**View Poll Results**: What Are Your Helmet Wearing Habits?

I've never worn a bike helmet

**52**

10.40%

I used to wear a helmet, but have stopped

**24**

4.80%

I've always worn a helmet

**208**

41.60%

I didn't wear a helmet, but now do

**126**

25.20%

I sometimes wear a helmet depending on the conditions

**90**

18.00%

Voters:

**500**. You may not vote on this poll# The Helmet Thread 2

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To predict is to estimate what will happen in the future. Kindly, show how prediction concerning populations works at the individual level, meaning that you show its practical value, if you can. For example:

If you take the prediction that one in seven people will die of heart problems, it is obvious such prediction has a practical value for any endeavor concerning the health care of the entire population, like knowing how many cardiologists will be required and such, but please point out the practical value for the individual.

To predict is to estimate what will happen in the future. Kindly, show how prediction concerning populations works at the individual level, meaning that you show its practical value, if you can. For example:

If you take the prediction that one in seven people will die of heart problems, it is obvious such prediction has a practical value for any endeavor concerning the health care of the entire population, like knowing how many cardiologists will be required and such, but please point out the practical value for the individual.

**What does the prediction say about the health of an individual's heart?**Apart from regular checks which will already include the heart, what is that he can do after hearing that prediction? Wear an extra sweater? Does it mean that if he knows seven people one of them must have a bad heart? Obviously not. Please explain the, in your own words, "predictive for individual elements," of the 1 in 7 prediction.The prediction says that, without knowing other information, you have a 14.3% chance of eventually dying from heart trouble. This simple datum by itself is of limited utility, except that the individual may realize that with such a high probability for one of many possible causes of death, he can take measures to reduce that number for his own case. He would be best served to survey the medical literature for statistical analysis of specific causes of heart disease, and having taken such measures consider other probable health risks.

The more information you know about the individual, along with associated statistical information, the better and more specific your probabilities become. You're getting sidetracked by wanting certainties, and wanting to reason from specific individual details which are unknowable from a particular data set. A quick general overview. Detailed information, combined with some silogisms, are fundamentals of deductive logic, and you derive some certainty thereby. Within the parameters of your space, or construct. You are essentially demanding that I provide a deductive conclusion about an element of the data set from general knowledge of the data set, and obviously that's not possible, but it's an error to presume that this means that probability is not predictive.

You can still use deductive logic with probability, but it's not a simple boolean statement but rather uses the probabilistic equivalents (of and, or, not etc) and results in a probability and confidence range. So, as with set theory, group theory or any other branch you don't actually give up boolean logic and deductive reasoning, but it does apply in different ways and you must interpret the conclusions within the particular system. Is that more clear?

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**1403**Senior Member

Mathematics is a discussion, where one or both persons can learn something. If you want an intellectual contest play Chess or Go. I don't "argue" about math, but I don't mind explaining basic concepts if someone is truly interested.

The prediction says that, without knowing other information, you have a 14.3% chance of eventually dying from heart trouble. This simple datum by itself is of limited utility, except that the individual may realize that with such a high probability for one of many possible causes of death, he can take measures to reduce that number for his own case. He would be best served to survey the medical literature for statistical analysis of specific causes of heart disease, and having taken such measures consider other probable health risks.

The more information you know about the individual, along with associated statistical information, the better and more specific your probabilities become. You're getting sidetracked by wanting certainties, and wanting to reason from specific individual details which are unknowable from a particular data set. A quick general overview. Detailed information, combined with some silogisms, are fundamentals of deductive logic, and you derive some certainty thereby. Within the parameters of your space, or construct. You are essentially demanding that I provide a deductive conclusion about an element of the data set from general knowledge of the data set, and obviously that's not possible, but it's an error to presume that this means that probability is not predictive.

You can still use deductive logic with probability, but it's not a simple boolean statement but rather uses the probabilistic equivalents (of and, or, not etc) and results in a probability and confidence range. So, as with set theory, group theory or any other branch you don't actually give up boolean logic and deductive reasoning, but it does apply in different ways and you must interpret the conclusions within the particular system.

The prediction says that, without knowing other information, you have a 14.3% chance of eventually dying from heart trouble. This simple datum by itself is of limited utility, except that the individual may realize that with such a high probability for one of many possible causes of death, he can take measures to reduce that number for his own case. He would be best served to survey the medical literature for statistical analysis of specific causes of heart disease, and having taken such measures consider other probable health risks.

