B A Statistical Freak

[Hornbein]

On the Metro to Sakura, Japan I was sitting in a section of 10 travelers. Only one was on a smart phone. I was amazed. In six weeks in Tokyo I have informally observed that usage is about 90%. If so the odds for this is one in 110,000,000. Indeed on the reverse direction ride home that day I was in a section of 14 riders with twelve on smart phone. Close.

 

[FactChecker]

Assuming independence. (Also, I don't get the same answer for the odds.)
Correction on the odds. One person used a phone.

 

[DaveC426913]

For ten people in that section, that would be 10%^10, no? Or 1 in a billion?

 

[Hornbein]

For ten people in that section, that would be 10%^10, no? Or 1 in a billion.

If all ten had been phone-free it would be one in ten billion. But there was one user. That makes it 90 times more likely.

If I assume phone usage prob is 5/6 then odds are about one in 1.2 million. That seems realistic but still very long odds.

 

[DaveC426913]

If all ten had been phone-free it would be one in ten billion. But there was one user. That makes it 90 times more likely.

.1x10^9 = 1:1,000,000,000

Why are we getting different numbers?

If I assume phone usage prob is 5/6

i thought you said 90%.

 

[gmax137]

.1x10^9 = 1:1,000,000,000

Why are we getting different numbers?

I think you mean (0.1)^9

 

[mjc123]

Probability is 10*0.1^9*0.9^1.

 

[Hornbein]

Probability is 10*0.1^9*0.9^1.

Close. It's the inverse of that. Y'all look up "binomial probability" and you'll get the formula. I bet there are online calculators that will do it for you.

 

[Hornbein]

.1x10^9 = 1:1,000,000,000

Why are we getting different numbers?


i thought you said 90%.

I made one assumption and did a calculation. Then made another assumption and did a second calculation.

 

[hutchphd]

On the Metro to Sakura, Japan I was sitting in a section of 10 travelers. Only one was on a smart phone. I was amazed. In six weeks in Tokyo I have informally observed that usage is about 90%. If so the odds for this is one in 110,000,000. Indeed on the reverse direction ride home that day I was in a section of 14 riders with twelve on smart phone. Close.

Very interesting. This observation may be less difficult to explain. By what criteria did you choose the subgroup of 10? There is a very large problem with your methodology here because of selection bias. The correct probability is likely far smaller

 

[DaveC426913]

I think you mean (0.1)^9

Yes. Google and my phone keep trying to correct me.

 

[DaveC426913]

By what criteria did you choose the subgroup of 10?

The section he was sitting in.

Any reason why it can't be a representative sample?

 

[DaveC426913]

On our trains here (Canada), there is a policy - I do not know if it is explicitly written anywhere - some sections of the train are understood to be phones free. (OK, actually phone call free.)

I believe it is the upper deck. The idea is that this gives people here a chance to sleep without having someone two feet away yelling into their phone. If you want to make a phone call, you go to the lower deck.

I'm not suggesting this is a actual case where you are/were, but it does suggest the possibility that there unwritten rules of conduct at-play for cramped, public spaces. And Japan is well-known for unwritten rules of conduct in cramped, public spaces.

 

[Hornbein]

Very interesting. This observation may be less difficult to explain. By what criteria did you choose the subgroup of 10? There is a very large problem with your methodology here because of selection bias. The correct probability is likely far smaller

I knew a wet blanket would appear sooner or later.

 

[Hornbein]

I just had a thought.

On our trains here (Canada), there is a policy - I do not know if it is explicitly written anywhere - some sections of the train are understood to be phones free. (OK, actually phone call free.)

I believe it is the upper deck. The idea is that this gives people here a chance to sleep without having someone two feet away yelling into their phone. If you want to make a phone call, you go to the lower deck.

I'm not suggesting this is a actual case where you are/were, but it does suggest the possibility that there unwritten rules of conduct at-play for cramped, public spaces. And Japan is well-known for unwritten rules of conduct in cramped, public spaces.

Japan has lots of written rules against smart phones. Talking on your phone in the Metro is banned. They are banned during concerts. They are seldom seen except in the Metro, which is so boring just about everyone uses them.

 

[hutchphd]

The section he was sitting in.

Any reason why it can't be a representative sample?

Is "section" a predefined thing? How many seats in a section? Bias is sneaky. The sample should be randomized if representing the general population. Was the section engaged in face to face interaction?

 

[DaveC426913]

Japan has lots of written rules against smart phones. Talking on your phone in the Metro is banned. They are banned during concerts. They are seldom seen except in the Metro, which is so boring just about everyone uses them.

That is has lots of written rules doesn't mean it doesn't have unwritten rules. I'm simply providing a possible exception to FactChecker's "assuming independence" in post 2.

Is "section" a predefined thing? How many seats in a section? Bias is sneaky. The sample should be randomized if representing the general population. Was the section engaged in face to face interaction?

I think you're missing the point.

The OP has said, effectively: "I just dropped a shuffled deck of cards on the floor in a mess, I picked up four of them and all four were aces. What are the chances of that?"

And your response is, in effect: "Why did you stop at four? Maybe it won't exhibit that behavor if you draw ten cards instead, or draw from a different area of the floor. The entire deck should be sampled at random to see if the entire thing is ordered."

OK but that would be a different observation - one the OP wasn't making.

 

[hutchphd]

n I was sitting in a section of 10 travelers. Only one was on a smart phone.

I think you're missing the point.

The OP has said, effectively: "I just dropped a shuffled deck of cards on the floor in a mess, I picked up four of them and all four were aces. What are the chances of that?"

No, you are missing my point. Following your hypothetical: The OP dropped the cards and noticed some were a slightly different hue. He picked up a bunch of cards from that part of the pile and counted only one in ten was ordinary color. Selection bias.