One of the subtle pleasures associated with reading this blog is the occasional opportunity to be experimented upon. Today is such a day.
Instructions:
- Read all these instructions before actually completing step two.
- Flip a coin.
- Please actually flip a coin. People who choose ‘randomly’ in their heads do not actually pick heads and tails equally. If you don’t have a coin use this online tool.
- If it landed heads, click here.
- If it landed tails, click here.
- When you click one of the links above, you will see a description of an event.
- Before looking at the comments below, estimate the probability of the event you see described happening in the next year.
- Write that as a comment, indicating whether you are answering the heads question or the tails question.
When you are done, you are naturally free to read the other question and the comments left by others.
Even if you don’t normally comment, please do so in this case. I want to get enough responses to permit a statistical comparison.
Heads: 60% chance
tails.
Didn’t that already happen?
It’s hard for me to estimate probability as a number, so I’m just going to say I wouldn’t be at all surprised if it happened (again?).
Two more things:
1) If you cheated and looked at both options before answering, please do not post an answer. Doing so would wreck the experiment.
2) If you want to know the reasoning behind the experiment, click here.
Tails- 10%
heads:
55%
heads – 5% chance.
Heads: 0.12
My answer is based on my belief that the event is easily possible, but unlikely.
Heads: 50%
Including Hurricane caused flooding as a factor.
Heads – 10%, because the figure seems unusually high.
Heads, 20% probability including the fact that stupid Americans can’t take care of each other and so a high death toll would be more likely in America than in more competent/compassionate countries.
I realize “hateful rant” wasn’t on your instructions, but oh well. ;)
Tails:
Not knowing any of the meteorological factors makes it hard for me to estimate this, but I would say… 10%. It’s not really based on any statistics or research.
Heads – 5%
Heads
5%
Heads 0.05
It’s a bit odd that we got 10 heads in 12 trials. We will need a lot more data if we are going to be able to draw any meaningful conclusions.
One last note: you can express your answer as a proportion (0.1) a percentage (10%) or a fraction (1/10).
Numbers less than one, without percentage signs, will be treated as a proportion. For example, 0.55 = 55%.
Incidentally, the mean heads estimate is running at 22.7%, compared with 10% for the mean tails estimate.
This Powerpoint presentation includes results from two experiments similar to the one above. It doesn’t provide any methodology, though it says that the second example was given to ‘forecasting experts.’
Example 1:
* Massive flood somewhere in North America in which more than 1000 people drown (2.2% probable)
* An earthquake in California causing a flood in which more than 1000 people die (3.1% probable)
Example 2:
* A complete suspension of diplomatic relations between USA and USSR sometime in 1983 (0.14%)
* A Russian invasion of Poland and a complete suspension of diplomatic relations between USA and USSR sometime in 1983 (0.47%)
The flood experiment is also mentioned on this page.
Between 1903 and 2002, there was never a year where 1,000 people died in a flood.
The worst years:
1903: 178
1913: 527
1914: 180
1922: 215
1927: 423
1935: 236
1955: 302
1969: 297
1972: 554
1977: 210
1982: 155
1983: 200
1986: 208
On the basis of these records, the people making estimates for heads are likely seriously overestimating the risk of so many flood deaths.
Only three hurricanes have ever caused more than 1,000 total deaths (all causes, not just flooding):
1900 – Galveston, Texas – 8,000 deaths
1928 – Lake Okeechobee, Florida – 2,500 deaths
2005 – Katrina – 1,800 deaths
Heads: 5%
Tails: 55%
Heads.
.00005
The highest ‘heads’ estimate is 12,000 times the lowest one.
Also, I wonder whether the very last ‘heads’ estimate inappropriately took into consideration the two comments above with actual flood and hurricane data.
(I am not posting a response of my own because I cheated and looked at the other answer, before coming up with an honest guess of my own.)
Heads: 4% chance
(I am not sure what good my input is though, considering that I don’t know a thing about flooding trends in North America. It’s more of a gut-response.)
Heads 5%
RK – No, I followed the rules and did not read the comments until after I guessed. (My prediction did take into account the time variable – ie, that the event would take place in the next year. I suspect others may have overlooked that.)
Running tally:
Heads (n=13)
– Mean: 18.2%
– Median: 5%
– Standard deviation: 0.2165
Tails (n=3)
– Mean: 25%
Median: 10%
– SD: 0.2598
The small number of tails responses remains a mystery
Probability of at least 13 heads in 16 trails = 1 in 94
So, not fantastically unlikely.