The more information you know about the individual, along with associated statistical information, the better and more specific your probabilities become. You're getting sidetracked by wanting certainties, and wanting to reason from specific individual details which are unknowable from a particular data set. A quick general overview. Detailed information, combined with some silogisms, are fundamentals of deductive logic, and you derive some certainty thereby. Within the parameters of your space, or construct. You are essentially demanding that I provide a deductive conclusion about an element of the data set from general knowledge of the data set, and obviously that's not possible, but it's an error to presume that this means that probability is not predictive.

You can still use deductive logic with probability, but it's not a simple boolean statement but rather uses the probabilistic equivalents (of and, or, not etc) and results in a probability and confidence range. So, as with set theory, group theory or any other branch you don't actually give up boolean logic and deductive reasoning, but it does apply in different ways and you must interpret the conclusions within the particular system.

**Is that more clear**?
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Sorry, he seemed to imply that you needed syllogism, or deductive reasoning basically, and a binary (yes/no) answer for there to be any useful prediction from mathematics. The insistence on absolute conclusions appeared to me to be a reliance on, or tunnel-vision of, boolean logic or what we used to call propositional calculus. Or more specifically, first order propositional logic because of his implicit use of quantifiers on variables such as "for every" and "only one" and so on. I'm running on here, but in a nutshell it means simple, every-day logic with enough formal rules added to make it useful.

I'm reading between the lines trying to envision where he is in his math studies and I tried to choose illustrations that would be clear. I probably failed there, so I apologize.

I'm reading between the lines trying to envision where he is in his math studies and I tried to choose illustrations that would be clear. I probably failed there, so I apologize.

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**1405**Senior Member

I'm reading between the lines trying to envision where he is in his math studies and I tried to choose illustrations that would be clear. I probably failed there, so I apologize.

*Last edited by 350htrr; 06-28-15 at 07:22 PM. Reason: add more info*

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**1406**Senior Member

Many people who hold mistaken and bewilderingly silly beliefs can at least claim some utilitarian effect. The difference between the rabbit who flees because mistakenly believes that the wind shaking the tall grass is a fox nearby, and the rabbit who refuses to budge until better data is available is that the analytical rabbit leaves fewer offspring. People who believe that the world is only six thousand years old and other bold claims from preachers and priests, draw at least the soothing benefits of ardent believers.

But it's hard to fathom out the utilitarian effect of believing that cycling is a low risk activity that does not warrant wearing head protection.

For a moment, it looks that there is some utility in using the pro-death faction as a bad example. Unfortunately, that may lead some folks with poor habits of thought to take it as an example to follow, so in the end it's a belief with no benefit at all anyway you look at it.

*Last edited by CarinusMalmari; 06-30-15 at 02:54 AM.*

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Mathematics is a discussion, where one or both persons can learn something. If you want an intellectual contest play Chess or Go. I don't "argue" about math, but I don't mind explaining basic concepts if someone is truly interested.

The prediction says that, without knowing other information, you have a 14.3% chance of eventually dying from heart trouble. This simple datum by itself is of limited utility, except that the individual may realize that with such a high probability for one of many possible causes of death, he can take measures to reduce that number for his own case. He would be best served to survey the medical literature for statistical analysis of specific causes of heart disease, and having taken such measures consider other probable health risks.

The more information you know about the individual, along with associated statistical information, the better and more specific your probabilities become. You're getting sidetracked by wanting certainties, and wanting to reason from specific individual details which are unknowable from a particular data set. A quick general overview. Detailed information, combined with some silogisms, are fundamentals of deductive logic, and you derive some certainty thereby. Within the parameters of your space, or construct. You are essentially demanding that I provide a deductive conclusion about an element of the data set from general knowledge of the data set, and obviously that's not possible, but it's an error to presume that this means that probability is not predictive.

You can still use deductive logic with probability, but it's not a simple boolean statement but rather uses the probabilistic equivalents (of and, or, not etc) and results in a probability and confidence range. So, as with set theory, group theory or any other branch you don't actually give up boolean logic and deductive reasoning, but it does apply in different ways and you must interpret the conclusions within the particular system. Is that more clear?

The prediction says that, without knowing other information, you have a 14.3% chance of eventually dying from heart trouble. This simple datum by itself is of limited utility, except that the individual may realize that with such a high probability for one of many possible causes of death, he can take measures to reduce that number for his own case. He would be best served to survey the medical literature for statistical analysis of specific causes of heart disease, and having taken such measures consider other probable health risks.

