Hey, it's been a while since I took my stat classes. Short summary: I'm trying to calculate the odds that a given adult will be chosen to participate in a national poll. Mostly to counter the whole "How can polls be successful? I was never asked my opinion!" nonsense.
There are aprx. 255,000,000 adults in America. Most national polls have a sample size of 1,000. Thus, for any given poll, someone has a 1 in 2,550,000 chance of getting the call.
My problem is how to determine the chance for multiple polls. Is it as simple as putting 2,550,000 over X, where X equals the number of polls in a given year? So for example there were roughly 600 national scientific polls (that I know of) in 2012. Would the odds that a single person be chosen for any of them equal 1 in 4,250 (2,550,000/600)? That is, a given adult has a 1 in 4,250 (or 0.00023%) chance of being chosen for any national poll in a hypothetical election year?
Thanks for any refreshers.
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Assuming the polls are completely independent events, you would multiply the chance by the number of events, as you did.
Now, polls aren't truly independent. They often use proxies which shrinks the voting pool. A company may reuse previous lists. Some of the polls are location or demographic dependent and so wouldn't necessarily include the whole population.
However, to avoid going completely insane, treating them as independent is good enough for a quick argument.
Paul Watson wrote: Assuming the polls are completely independent events, you would multiply the chance by the number of events, as you did.
Now, polls aren't truly independent. They often use proxies which shrinks the voting pool. A company may reuse previous lists. Some of the polls are location or demographic dependent and so wouldn't necessarily include the whole population.
However, to avoid going completely insane, treating them as independent is good enough for a quick argument.
Okay cool, thanks.
Whoops. Totally messed up my numbers: with 255,000,000 adults and a sample size of 1,000, that's a 1-in-255,000 chance to be picked for any specific poll. Meaning the odds are technically 1-in-425, or 0.002%, for an adult to be chosen for any national poll at all.
...Hey, I went to public school, it's a wonder I can even wipe myself.
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Another factor is how the polls are conducted.
Do they knock on doors? If so, what is the chance that they do the poll while somebody is home?
Do they make phone calls? If so, are the phone numbers selected from a list of land lines or do they include cell phones in their list of numbers to call? And with the prevalence of caller ID, what is the chance that you will answer a phone call from a pollster since you would not recognize it as belonging to anyone you know?
I think factors like these rather than sheer chance would explain why I have not been polled in recent years.
I messed up my numbers yet again (sigh): a 1-425 chance is equal to 0.23%, not 0.0023%. I aced both stats classes, but am increasingly wondering how. Maybe a truly tragic curve?
David knott 242 wrote: Another factor is how the polls are conducted.
Do they knock on doors? If so, what is the chance that they do the poll while somebody is home?
Do they make phone calls? If so, are the phone numbers selected from a list of land lines or do they include cell phones in their list of numbers to call? And with the prevalence of caller ID, what is the chance that you will answer a phone call from a pollster since you would not recognize it as belonging to anyone you know?
I think factors like these rather than sheer chance would explain why I have not been polled in recent years.
Agreed entirely. In fact I was reading how 18-34s are considered very lucky "gets" by pollsters, on account of how many of them don't have land-lines. It was that very factor that lead to the infamous Dewey Beats Truman headline in 1948. Though in that case, because only the wealthy owned phones, it unintentionally weighted polls of the day in their favor, despite them being a minority.
Still, my little exercise is only meant as a quick and dirty counter to those who discount polls because they, themselves, were not asked. Like really? The point of a poll is to generalize answers from a representative population, not ask all 250 million of us.
Also, aren't polls usually predicated on getting the opinions of voters? Polls I've experienced will often ask first if I'm registered to vote/plan to vote before asking anything else.
So, instead of total adults you want to look at adults that are registered to vote and have landline phones. That's a significantly smaller number, I'd wager.
Scythia wrote: Also, aren't polls usually predicated on getting the opinions of voters? Polls I've experienced will often ask first if I'm registered to vote/plan to vote before asking anything else.
So, instead of total adults you want to look at adults that are registered to vote and have landline phones. That's a significantly smaller number, I'd wager.
All salient points. But too much work for a single Facebook post to try to account for even some of those factors.
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Paul Watson wrote: Assuming the polls are completely independent events, you would multiply the chance by the number of events, as you did. This isn't quite right. For example, if you roll 6 d6's, are you guaranteed to roll a 1? In fact, you could roll 30 d6s and still not roll a 1, if you're really luck --- or you could roll 30 of them.
To calculate the probability correctly, you actually multiply the chance of failure to represent the chances of multiple failures.
For example, the chance of rolling a 6 is 1/6. The chance of rolling double sixes is 1/6*1/6, or 1/36.
The chance of rolling not-a-6 is 5/6. The chance of rolling no sixes in two dice is 5/6*5/6 or 25/36. The chance of rolling no sixes in three dice is 5/6*5/6*5/6 or 125/216, roughly 50/50.
The chance of being selected in one poll is (by assumption) 1 in 255,000 or 1/255000. The chance of NOT being selected is therefore 254900/255000. The chance of not being selected in X polls is thus (254900/255000) raised to the power X.
Having said that, when you're dealing with probabilities this small, 1/255000 times X is not a bad approximation. And it will keep you from "going completely insane" "for a quick argument," as Paul Watson put it.
Orfamay Quest wrote:
This isn't quite right. For example, if you roll 6 d6's, are you guaranteed to roll a 1? In fact, you could roll 30 d6s and still not roll a 1, if you're really luck --- or you could roll 30 of them.
To calculate the probability correctly, you actually multiply the chance of failure to represent the chances of multiple failures.
For example, the chance of rolling a 6 is 1/6. The chance of rolling double sixes is 1/6*1/6, or 1/36.
The chance of rolling not-a-6 is 5/6. The chance of rolling no sixes in two dice is 5/6*5/6 or 25/36. The chance of rolling no sixes in three dice is 5/6*5/6*5/6 or 125/216, roughly 50/50.
The chance of being selected in one poll is (by assumption) 1 in 255,000 or 1/255000. The chance of NOT being selected is therefore 254900/255000. The chance of not being selected in X polls is thus (254900/255000) raised to the power X.
Having said that, when you're dealing with probabilities this small, 1/255000 times X is not a bad approximation. And it will keep you from "going completely insane" "for a quick argument," as Paul Watson put it.
Cool, thanks for the rundown. I really like stats, love how counter-intuitive it can be. The Monty Hall problem is still somehow mindblowing to me.
If anyone wants to read a short, fairly entertaining Cracked.com article on the trials and tribulations of telephone pollsters, point thine browser this way. Assuming the author is representative of the field as a whole, it seems to me that the classic methodology of polling is on a fast track towards obsolescence. Mostly for the reasons raised by some of the posters here.
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