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At this moment of vindication for Nate Silver and even for less-sophisticated poll averagers,

can we shame the MSM about their "statistical tie" lies sufficiently to reduce their resort to this particularly shameless method of propping up Republican candidates?

Statisticians can refine this point (please comment or start a new diary on this), but even a layperson like me can see the following:

1. If the margin of error (MOE) is 2%, and Obama's reported lead is 2%, then the likelihood of the race being "tied" is the same as the likelihood of Obama having a lead of 4%.

2. If the MOE is dictated in large part by the size of a poll's sample (such as 1,000 respondents), and if ten similar polls are added together (with a combined total of 10,000 respondents), then [corrected to reflect input from the comments:] the MOE is substantially reduced -- although not in a linear or obviously proportionate manner.

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Comment Preferences

  •  There is the old expression (0+ / 0-)

    "Lies, damn lies, and statistics"

    When I see things like "statistical tie" and look at the numbers all too often I figure out that phrase means, "Please excuse me while I cover my ass". Yes, statistics of these sorts are inexact by their very nature. It's why you print a range and a confidence number. But it's also clear many stats are given (and reported) with the hope that lots of people won't look at the numbers and figure out what they really mean.

    Math illiteracy is a bad thing.

    Attention rich bastards, this is real important,
    I thought you might want to know
    That $5,000 suits don't hide your 5¢ souls.

    by ontheleftcoast on Wed Nov 07, 2012 at 05:49:38 PM PST

  •  Without knowing the composition of the (0+ / 0-)

    samples, just increasing the sample size does nothing to reduce the margin of error, in and by itself.

    "If you tell the truth, you'll eventually be found out." Mark Twain

    by Steven D on Wed Nov 07, 2012 at 05:54:28 PM PST

  •  you may find this useful - (1+ / 0-)
    Recommended by:
    JMcDonald
  •  when the sample size equals the "universe" (1+ / 0-)
    Recommended by:
    Karl Rover

    in this case, the actual voter count, then the margin of error is zero. That's obvious, right?

    An Obama win of 1.5% can not mean he might be ahead by 3.5% or behind by 0.5%. It means he won by 1.5%, period.

    As for the question of polling, based on samples of 400, 800, 1000 or whatever, the margin of error means that 95% of the time a similar poll will have similar results, within that margin.

  •  Don't know the answer.. (0+ / 0-)

    ...to your questions but I've read a piece by Nate that sort of explains it that way. One thing I will say...Nate had a column a few days before the election saying that the only way his projections could be wrong would be if they were ALL wrong. He explained this in depth. When the first exit polls started to come in and New Hampshire was clearly very close, like Nate's prediction, I new that his numbers were going to right and I started celebrating.

    "Good to be here, good to be anywhere." --Keith Richards

    by bradreiman on Wed Nov 07, 2012 at 06:00:37 PM PST

  •  Doubling a sample reduces MoE by ~30% (0+ / 0-)

    2x sample -> MoE * .7
    4x sample _> MoE * .49
    16x sample -> MoE * .24, so 16 polls drops the MoE by 3/4.

    Adding samples from different pollsters isn't very statistically sound, though it should work in general.

    Disclaimer: If the above comment can possibly be construed as snark, it probably is.

    by grubber on Wed Nov 07, 2012 at 06:03:18 PM PST

  •  You can't linearize in this instance. (0+ / 0-)

    MOE is not a linear process.

  •  A calculator that addresses this question: (0+ / 0-)

    Ballot Lead Calculator

    It shows the likelihood that A is actually winning, given the sample size and the sampled percentages for A and B.

    For example, it shows that given a sample size of 1,000,
    if A has 50% and B has 49%, a mere 1% difference when the MOE is 3.1%,  then the odds of A being ahead are 62%.

    So even slight leads can be quite meaningful for making predictions.  You don't don't want to offer even odds (presumably what you would offer for a true tie) if your chances are really 38%.

  •  Thanks for links & comments on aggregated MOE (0+ / 0-)

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