The more information you know about the individual, along with associated statistical information, the better and more specific your probabilities become. You're getting sidetracked by wanting certainties, and wanting to reason from specific individual details which are unknowable from a particular data set. A quick general overview. Detailed information, combined with some silogisms, are fundamentals of deductive logic, and you derive some certainty thereby. Within the parameters of your space, or construct. You are essentially demanding that I provide a deductive conclusion about an element of the data set from general knowledge of the data set, and obviously that's not possible, but it's an error to presume that this means that probability is not predictive.

You can still use deductive logic with probability, but it's not a simple boolean statement but rather uses the probabilistic equivalents (of and, or, not etc) and results in a probability and confidence range. So, as with set theory, group theory or any other branch you don't actually give up boolean logic and deductive reasoning, but it does apply in different ways and you must interpret the conclusions within the particular system. Is that more clear?

I asked a very specific question, and you did not quite answer it, though you managed to include the kitchen sink in your reply.

You need not preface posts with admonitions because I neither seek math instruction nor I believe that asking you to support your statements is looking for a contest. It is what people do in a proper debate, before it degenerates into dog poo as all Internet debates eventually do.

I asked specifically what is the utility of statistics to the the individual that would apply to himself in particular, and by "statistics" I mean also the probabilities derived from them. I assure you I know the difference between statistics and probability. They are both branches of mathematics, one applied the other pure or theoretical, primarily. Statistics analyses the frequency of past events, probability is a way to handle uncertainty.

You seem to resent that I demand certainty for the individual case How not? If a tool to deal with uncertainty can't provide any certainty what good is it?

The problem is that some people believe that the likelihood of future events, derived from population statistics is as useful for the individual as it is for the population, and that is a mistake. Proof of it is in your own very reply. When asked what the 1 in 7 means for the individual, you say that it tells the individual that he has 14.3% probability of dying of heart disease. Well... that adds no new information at all, it just translates the probability from a per-seven to a per-cent. Neat trick though.

Let me clarify my example. If statistics show that in say, New York City one person in seven die of heart disease in 2015, the city mayor will do well to expect one seventh of all deaths to involve heart problems next year, and he should work this likelihood into the city's health plans. The statistic, however, says absolutely nothing about Joe Babaloo at 661 4th Avenue, apartment 16. He may die of cancer, or in a bike accident because he does not wear a helmet, who knows.

In other words, if you cannot find anything that 'statistics' can say for a particular individual, you should concede the point. I grant that knowing that in a statistically significant sample 1 in 7 die of heart problems is far better than knowing absolutely nothing about the lethality of heart disease, but again, it is GENERAL information, not particular. There is a difference, you know. .

*Last edited by Tiglath; 07-01-15 at 02:23 AM.*

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The most successful cycling cultures come without helmets,

There's no reason to believe bicycle helmets are of any importance to bicycle safety, and shouldn't be viewed as anything else than an additional thing you can do. That's not a belief, but a fact.

Let me show you what a fact looks like: In 2009, 97% of cyclists killed in NYC by head injury did not wear a helmet. Other years' numbers are similar. I provided a link to the study earlier in this thread, take a look and learn at long last what a fact looks like.

*Last edited by Tiglath; 07-02-15 at 10:20 PM.*

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Just look at all the baboons as per Tiglath...

https://www.youtube.com/watch?v=q8h_DalTjV0

*Last edited by 2 Piece; 07-01-15 at 04:50 AM. Reason: add video*

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That's why I admonished you. There is no "point" to cede because I do not "debate" mathematics.

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Just look at all the baboons as per Tiglath...

https://www.youtube.com/watch?v=q8h_DalTjV0

I live in the US and so I act accordingly. When I ride my bike on the boardwalk in my summer vacation town I don't wear a helmet. I ride gently on wood planks with no traffic in sight. It's light years from say, Manhattan streets. When I lived in Amsterdam many years ago I did not wear a helmet either, it's socially uncool and it's about the safest place to ride a bike.

Holland has the one of the safest traffic system in the world, including all traffic. The Dutch setup for bikes is extraordinarily well thought out. They have thousands of miles of bike paths, with traffic lights just for bikers; bikers get priority on most roads and drivers defer to bikers. It's Planet Bike.

