Skip to comments.Balls and Urns: Iowahawk explains "margin of error"
Posted on 10/27/2008 8:22:48 PM PDT by xjcsa
[excerpting the end of the article; click below for the whole thing]
This is, for all intents and purposes, how political pollsters compute the ubiquitous "margin of error," which has everything to do (and only to do) with pure mathematical sampling error. If you look at the formula above and round it just a smidge, you get a simple rule of thumb for margin of error:
Margin of Error = 1 / sqrt(n)
So if the sample size is 400, the margin of error is 1/20 = 5%; if the sample size is 625 the margin of error is 1/25 = 4%; if the sample size is 1000, it's about 3%.
Works pretty well if you're interested in hypothetical colored balls in hypothetical giant urns, or growth of plants in a controlled experiment, or defects in a batch of factory products. It may even work well if you're interested in blind cola taste tests. But what if the thing you are studying doesn't quite fit the balls & urns template?
* What if 40% of the balls have personally chosen to live in an urn that you legally can't stick your hand into?
* What if 50% of the balls who live in the legal urn explicitly refuse to let you select them?
* What if the balls inside the urn are constantly interacting and talking and arguing with each other, and can decide to change their color on a whim?
* What if you have to rely on the balls to report their own color, and some unknown number are probably lying to you?
* What if you've been hired to count balls by a company who has endorsed blue as their favorite color?
* What if you have outsourced the urn-ball counting to part-time temp balls, most of whom happen to be blue?
* What if the balls inside the urn are listening to you counting out there, and it affects whether they want to be counted, and/or which color they want to be?
If one or more of the above statements are true, then the formula for margin of error simplifies to Margin of Error = Who the hell knows
Because, in this case, so-called scientific "sampling error" is meaningless, because it is utterly overwhelmed by non-sampling error. Under these circumstances "margin of error" is a numeric fiction masquerading as a pseudo-scientific fact, and if a poll reports it -- even if collected "scientifically" -- the pollster is guilty of aggravated bulls**t in the first degree.
The moral of this midterm for all would-be pollsters: if you are really interested in how many of us red and blue balls there are in this great big urn, sit back and relax until Tuesday, and let us show our true colors.
Until then, fondle your own balls.
Very good. Thanks for posting it.
Interesting point - what if the “fired” acorn workers are now doing the phone polling?
The moral of the story is:
Don’t listen to the media or the polls.
In the immortal words of Yogi Berra:
It gets late early around here...but it ain’t over til it’s over!
VOTE. No matter what you VOTE.
I answered the whole thing as a rabid socialist.
The chances of a given state falling outside the MOE = 1/20 =.05. The calculation for the probability that 16 out of 57 states would fall outside the MOE is a simple one which uses the BINOMIAL DISTRIBUTION FUNCTION:
The Probability (P) that at least 16 out of 57 states would deviate beyond the exit poll MOE is:
P = 1-BINOMDIST(16,57,0.05,TRUE)
This returns P= 0.0000000218559% or 1 out of 4,575,415,347!
Therefore, McCain will win - so there!
Brilliantly said! This is precisely why I have been increasingly frustrated with the endless panicked posting and re-posting of the commercial political poll results on FR as they are incomplete without the MoE, and utterly meaningless and irrelevant because of the non-gaussian sample abberations summarized in the bullet points at the end of this piece.
Forget about polls. Ignore them, realize they are pure propaganda that may as well be based on Tarot cards or the reading of entrails! Just Get Out the Vote!
I heart Iowahawk.
Operation Chaos, Phase III.
I think there is an error in the sampling within the population too that isn’t accounted for.
Since the sampling of any sub-group would introduce the same amount of error within the sub-group.
The error rate for the entire poll is only accurate if you assume the sampling rates of the sub-groups are correct.
Blessings be upon thee!
And, if you be so lucky, don't forget to do the same with any exit pollsters.
Bumpity-bump for the night crew.
An mass organized effort to tell exit pollsters we voted for Nader would give Team Obama the freakout tomorrow evening.
It’s too late to do that, but the thought of it makes me giggle.