiki/Law_of_truly_large_numbers https://en.wikipedia.org/wiki/Law_of_truly_large_numbers

peteradio 7y ago

What a stupid reckless comment, do you have evidence this is in the realm of statistical variance if no then jeez what a pointless general reckless dismissal of a well researched article.

sctb 7y ago
Could you please review the guidelines and stop breaking them? https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- peteradio 7y ago
  Apologies. Will be more thoughtful.

mcguire 7y ago

Some quick Googling and bad math (let me know where I screw up): 36,000 people in Ware County, GA. 3 cases of RMS, 1 of Ewing's. 327,000,000 people in the US. 400-500 cases of RMS in the US per year. Chance of a case: 0.0000015 Chance of 4 cases: 5.5e-24 ...in Ware County: 2.0e-19 ...in any Ware County-sized population: 1.8e-15 [edit; I'm an idiot] [think I was right the first time] Bonus: number of cases in US based on Ware Cty: 36,000 (weird, eh?) or about 73× more common.

DangerousPie 7y ago
Wait, how can the chance of 4 cases in any population be lower than the chance of 4 cases in a specific population? That can't be right can it?
- mcguire 7y ago
  Yep, it can't.

crimsonalucard 7y ago

Your logic has some flaws. Allow me to elucidate: The probability of you randomly selecting a sample of people who happen to have a high rate of cancer is very low. The probability of you EVENTUALLY selecting a sample of people who have a high rate of cancer after selecting many samples is actually very high. The probability of you eventually selecting a sample of people who happen to have a high rate of cancer AND happen to live in the same town AND happen to have cancers that are classified as rare is very very low. There is no doubt this is an anomaly by every logical measure and not a statistical quirk. This is an example of where your gut notion of a cancer cluster actually trumps the statistical logic. While logic is always correct and the logic you were using was technically wrong, this is a good example of how your intuitive gut feeling of what a cluster is, trumps your logical mind. Don't ignore your gut feelings, don't ignore your intuitions. The logical part of the human mind is just as flawed as your intuitions and it can build an incorrect scaffold of compositions that support an incorrect conclusion. When your logic collides with your intuitions, do not automatically assume that logic trumps all. Evaluate both.

psychometry 7y ago
Your reliance on "logic" and not statistical training (it appears you don't have much) has lead you astray. Read the other replies to my comment to understand why you haven't understood.
- crimsonalucard 7y ago
  I read it and it appears to me you are still wrong. You are better served to explain to me explicitly why you think you are not wrong then for me to read your mind. There are events that contain so much information that the probability of the event occurring due to entropy are basically impossible. The event fitting those 3 conditions I mentioned is one example. Let me add one more conditional to the cancer-cluster event: Happening within the same time-frame.