You are more likely to get murdered in the US than to die in a biking accident in Holland.

Another factor is that most bike miles are utility trips, ordinary rides about town. The safety of biking this way comes out in this startling statistic. Less than 1% of bikers wear helmets in Holland, but 13 % of bikers injured wore helmets.

The pro-death faction will be quick to point out that this must mean that helmets are the cause of accidents, but there is a different explanation. Most biking accidents in Holland don't come from utility riders, but from sports biking, which involves substantially higher speeds, more risk-taking, and mountain biking. So as you up the pace, up goes the risk -- just like everywhere else.

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That's why I admonished you. There is no "point" to cede because I do not "debate" mathematics.

Your explanation that "Probability is applicable to every individual" explains nothing, it just rephrases your claim. Repeating a claim using different words is no evidence for the claim, and the burden of proof remains on the claimant.

You don't seem to grasp this contrast:

(1) For the population of NYC, you can actually turn the 14.3 % probability into concrete measures that will meet the needs the city is about to face regarding heart patients. Those are measures and resources you can enumerate and count, like number of hospital beds and doctors in cardiology departments, and the necessary equipment. And the prediction will turn out to be correct in a nicely approximate way. That is, for the population, probability is of great utility

(2) For the individual New Yorker there is nothing comparable. All you say is that the probability applies, but it signifies nothing further. A probability of 14.3% offers no guidance to the individual on anything practical, like how often to check the heart, and in the end inferences may turn out to be totally incorrect because that particular individual may not die of heart failure.

Why can't you see this contrast, I wonder.

This is a problem inherent to probability. Just because multiple human events form a pattern it does not mean that any single particular human shall conform to the pattern. All you can say is that under similar conditions the same set of individuals will likely exhibit a similar pattern again.

The only exception is for the extreme cases of probability. The probability that all persons in their eighties will die is 100%. That tells any octogenarian unequivocally that he is doomed.

I don't know how you figured that I asked you for a syllogism, or a yes/no answer, a propositional calculus lecture, some boolean mis-mash, or the kitchen waste disposer, but I did not. Perhaps you just like to throw around big words to dazzle the natives but I assure you that all I wanted to know and I still want to know is how probability benefits the individual the way it benefits the population, which according to you it does, but you are stuck in saying that it just applies. Explain further or admit that you cannot.

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Of course there is a point. If you remember, I contrasted how probability has tangible utility to the population, but hardly any to the individual. You disagreed.

Your explanation that "Probability is applicable to every individual" explains nothing, it just rephrases your claim. Repeating a claim using different words is no evidence for the claim, and the burden of proof remains on the claimant.

You don't seem to grasp this contrast:

(1) For the population of NYC, you can actually turn the 14.3 % probability into concrete measures that will meet the needs the city is about to face regarding heart patients. Those are measures and resources you can enumerate and count, like number of hospital beds and doctors in cardiology departments, and the necessary equipment. And the prediction will turn out to be correct in a nicely approximate way. That is, for the population, probability is of great utility

(2) For the individual New Yorker there is nothing comparable. All you say is that the probability applies, but it signifies nothing further. A probability of 14.3% offers no guidance to the individual on anything practical, like how often to check the heart, and in the end inferences may turn out to be totally incorrect because that particular individual may not die of heart failure.

Why can't you see this contrast, I wonder.

This is a problem inherent to probability. Just because multiple human events form a pattern it does not mean that any single particular human shall conform to the pattern. All you can say is that under similar conditions the same set of individuals will likely exhibit a similar pattern again.

The only exception is for the extreme cases of probability. The probability that all persons in their eighties will die is 100%. That tells any octogenarian unequivocally that he is doomed.

I don't know how you figured that I asked you for a syllogism, or a yes/no answer, a propositional calculus lecture, some boolean mis-mash, or the kitchen waste disposer, but I did not. Perhaps you just like to throw around big words to dazzle the natives but I assure you that all I wanted to know and I still want to know is how probability benefits the individual the way it benefits the population, which according to you it does, but you are stuck in saying that it just applies. Explain further or admit that you cannot.

Your explanation that "Probability is applicable to every individual" explains nothing, it just rephrases your claim. Repeating a claim using different words is no evidence for the claim, and the burden of proof remains on the claimant.

