Airplane crash probability fallacy

[Username34]

TL;DR Summary

Probability fallacy

https://anxieties.com/self-help-resources/fear-of-flying/how-safe-is-flying/

"In fact, based on this incredible safety record, if you did fly every day of your life, probability indicates that it would take you nineteen thousand years before you would succumb to a fatal accident."

The probability statement above is wrong, even if we ignore asymetrical time evolution (no fixed stats.)

Suppose we can save me after an airplane crash... And I go through the 19 000 flights regardless

There is no reason why my first flight doesn't crash by random distribution, and the rest 18 999 are crash free.

The only thing that can be calculated as fact (assuming the past stats are set in stone), is that I will die once in 19 000 flights. You won't know which flight it is.

These stats charlatans remind me of string theorists:)

What say you guys?

 

[FactChecker]

There is no reason why my first flight doesn't crash by random distribution, and the rest 18 999 are crash free.

Yes, the rate should be divided in half to account for the early flight deaths and latter flight deaths. Your luck would average out to dying at the middle flight. But I don't see the rate numbers that I would like to use.

Looking at the link you provide, I have trouble finding an applicable rate of accidental deaths. I think that the rate of deaths per passenger flight hour might be the rate to use to determine how many years you could fly before an accidental death. I would just divide the rate in half to get the expected number of personal flight hours before being killed. But I don't see that rate in the link. Maybe I missed it.
CORRECTION: @Frabjous has pointed out that the number of flights is better than the number of flight hours for accident rates because the vast majority of accidents is during takeoffs and landings.

 

[DaveE]

TL;DR Summary: Probability fallacy

https://anxieties.com/self-help-resources/fear-of-flying/how-safe-is-flying/

"In fact, based on this incredible safety record, if you did fly every day of your life, probability indicates that it would take you nineteen thousand years before you would succumb to a fatal accident."

The probability statement above is wrong, even if we ignore asymetrical time evolution (no fixed stats.)

Suppose we can save me after an airplane crash... And I go through the 19 000 flights regardless

There is no reason why my first flight doesn't crash by random distribution, and the rest 18 999 are crash free.

The only thing that can be calculated as fact (assuming the past stats are set in stone), is that I will die once in 19 000 flights. You won't know which flight it is.

These stats charlatans remind me of string theorists:)

What say you guys?

I think you are missing the whole point of statistical analysis. Yes, you could die on your first flight, that is possible. We all can agree on that, let's move on. What might happen isn't very relevant, how likely an outcome is is the whole game here. The only significant "facts" in statistics are likelihoods. The key word here is "probability".

Anyway, what exactly is your question about statistics (some math would be helpful for us)?

 

[Frabjous]

I think that the rate of deaths per passenger flight hour might be the rate to use to determine how many years you could fly before an accidental death.

The proper death rate for air travel is per trip (majority of crashes take place during takeoff/landing) while for car it is per mile.

 

[pbuk]

The only thing that can be calculated as fact (assuming the past stats are set in stone), is that I will die once in 19 000 flights.

No that cannot "be calculated as fact": show your workings please.

 

[Username34]

I think you are missing the whole point of statistical analysis. Yes, you could die on your first flight, that is possible. We all can agree on that, let's move on. What might happen isn't very relevant, how likely an outcome is is the whole game here. The only significant "facts" in statistics are likelihoods. The key word here is "probability".

Anyway, what exactly is your question about statistics (some math would be helpful for us)?

You can't deduce how likely it is for you to crash within your lifetime in a random sampling. What you can do is provide the distribution of events. And the distribution is 1 in 19 000 (or whatever the solution is)

It's the same fallacy involving civilization ending comet strikes. You know the frequency but not the chronology.

 

[berkeman]

It's the same fallacy involving civilization ending comet strikes. You know the frequency but not the chronology.

show your workings please.

@Username34 -- your have about 35ns to post your math supporting your question before this thread is closed and you receive yet another warning...

 

[DaveE]

Sorry if this sounds insultingly simple, that's not my intent. But do you understand about how probabilities are expressed as rates? Like, it would take 1000 years on average for a single event. That is a measure of the likelihood (OK, depending on your distribution, etc.) of the event happening in the next year, hour, minute, second, etc. If my car is driving 60mph that doesn't mean that I will be driving for at least an hour, or that if I did I would cover 60 miles during that time. There is an underlying assumption that things won't change, so you can scale it appropriately for the duration you care about.

 

[DaveE]

It's the same fallacy involving civilization ending comet strikes. You know the frequency but not the chronology.

Yes, we know that. Everyone knows that. That is irrelevant in the study of statistics. You need to get past the idea that we know about single or occasional events. As you have said repeatedly, it doesn't work. We know that*. OTOH, it can be really useful if you have 10³⁰ air molecules in a box, because we just don't know, or really care what happens to the 34,102,384^th molecule.

