Need help with Stats

[Wistarmo]

 

Forgive me, but I need to correct my previous post.  The statistics for driving, motorcycles, and airlines are fatalities per 100 million passenger miles.  The exact web page is: http://trafficsafety.org/safety/sharing/motorcycle/motor-facts/motor-injuries-fatalities for cars and motorcycles and http://www.airlines.org/economics/dataanalysis/pages/safetyrecordofusaircarriers.aspx for airlines.

I misread/misstated the Nall report which showed fatal accidents per million flight hours.  Therefore, there were two errors I made in quoting that report, as the number of fatalities is higher than the number of fatal accidents and the rate was per million flight hours, not 100 million passenger miles.  I cannot find the 100 million mile general aviation data anywhere; most analyses are using the number of flight miles flown provided by the FAA.  Both the Greenspun article quoted by ChrisH and another article by Mantakos (http://www.meretrix.com/~harry/flying/notes/safetyvsdriving.html) use 100 mph as an average speed by general aviation aircraft to convert million hours flown to 100 million passenger miles.  

In 2008, there were 433 general aviation fatalities in 236 accidents with 19.78 million hours  flown.  433/19.78 equals 21.9 fatalities per million flight hours. The number of passenger miles this represents depends on what value you wish to chose for a general aviation average speed.  If you use 100 mph, then the numbers are equivalent to 100 million mile data.

I compare this to a book called, "Flying Out of Danger" by Goldstein (1984) who does show data for 100 million passenger miles at that time, with fatality rates per 100 million passenger miles of 1.0 for driving, 13 for general aviation, and 0.086 for airlines.  I will try and find more current estimates of general aviation fatality rates per 100 million passenger miles to provide a more accurate comparison to driving, motorcycles, and airlines.

 

[aviatoreb]

Quote: Wistarmo

I compare this to a book called, "Flying Out of Danger" by Goldstein (1984) who does show data for 100 million passenger miles at that time, with fatality rates per 100 million passenger miles of 1.0 for driving, 13 for general aviation, and 0.086 for airlines.  I will try and find more current estimates of general aviation fatality rates per 100 million passenger miles to provide a more accurate comparison to driving, motorcycles, and airlines.

[David Mazer]

Quote: aviatoreb

Fatalities per million hours

Skydiving = 128.71

General aviation = 15.58

On-road motorcycling = 8.80

Passenger cars = 0.47

Bicycling = 0.26

Flying (domestic airlines) = 0.15

Home living (active) = 0.027

Compiled by Failure Analysis Associates, Inc. (Design News, 10/4/93)

[aviatoreb]

Mazerbase, I don't understand what is the meaning of your adjusted risk column.

Ummm - Also - your bicycle is shockingly slow.  You need a faster bike.  I bike at least double that speed on average.  Sometimes a lot more than that.

I saw a comment above regarding the low numbers being low enough not to worry about.  From above, "as opposed to the rather miniscule risk.Even at 1or 2 fatals per 100000 flying hours...actual risk is low...or too put into odds..how many eons would it take to win the lottery at those odds???"  It does not take as many eons as you might think, and the accumulated risk can be surprisingly high:

In the following for simplicity of computation I will assume statistical independence of an event during each hour to the next - this is not quite right but good enough for a rough estimate I believe and definitely the non-independent computation is MUCH harder.

Let p=1.5/100000 be the probability of a fatality event in 1 hour of exposure.

1-p is the probability of no fatality in 1 hour of exposure.

(1-p)^n is the probability of no fatality in n-hours of exposure

1-(1-p)^n is the probability of a fatality in n-hours of exposure.

Take an average pilot such as myself who flies roughly n=100 hours in a year.  Then,

1-(1-p)^n=1-(1-1.5/1000000)^100=0.0015=0.15% chance of a fatality event per year.  Let q=0.0015

If you fly for 30 years, then the chance of a fatality event in 30 years is.

1-(1-q)^30=0.0440=4.4%

1-(1-q)^40=0.0582=5.82% in 40 years

...or if you fly more, then q=0.003 and 1-(1-q)^30=0.0861=8.6% and 11.31% for 40 years.

