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I've wondered for a long time if there's a way to condense certain statistical (and probability) information into a single How-Much-Should-I-Care number. Can so

I've wondered for a long time if there's a way to condense certain statistical (and probability) information into a single How-Much-Should-I-Care number. Can someone shed some light on this? To pick a couple examples from health news in the popular press: NB: I'm making up all the numbers here for the sake of example. (1) A study shows that people who consume more than 10g of added salt a day live shorter lives. But how much shorter? If it's 30 minutes shorter, I don't care about the study and I'm not going to change my behavior. If it's 6 months longer, then I'm interested and might very well do something. (2) A study shows that people who drink 2 or more cups of coffee a day have lower risk of Alzheimer's Disease. But how much lower risk? If the average lifetime risk is 1 in 50, and drinking coffee lowers it to 1 in 49.997, then I don't want to waste time even reading the article. If it lowers it to 1 in a 1000, then yes, I might change my behavior. So, in the above examples, is there any way to reduce the information into a single How-Much-Should-I-Care number? Like this: (1) A study shows that people who consume more than 10g of added salt a day have an ____x____ factor shorter life. (2) A study shows that people who drink 2 or more cups of coffee a day have a ____y____ factor lower risk of Alzheimer's Disease. Then, by looking at x and y, I can tell at a glance whether some result is irrelevant, trivial, useful, or groundbreaking. I understand that it'll still be subjective in the end -- like whether $1, $10, $1000, or $10,000,000 seems like a lot of money to an individual -- but at least it'll be one number.

idm 13y ago
See https://en.wikipedia.org/wiki/Odds_ratio https://en.wikipedia.org/wiki/Odds_ratio for one answer. Another "single number" answer is generated by the class of tests that determine the statistical significance of an observation; see https://en.wikipedia.org/wiki/Alpha_level https://en.wikipedia.org/wiki/Alpha_level for more about this. There are many other ways to accomplish what you're talking about. The biggest problem with your made-up examples is that they are just cases of "bad reporting."
kmm 13y ago
Just a factor is often not enough. If a study would show that cell phone usage increased the risk of a certain cancer with 40%, that might still not be interesting if it's an extremely rare cancer and they found 7 cases instead of 5. Or it doesn't show whether various correlation factors matter, or whether this is a statistical paradox. Did you know that babies of smokers are healthier than babies of non-smokers of the same weight? This is because baby born to the smoker will have decreased weight because of the smoking, whereas if the baby of the non-smoker is underweight it will be for other reasons that are often worse. There's heaps of these kind of paradoxes and pitfalls that need to be taken in account. What we need in newspapers and other media is a simplified abstract of the paper and an explanation or approval of a real life statistician, with no relation to the study.

idm 13y ago

See https://en.wikipedia.org/wiki/Odds_ratio https://en.wikipedia.org/wiki/Odds_ratio for one answer. Another "single number" answer is generated by the class of tests that determine the statistical significance of an observation; see https://en.wikipedia.org/wiki/Alpha_level https://en.wikipedia.org/wiki/Alpha_level for more about this. There are many other ways to accomplish what you're talking about. The biggest problem with your made-up examples is that they are just cases of "bad reporting."

kmm 13y ago

Just a factor is often not enough. If a study would show that cell phone usage increased the risk of a certain cancer with 40%, that might still not be interesting if it's an extremely rare cancer and they found 7 cases instead of 5. Or it doesn't show whether various correlation factors matter, or whether this is a statistical paradox. Did you know that babies of smokers are healthier than babies of non-smokers of the same weight? This is because baby born to the smoker will have decreased weight because of the smoking, whereas if the baby of the non-smoker is underweight it will be for other reasons that are often worse. There's heaps of these kind of paradoxes and pitfalls that need to be taken in account. What we need in newspapers and other media is a simplified abstract of the paper and an explanation or approval of a real life statistician, with no relation to the study.