*Note, way beyond this level of discussion: people that really do statistics really care about things like error bars, p-values, and standard deviations. All are measures of "how good is our model?"

 

[phinds]

If my car is driving 60mph that doesn't mean that I will be driving for at least an hour,

Exactly. As Stephen Wright said, "I was pulled over for speeding and the cop asked me if I realized I was doing 60mph. I told him 'yeah, but I'm not going to be out that long' "

 

[Dale]

I am sympathetic to the OPs general point. Statistics and probabilities are often misunderstood or misrepresented. The article cited is neither unique nor even extreme in that regard. However, in a thread criticizing other people’s distortions of statistics, it behooves the critic to be careful in their own statistical statements

You can't deduce how likely it is for you to crash within your lifetime in a random sampling.

You cannot deduce that you will crash at a specific time, but you can infer how likely it is to crash over some specified period.

And the distribution is 1 in 19 000 (or whatever the solution is)

That would be a point estimate, not a distribution.

 

[Hornbein]

Id guess that 1 in 19000 is an average.

 

[Username34]

Sorry if this sounds insultingly simple, that's not my intent. But do you understand about how probabilities are expressed as rates? Like, it would take 1000 years on average for a single event. That is a measure of the likelihood (OK, depending on your distribution, etc.) of the event happening in the next year, hour, minute, second, etc. If my car is driving 60mph that doesn't mean that I will be driving for at least an hour, or that if I did I would cover 60 miles during that time. There is an underlying assumption that things won't change, so you can scale it appropriately for the duration you care about.

But airplaine statistics isn't nature. Airplaines are built by humans, humans are fallible, and possibly corrupt. That alone can throw stats off.

Take the Boeing controversy. Those accidents make no sense statistically, but a 100% sense psychologically.

Samsungs exploding batteries the same thing.

 

[Dale]

That alone can throw stats off.

While that is true, it is not the same issue as mentioned in the OP. In the OP you describe a mistaken understanding of the meaning of probability. Here you are describing a situation where the probability model is wrong.

In the OP even if the probability is correct, people can misunderstand that you could just as well die on your first flight as your 19000th flight. Even if 1/19000 is the correct probability.

But airplaine statistics isn't nature. Airplaines are built by humans

The human vs nature thing isn’t relevant. The same thing applies to statistics about nature.

The issue is the correctness of the statistical model. Instead of being about a misunderstanding of a correct probability, the probability number itself is wrong.

In statistical language you are saying that the probability of a crash depends on corruption which was not modeled and which greatly increases the probability, $P(crash|corruption)>P(crash)$.

The same thing happens when modeling natural systems, and in about the same statistical circumstances. Your model can ignore things, for example a model of rabbit populations may include predation by foxes, availability of food, and typical diseases, but not novel diseases. That may be fine for most situations, but when you start talking about rare circumstances, then what may normally be a small risk may become large. Basically, the “tails” of any distribution are more often determined by unmodeled effects. Often extreme probability events are substantially more likely than a simple model indicates. Regardless of whether we are modeling humans or nature.

 

[phinds]

The only thing that can be calculated as fact (assuming the past stats are set in stone), is that I will die once in 19 000 flights.

SInce @pbuk pointed out that this is nonsense, I assume you now understand that it is nonsense, yes?

 

[Username34]

SInce @pbuk pointed out that this is nonsense, I assume you now understand that it is nonsense, yes?

It's not nonsense. People clearly die before those nr of flights in their lifes.

 

[DaveE]

It's not nonsense. People clearly die before those nr of flights in their lifes.

So your answer is clearly 'no, I don't understand probability at all'. If you are actually interested in this, you'll do well to study a bit more. Khan Academy has some good tutorials about this.

 

[phinds]

It's not nonsense. People clearly die before those nr of flights in their lifes.

They MAY, but your argument is that they WILL, and yes, that is nonsense. You clearly do not understand statistics and apparently have no desire to, else rather than being argumentative, you would try to understand why I say what I say.

EDIT: I see that @DaveE already pointed this out in post # 18 but rather than address the issue in post#19, you just changed the subject.

 

[Username34]

They MAY, but your argument is that they WILL, and yes, that is nonsense. You clearly do not understand statistics and apparently have no desire to, else rather than being argumentative, you would try to understand why I say what I say.

EDIT: I see that @DaveE already pointed this out in post # 18 but rather than address the issue in post#19, you just changed the subject.

I am addressing the way it's framed by people who knows better.

 

[berkeman]

Thread closed for Moderation.

 

[Dale]

A bunch of off topic posts have been removed and the thread will remain closed.