You don't seem to grasp this contrast:

(1) For the population of NYC, you can actually turn the 14.3 % probability into concrete measures that will meet the needs the city is about to face regarding heart patients. Those are measures and resources you can enumerate and count, like number of hospital beds and doctors in cardiology departments, and the necessary equipment. And the prediction will turn out to be correct in a nicely approximate way. That is, for the population, probability is of great utility

(2) For the individual New Yorker there is nothing comparable. All you say is that the probability applies, but it signifies nothing further. A probability of 14.3% offers no guidance to the individual on anything practical, like how often to check the heart, and in the end inferences may turn out to be totally incorrect because that particular individual may not die of heart failure.

Why can't you see this contrast, I wonder.

This is a problem inherent to probability. Just because multiple human events form a pattern it does not mean that any single particular human shall conform to the pattern. All you can say is that under similar conditions the same set of individuals will likely exhibit a similar pattern again.

The only exception is for the extreme cases of probability. The probability that all persons in their eighties will die is 100%. That tells any octogenarian unequivocally that he is doomed.

I don't know how you figured that I asked you for a syllogism, or a yes/no answer, a propositional calculus lecture, some boolean mis-mash, or the kitchen waste disposer, but I did not. Perhaps you just like to throw around big words to dazzle the natives but I assure you that all I wanted to know and I still want to know is how probability benefits the individual the way it benefits the population, which according to you it does, but you are stuck in saying that it just applies. Explain further or admit that you cannot.

My suggestion, seriously, is that you bring it up in class and discuss it there. This is not an appropriate forum for more than one or two explanatory posts on this

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You don't seem to grasp this contrast:

(1) For the population of NYC, you can actually turn the 14.3 % probability into concrete measures that will meet the needs the city is about to face regarding heart patients. Those are measures and resources you can enumerate and count, like number of hospital beds and doctors in cardiology departments, and the necessary equipment. And the prediction will turn out to be correct in a nicely approximate way. That is, for the population, probability is of great utility

(2) For the individual New Yorker there is nothing comparable. All you say is that the probability applies, but it signifies nothing further. A probability of 14.3% offers no guidance to the individual on anything practical, like how often to check the heart, and in the end inferences may turn out to be totally incorrect because that particular individual may not die of heart failure.

...

You don't seem to grasp this contrast:

(1) For the population of NYC, you can actually turn the 14.3 % probability into concrete measures that will meet the needs the city is about to face regarding heart patients. Those are measures and resources you can enumerate and count, like number of hospital beds and doctors in cardiology departments, and the necessary equipment. And the prediction will turn out to be correct in a nicely approximate way. That is, for the population, probability is of great utility

(2) For the individual New Yorker there is nothing comparable. All you say is that the probability applies, but it signifies nothing further. A probability of 14.3% offers no guidance to the individual on anything practical, like how often to check the heart, and in the end inferences may turn out to be totally incorrect because that particular individual may not die of heart failure.

...

Help me grasp the contrast beyond that.

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**1415**Senior Member

I can see that the individual's chances may be totally different than the 14.3% of the group... Just like the bare headers here are saying their chances are lower of needing a helmet than the group because of where they ride, how they ride, their skill level... The individual can often have a different chance than the group because he doesn't fit the pre-disposition, profile of that particular event... JMO as I see it... As Tiglath is saying, statists like the 14.3% for heart attacks apply to hospital preparedness but for the individual, not so much, depending on lifestyle, hereditary traits... A particular individual could have a basically 0.0% chance of dying from a heart attack depending on lifestyle, and hereditary traits... JMO

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Maybe I don't grasp the contrast either. It would seem that the same probability applies to the individual. However, the individual may be lacking the knowledge or resources to prepare for or avoid the heart issue. If said individual is a educated and has access to preventive medical care, then he or she would likely be just as prepared as the city, in the case of a heart issue.

Help me grasp the contrast beyond that.

Help me grasp the contrast beyond that.

City: if they prepare for what the probability predicts, they will be proved largely correct.

Individual: Any preparation may well prove totally unnecessary.

Cannot be clearer.

*Last edited by Tiglath; 07-02-15 at 10:26 PM.*

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**1417**Senior Member

why would this same concept not apply to helmets for individuals?

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**1418**
I.e.: most people don't crash, so helmets are not necessary?

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You are correct, sir. Put another way yet

Statistics may predict that 1 in 7 will die of heart problems this year, but a hotter summer may cause more hearts to give out and make the final proportion 1 in 6, instead of 1 in 7, but the prediction will still have been a useful approximation, and preparations for it appropriate.

