Right again. The individuals in the probability remain anonymous any way you dice it. There is no way for anyone to have any certainty at all. That is the whole point. Back to Lenscrafters, folks.

Oh. So you are operating under the misconception that we blind, ignorant masses on the internet are looking for certainty. Do you really think that's how we think statistics work? Thrilled you could come and condescend to us.

It's semantics. As I said in # 1424 (which you ignored), the statistics are based on individuals. You can't dodge your odds and pretend they don't apply to you as an individual. You can hope to fall on one side or the other and/or do what you can to better your chances. That is how they apply to individuals. But please continue to act like you have some heightened awareness of statistics.

That is a misleading statement. Statistics, the kind we are discussing, are based on GROUPS of individuals, rather. If you do not know that no progress is possible. And it is an essential requirement that the group be large enough to be statistically significant, given a purpose. I've been calling such groups a (sample) population, and I gave New York City as an example. Therefore an analysis of the frequency of events in the sample will refer first and foremost to the WHOLE sample, not the individual components of it. Individuals may fall anywhere in the spectrum of the sample. Therefore statistics about the sample inform about the sample, and do not identify which individuals will confirm or deviate from the predictions.

That is a long way to say the if we want the 1-in-7 probability to provide more information and have some utility for the individual, we have to add more information about the individual to start with, which is again loading the dice.

If you add to the 1 to 7 probability more information needless to say you can get more out. That is not the question or in dispute.

If for a particular individual, for example, you take into account his heart health metrics his odds may change because you just customized them for that individual. That is not what we are talking about. What we are talking about is the raw probability for the entire population being useful to a particular individual, nothing added. You still can't get past that, theorems notwithstanding.

No kidding. Sir, with all respect, you are moving the goalposts while the lights are still on.

New to this forum, tho not to cycling, and happened on this thread....

Thirty five years ago when I got into adult cycling pretty much none of us wore helmets. I was off of road bikes for 20 years and when I, recently, got back I continued with my old, no helmet, habit. Then one day as I was sorta cruising down hill at 25+ mph it occurred to me....I don't ride a motorcycle without a helmet, so why in the hell am I doing this on a much more fragile platform?? Helmet and leather fingerless driving gloves always since.

Exactly, That's what they do when you want to buy life insurance, They ask a lot of questions to make the general statistics work out to show that persons individual probability of dying or getting sic, or into an accident depending on what that person does and what his relatives died from, what kind of sicknesses they had... They don't just use the general statistics... :rolleyes:

Get a refund at least... Just kidding...

Please remember that at every step of the discussion, because that is precisely what a guy (the individual) wants to know, and the 14% is not telling him.

Not in dispute and not my point.

We are discussing cases (hearts and helmets) in which fate is the major player. Many times the first symptom of heart problems is death; many bicycle accidents are sudden, unexpected and the cyclist did not cause it.

I've already said that knowing a probability is better than knowing nothing. 14.3% tells you the lethality of heart disease in a given population, FULL STOP. Needless to say, you may then in prudent avoidance live as healthily as possible. That is not the point either. The point is that unlike a city, which is pretty well damn sure that 1/7 of people about to die will require cardiology services, the guy in the street has no idea whether he will be in the 14.3 % or in the the remainder of the population, and the probability remains silent about it. And one reason for this silence is that the probability was derived from information that excluded everything about that individual, and included only information about the population at large.

No info about the individual in, not info about the individual out. Is that more clear?

No one is trying to "dodge the stats," what will be will be. And again, statistics are not made from individuals; two guys are "individuals" and any statistic based on what happens to two guys on bikes would fall into the fallacy of statistics of small numbers:

Hasty Generalization

Sound statistics, of the kind we discuss, involve groups of individuals large enough to be significant: a population. Determining what is large enough to be statistically significant is part of the science.

Congratulations! Something similar happened to St. Paul on the road to Damascus.

That is not what needs grasping. You seem to intentionally refuse to address what needs grasping, Again:

We have a prediction derived from statistics of a sample population.

What needs grasping is the discrepancy in the utility of such prediction for the sample and for the individual.

Translation: "I'd better exit this issue. I keep having to skirt this guy's point and go on evasive tangents because I can't explain why a particular New Yorker should feel personally alluded when hearing that 14.3 % of New Yorkers will die of heart disease, other than by the fact the lives in New York."

That's utterly wrong no matter how many times you write it.

I'm just being polite and don't want to argue with a student who doesn't appear to understand probability.

If you don't grasp the explanation of the mathematics, directed to another individual, please don't post about it.

Go to the thread "Ms Hall did not observe any traffic. Note what I have been saying many times. In the article it is stated that the cyclist was wearing a helmet. You can bet your bottom dollar that if he haddnt been wearing a helmet, the girls lawyer would state that the cyclist contributed to his own injury. Like helmets or not, ALWAYS in accidents like this it is stated wether the cyclist was wearing a helmet. So---------------for your legal protection wear a helmet.