Tails: 5%
After posting that, I realize that I have fallen victim to this phenomenon. I doubt if I had the heads question, I would have picked a number above 5%.
Do you still need more responses Milan? If so, I could post something on my blog to point a few more people in this direction.
Heads question – pretty improbable. Small number.
zoom,
The responses above are quite varied and not really sufficient to draw conclusions from. Perhaps more data would help.
Tails.
1 in 50.
Heads 1%
tails
5%
Tails.
5%
70% chance (Tails)
Heads, 10 % .
Running tally:
Heads (n=15)
– Mean: 16.5%
– Median: 5%
– Standard deviation: 0.2060
Tails (n=8)
– Mean: 20.2%
Median: 7.5%
– SD: 0.2652
The distribution of guesses is extreme on both sides:
Heads: 60% v.0 005%
Tails: 5% v. 70%
Heads: 0.5%
Heads – 2% and only because I’m not sure what flooding would include – more than 1,000 died during Katrina, but that was flooding and a bunch of other stuff related to the reason for the flooding and the aftermath of the flooding.
Heads – 50%
tails & 70%
It’s a guess, but a (speciously) reasoned one:
“Well. 100%. Of course that’s going to happen. It’s *Florida*. And the end times are coming so the hurricanes are getting worse. New Orleans. Wait. 1000 people is a lot of people. Generally not many people die in hurricanes. Maybe one or two? How many died in Katrina? 3000? No, that was 9/11. Hmm. 1000 is a lot. Not 100%. But the end times still makes it higher than 50%.”
Tails: 75% or better
Heads – less than 1% chance. Thats a pretty high death toll if it was 200 ppl I’d say 50%
Tails. 0% probability of happening.
Heads – 20% chance, probably involving an earthquake.
5% – just flat out guessing.
Dan,
Is that for heads or tails?
Heads
n: 21
Mean: 0.155002381
SD: 0.198693797
1st quartile: 0.04
Min 0.00005
Median: 0.05
Max 0.6
3rd quartile: 0.2
IQR: 0.16
Tails
n: 10
Mean: 0.279090909
SD: 0.318761809
1st quartile: 0.05
Min 0.02
Median: 0.1
Max 0.75
3rd quartile: 0.625
IQR: 0.575
Heads, my bad.
Here is a boxplot based on the first 32 guesses:
Heads / Tails boxplot
Heads; 15.4%
1 %; heads
Heads….10%
tails: 20%
Heads: 32%!
heads
Well, it will happen or it won’t… I don’t like being quizzed… but I am trying to be a good sport… so here’s a number that popped into my head:
69.9%
Tails: 45%
heads – 90%
2% – I got the heads question.
Tails question: 30%
Tails :30% I guess.
Heads – 40% but it’s a total guess
Tails: 6%
Tails: 20%
Heads… 1%
Tails: one percent.
Tails: one percent.
Heads
5% chance of the exact circumstances. Hard to say as it is very specific.
It the numerical value given in the event description are not a rigourously adhered to criterion, then I think the chances are 25% or greater.
tails 1/1000
I did not cheat, but when I looked at your reasoning, I just wanted to say that I am a person who works with numbers a lot, and I actually worked with flooding/storm statistics in a former job. Totally random, but wanted to let you know. It is a pretty rare storm event that will affect never mind kill 1000 people in the world, never mind one state.
Tails
Odds; 1:100
Heads – 50%
(Zoom “sent” me btw)
tails – how about 40%?
Not that I know much about hurricanes or Florida..
Heads – less than 10% chance.
I’m in the UK, so I don’t know if you’d include my response or not, given that our news coverage is more concerned with our own country I may have a slewed attitude towards this.
Thank you all for your answers. I am going to use the ones collected so far to write up the results.
The results of this experiment will be posted here as of 7:00pm on April 25th.
The chances of a flood in the U.S. leading to 1,000 deaths happening in the next year are 90%. This was the heads question.
I got tails and think it has a 33% chance of occuring
Heads
20%
Tails :
Extremely unlikely, something like 0.05 % or even less.
In one experiment described by Mr Kahneman, participants asked to imagine that they have been given £50 behave differently depending on whether they are then told they can “keep” £20 or must “lose” £30—though the outcomes are identical. He also shows that it is more threatening to say that a disease kills “1,286 in every 10,000 people”, than to say it kills “24.14% of the population”, even though the second mention is twice as deadly. Vivid language often overrides basic arithmetic.