The punchline is that even a small number like 1.5/100000 becomes a large number with repeated exposure and it does not take eons.  As I said, the real way to do this computation is by a field called rare statistics which has its own tools and a great pain in the neck but the above gives you an idea.

No two ways about it - flying is not a no risk activity.  That said, I bike race - and I ride roughly 12hrs per week.  I incur a much greater total risk cycling than flying.  But then I like to think that this activity mitigates some of the other usual risk like heart disease and cancers, etc.  Bath tubs are dangerous too and I stand in a bath tub to take a shower after each bike ride.  Sometimes I go in a canoe ride.

Nice thing about any of these activities, flying included, is that bulk average probabilities like p=1.5/100000 across a population is not likely your personal probability.  You might be much worse but hopefully you are better.  I am a believer that in this particular activity, that 90% of the risk is concentrated on 10% of the people.  I.e., those hotdoggers who have no fear or hesitation to launch into a building thunderstorm.  So if I am right, I like to think that with good aeronautical decision making (vow to make the right decision every time and don't launch even if you will be late if the weather aint right), excellent recurrent training (I do believe that statistically skills are not as important as basic decision making - this is why airline pilots still die in Cessna 172s sometimes - but skills are important nonetheless!), make the decision to maintain your airplane in absolute tip-top shape and never skimp on premptive maintenance (and this too is a smaller term in the risk too since we know that mechanicals are the smaller part of the incident scenario risk - nonetheless chase out all the demons!) - do all these things and believe my 90% risk on 10% of the people concept and you may put yourself out of that 90% of the risk category.  If so, then maybe-maybe p=1.5/(10^6) for you personally.  This is not mathematics, just a wish.  And a working principle on how I approach the activity.  And a promise to myself.

[David Mazer]

I calculated adjusted risk as speed of plane/ speed of mode of transportation * risk per hour to show what the risk is if you are in that mode of transport for the time it takes to cover the same miles.  Since my average speed in my car was only 30 mph per my GPS (and I'm not considered a slow driver by any stretch of the imagination), I had to assume some total mph for a bike that includes the time spent stopped, turning, etc.  It was only a swag in relation to my car's average.  Maybe bike mph isn't the same as a car's mph because they are used so differently but if you are commuting on a bike, I would guess there is a lot of stopped/slow time involved.  Like I said, just a guess.

[aviatoreb]

Quote: Mazerbase

I calculated adjusted risk as speed of plane/ speed of mode of transportation * risk per hour to show what the risk is if you are in that mode of transport for the time it takes to cover the same miles.  Since my average speed in my car was only 30 mph per my GPS (and I'm not considered a slow driver by any stretch of the imagination), I had to assume some total mph for a bike that includes the time spent stopped, turning, etc.  It was only a swag in relation to my car's average.  Maybe bike mph isn't the same as a car's mph because they are used so differently but if you are commuting on a bike, I would guess there is a lot of stopped/slow time involved.  Like I said, just a guess.

[fantom]

According to all these morbid "stats" I should have died 18.7 years ago..... ;-)

[aviatoreb]

Quote: fantom

According to all these morbid "stats" I should have died 18.7 years ago..... ;-)

[Barry]

Quote: fantom

According to all these morbid "stats" I should have died 18.7 years ago..... ;-)

[1964-M20E]

I figuure 1 death in 1M hours I'll be 114 by time it catches up to me. :-))

[fantom]

It's not when we go, it's how we go to that all too crowded pilot lounge n the sky.

[jlunseth]

Quote: Wistarm

Both the Greenspun article quoted by ChrisH and another article by Mantakos (http://www.meretrix.com/~harry/flying/notes/safetyvsdriving.html) use 100 mph as an average speed by general aviation aircraft to convert million hours flown to 100 million passenger miles.  

[Hank]

Hear, hear for Mark Twain!!  :-)

I fly ~100 hrs/year. Since I started lessons, I'm averaging 8 hours/month and am currently pushing towards 500. Guess I died last fall . . . but the fun won't stop until I'm in the box.

[jlunseth]

I will be dead my second time pretty soon here, probably by the end of the year.  I fly a little over a half a life per year generally, somewhere in the 200-250 range. 

[thinwing]

who was it who said...there are lies,damned lies and statisics!!!

[Hank]

That would be Mark Twain [see posts above].