Her lawyer might say that, and it might even work if the court is particularly biased against cyclists, but legally speaking it's generally not a valid "contributory negligence" defense.

I'll grant you this much though. If I'm killed by some driver or recovering in the hospital, I don't want to be held up to public ridicule by the news reports stating "the rider was not wearing a helmet" and that does factor in with my decision to wear or not wear one on a given day.

The "problem" with math and statistics is that it's an average number that represents the average of a bunch of people % like 14.3% heart problems in NYC if I remember right, but in reality for me personally, I may actually have a much closer to 0.0% chance and others may have closer to 28.6% chance of having that problem, thus the average 14.3%, that's the way I see it... So, with such a wide range I don't really see how that 14.3% applies to me personally other than vaguely pointing out what "could be" my "personal" odds if I didn't know anything about my ancestors... Now as said before that 14.3% statistic certainly does help the health system prepare for what's to be expected... But for me personally knowing my ancestry and how they died, and what they died from, all of them from both sides of the family were between 85 to 90 years of age when they died and none of them had heart problems. I try to stay/live healthy, I suspect that 14.3% doesn't in the least apply to me personally... :bike:

EDIT; As to wearing a helmet, I do wear a helmet because I suspect I am on the high side of the masses risk % because of how and where I ride... Meaning, if the chance of a crash on a bike for the average rider is 5% and the chance of the head hitting the ground is 5% when you do have a crash I think/suspect my odds are more like 10% chance of having a crash and 10% chance of my head hitting the pavement when I do crash. ;) :p

???

The "14.3% risk" is the risk to the overall population. It's basically an average. And an average is a property/characteristic of a particular population (not an individual member of that population **).

There's a high probability of the risk being different for randomly selected subpopulations (especially, if the subpopulations are small). If the subpopulations are selected based on factors that contribute (negatively or positively) to the risk, then the risk almost certainly won't be the same.

The "14.3% risk" is determined from a historical (past) population. It's assumed to apply to future populations because the properties of large populations doesn't change that fast. That is, the unknown actual risk of the future population will likely be different but it won't be very different.

The probability only applies to the group. People can do all sorts of things to influence their individual risk of getting a heart attack. The risk of getting a heart attack isn't 100% random.

You should know that health insurance companies prefer healther subscribers because their risk for things like heart attacks is lower than the general population.

The purpose of gaining experience and taking safety classes (or wearing helmets) is based on reducing one's risks relative to the general population.

No. In fact, the risk to an individual is unknown (and pretty-much unknowable). The "14.3%" is an estimate and, very likely, a bad one at that. The idea is that a crappy estimate is better than none.

What you are doing is saying that everybody is 6 feet tall (assuming 6 feet is the average height) "without knowing other information".


(** nitpicking: the average of a population of one is characteristic of the individual.)

A student that notices that your replies contain only naked assertions like, "it's utterly wrong," "it applies," "it is predictive for the individual," but never a to-the-point explanation of how and why, despite multiple request that you go into the weeds of your assertions.

You saying so does not make it so, professor.

Who told you that arguing is impolite? I doubt politeness is what keeps you from providing a valid and sound argument for your claim, though I thank you for the polite way you disagree with me. I won't be first to be rude.

In science and logic people use arguments with premises, which anyone can follow how they lead to conclusions. You arguments have only conclusions, backed by what you presume to be sufficient, your authority. Well, it is not sufficient.

Sending me to "class" or to ask a teacher is too thin a veil for your enduring inability to back up your statements.

Sir, I don't care who wins or loses a debate. We all like to be right, but it pleases me most when a debate reaches a resolution point. For the purpose is not to feed the sense of importance but to arrive at some new truth and share it with all participants.

You wrote about probabilities derived from statistics:

"[Y]es these are predictive for individual elements within the population."

To predict is to say what will happen in the future.

In a population with a mortality of say, 100,000 deaths, the 14.3% probability we've been using as example would predict 14,300 deaths from cardiac problems. That's a no-nonsense, concrete, actionable prediction of actual events.

Please tell me what concrete events does the 14.3% probability predict for any one, single, particular citizen (the individual)?

A persuasive answer will back up and explain your claim that probability is just as predictive for the individual as it is for the population. A reply with bluster won't do, it will earn you no credit for your assertion, and the Gentle Readers and I will know that you are too big to admit a small error.

Here is another chance to support your claim, which I quote in bold above. No academic tour, please, a plain and succinct answer will do and let's be done with it. And if you can't or won't, say so an let's be done with it too.

Regardless... happy 4th of July.

Well said.

I have been at pains to make that poster realize that much. A man who does not get averaging accuses me of not understanding probability. What's next?