No such thing for the individual. For the individual exist only outcomes that include the individual 0 or 100%. No approximations.

Therefore, for the city the prediction removes most of the uncertainty from what to expect, which is of great utility.

In CONTRAST, for the individual the prediction removes next to no uncertainty from what to expect, which is of negligible utility.

Thus, the point to concede is about the WIDE discrepancy of the probability's utility, between city and individual.

If anyone can't see the contrast yet, run, don't walk to Lenscrafters.

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It DOES!

That's the whole point of the example. The individual has no way to know what's in store for him or her, regardless of statistics. Statistics determine nothing for individuals. It's only useful for hospital trauma centers and entities concerned with the whole population.

That's the whole point of the example. The individual has no way to know what's in store for him or her, regardless of statistics. Statistics determine nothing for individuals. It's only useful for hospital trauma centers and entities concerned with the whole population.

*Last edited by Tiglath; 07-02-15 at 10:27 PM.*

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**1422**Senior Member

True, but nobody personally knows who that actual risk will be including... Same with helmets, for the people who's head bounces off the pavement wearing one when it happens is better than not wearing one in general I predict. Thus the helmet thread, some people are willing to take more risk than others, some use the population's risk % factor as to weighing their risk, others use their own risk calculations done by their own senses/idea of personal risk. Not that the risk is big but it's there...

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We can use statistical inference related to conditional probabilities to get a more precise probability. In the heart disease example, Baye's Theorem. Not intending to get technical, but in addition to the 14% base probability you'd need to know two more things about the individual with respect to a particular dependent probability. Such as exercise which we know improves our chances of not suffering heart failure. We'd need to know the base probability, the percentage of people who exercise, and the statistical probability that people who exercised died of heart disease. From this and using the formula that expresses Baye's theorem we obtain a new probability that the person who exercises regularly will die of heart failure.

Similarly for other factors such as diet, stress levels etc, knowing the related statistical data for those factors we can derive a probability for the individual - more precisely, for progressively smaller subsets of the population which include the individual. To be clear, this represents the probability that the given individual will experience heart failure.

One common fallacy in interpreting statistics is when you ignore the base rate. This error occurs when someone is presented a base rate probability, and a specific case, and instinctively focuses on the specific case while ignoring the base rate. We see it a lot in helmet literature, and sad to say, in this list. If we say for example, 97% of the people who died from heart failure did not take Vitamin C supplements, and from just that fact advise to take the supplements regularly, it's an example of the base rate fallacy (and one or two more).

With regards to fatalities related to helmet use or non-use, the base rate probability is extremely small which makes avoiding the base rate fallacy particularly important.

From accident data there are more elements, other statistics, from which probabilities may be inferred. Where you ride, time of day, even age group, and you can get more specific as well with variously credible data sets. You can formally calculate a refined "population's risk %" from these statistics, or, if you are one to "use their own risk calculations done by their own senses/idea of personal risk" I posit that both are the same general concept. You are using statistical data from observed events (your own or aggregated or both) and inferring a probability representing risk.

*Last edited by wphamilton; 07-02-15 at 01:04 PM.*

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It DOES!

That's the whole point of the example. The individual has no way to know what's in store for him or her, regardless of statistics.

That's the whole point of the example. The individual has no way to know what's in store for him or her, regardless of statistics.

**Statistics determine nothing for individuals. It's only useful for hospital trauma centers and entities concerned with the whole population.**.A person either will have heart disease or not. 100% or 0%. Fine.

However, any individual can look at the 14% and decide how to live their life, based on that risk. If 14% is more than they are comfortable with, they can decide to change their lifestyle or see a cardiologist to increase their chances of climbing above the 14%. The statistics are made up from individuals. You don't get to dodge the stats. You're either on the 14% side or the 86% side of the stats. It only means nothing if you fall on the 86% side.

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You just repeated the odds using your own words and added an obvious remark, but still nothing new for the individual to learn.

Here are two more ways to do it.

If nobody get his heart checked, 1 in 7 or 14.3 in 100 may be guilty of imprudently neglecting their heart.

If everybody gets his heart checked 6 in 7 or 85.7 in 100 (take your pick) will turn out to have acted on unfounded fear.

And so on...

Please keep trying. I'd love to be proven wrong and learn something new. An Internet debate bearing useful fruit is a pretty rare experience.

*Last edited by Tiglath; 07-02-15 at 10:29 PM.*