I doubt he will reply anything like, "I stand corrected," which would be refreshing after the gaggle of posters this thread has seen that just can't face evidence counter to their misconceptions, and keep throwing spitballs from the back bench.

Fortunately, a few other posters possess the fundamental clarity to navigate these rather obvious issues, which makes being here still worth it, for now.

Happy holiday

Have your misconceptions no end? First probability now the law.

So much for not wearing a helmet being 'not a valid "contributory negligence" defense' for a defendant accused of injuring a cyclist. It's not only valid, but also requires combat:

------

Combating Comparative Fault for an Unhelmeted Cyclist

The bike helmet issue is somewhat comparable to when a plaintiff fails to wear a seatbelt or rides a motorcycle without a helmet; in these instances, the defense can argue comparative fault. This is a very big deal, because comparative fault is a finding that reduces an entire judgment based on the percentage of fault attributed to the plaintiff.

Combating Comparative Fault for an Unhelmeted Cyclist | CEBblog?

-----

The article goes on to point at things one can do to attack that defense, but it is certainly false that such a defense is not valid.

Only four states make not wearing a helmet an easy case of contributory negligence, but that does not mean that in the other states you will have no problem at all. Vigorous cases are still being brought and you will have to fight in court to prevail. Here is another one.

Contributory negligence and cycle helmets | Kennedys

So at best it is a grey area which may well drag you through court and obstruct, delay, or reduce any settlement you get for your injuries. In sum, it's nothing like what the poster states, that there is no valid case to it.

Unless you are in Bike Haven like Holland and such, there are multiple good reasons to wear a helmet.

I would even wear a helmet in Holland.

It appears that this might be a UK case.

Politeness is not the issue with "arguing" math, and aside from not jumping your case I know that I haven't been that patient with you. My suggestion to take it up in class was sincere, since that's the only place where you'll likely get the "debate" about statistics that you're looking for.

Simply put, debating and arguing is not appropriate for the subject matter, particularly the elementary concepts such as these. I am a helpful person but teaching is not my profession and if someone doesn't get it, that's fine also.

Whenever we speak of an individual's "risk" in this context*, we mean the probability of an outcome in the general context. In risk analysis you can infer the probability from statistical data.

This risk analysis is utilized by everything from credit checks to insurance premiums. We don't look at one statistic and produce a number. The more that is known, applicable to the individual, along with the appropriate statistical data, the greater confidence you have regarding the probability of a particular outcome for the given individual.

*Let me state here that I am speaking in general of my own views and not for the policies, opinions or practices of my employer.

I would probably express it as a probability distribution function, and give you a probability that a randomly selected individual is 6 feet tall.

Yes, but the risk analysis is for a population (for an imaginary "individual" that represents the population).

The risk for an actual individual is going to be different. That's why insurance pools risk across a population.

The point of insurance is because individual risk isn't known.

As long as the risk of the population is determinable, insurance doesn't really care about the individual risk (it all balances out). On the other hand, the individual cares about his particular risk.

Since one is talking about predicting the future of a complicated event, one will never know the actual risk for a particular individual. Insurance will always require a population to average-out the unavoidable variation in individual risk.

You'd actually have to indicate a range since the probability their height would be 6 feet is very, very low.

Risk has a probability distribution too.

That means, to be accurate, you have to give a probability that a randomly selected individual has a risk of 14.3%.

That is, 14.3% isn't really the risk to a randomly selected person the same way that 6 feet isn't their height (except as a random coincidence).

With a single post, the member nkkayaker, has chopped, diced, concassé and fricasée your argument far more eloquently than I have been able to with several.

Read, parse, and inwardly digest his post and learn about probability basics. You are a long way from being able to impart statistics or math tuition on me or just about anybody.

The honorable thing for you to do at this point is to admit that your claim was incorrect, so that at least you don't compound your error with the disgrace of not admitting it.

Kind regards

Translation: "I can't tell this guy what concrete events the 14.3 % probability predicts for the individual but, but I am too proud to admit it. I'll just stick to saying that he does not get it and should go back to school because it's not my job to teach him; it might work this time"

Such gall... YOUR math coach would not approve.

That is amazing. The guy completely ignores the point at hand and what njkayaker wrote, and tries to obfuscate what is plain to see in a most hilarious manner. Who does he thing he is talking to, first graders?

Without a word or missing a beat, he abandons the issue at hand and starts riffing about how to figure risk for an individual from his personal data, which is a different subject. And hopes no one will notice the switch... <shake head ruefully>

His posts are a joy to watch though, from an entertainment perspective. In order to avoid, dodge, evade, elude and sidestep the point that has him cornered, he throws all kinds of jargon and red herrings that might confuse pursuers: theorems, Boolean logic, calculus, platitudes, lofty admonitions and here even his employer puts in an appearance. It's hilarious.