AskBwog: What’s the NROTC Survey Margin of Error?

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As the NROTC results are being discussed and debated, it’s likely that the term margin of error is going to get thrown around. So, what is the margin of error? According to Jon Hill, Bwog’s Nate Silver Correspondent of Mathematical Wizardry, there is none. Here’s why:

Votes counted: 2,971

Undergraduate enrollment (2007 [2008 figure was unavailable]): 7,411

At a 95 percent confidence level:

= [1.96 * ((0.5)/sqrt(2971))] = 1.80 percentage points

With finite population correction

= sqrt[(7411-2971)/(7411-1)] * 1.80 = 1.39 percentage points

So the figure +/- 1.39 percentage points would be the MOE, and that would take in the 1.32 percentage point difference between the YES and NO votes.

However, because this survey is not a random sampling by any means, there can be no true margin of error calculated. You can’t extrapolate these results to the entire undergraduate population. As a result, any criticism based on MOE in this case is a statistical canard, especially since there are plenty of other legitimate flaws in the survey results to point to.

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  1. ...


    Even if the results were legitimate, I doubt it will have any effect on university policy.

    Student councils should be focussing their attention on issues on which they can actually effect change and would improve student life. This NROTC debacle is nothing more than a political circus that gives the appearance of action.

  2. jesus  

    This is not a sampling, and hence the idea of 'margin of error' doesn't apply. You're not estimating the outcome of the vote, this IS the actual outcome of the vote.
    Stat noobs.

    • agreed!  

      determining a margin of error is erroneous in this case.

    • I think  

      that was his point... "any criticism based on MOE in this case is a statistical canard"

      • nope  

        His point was that because the sampling is not random (ie only the people really interested int he issue are voting), there's a bias in the results so MOE is pointless.

        The fact of the matter is that this is not a sampling of any kind, it is the actual population distribution. When CNN or Bwog conducts an exit poll to estimate actual votes that will be cast, that's where MOE comes in - what is the wiggle room in extrapolating results to the actual scenario? But this IS the actual scenario. So this whole post is wrong.

        • yeah  

          That's correct - we don't need to worry about margin of error, because the term 'margin of error' implies that there are individuals who were left out of the sample. In other words, we sampled 100% of the population, and there was around a 57% nonresponse rate. Of the 43% who voted, 50.56% voted no and 49.24% voted yes.

          In other words, 'margin of error' doesn't apply because it only applies to samples. There IS no sample here (or the sample = population) - so it is wrong to say that the margin of error cannot be calculated. It doesn't exist!

  3. err  

    the difference in percentage between the two outcomes was only 1.32, falling within the error. Additionally the sample size was only 2971, meaning the error should be much larger anyways.

  4. shame  

    Shame on you, bwog, reporting pseudo-statistics as fact! Lots of people have already commented explaining why this entire post is wrong, so I won't waste my time, but seriously. I expect better - and at least a redaction.

  5. DHI  

    What is the margin of error in a 5-4 Supreme Court decision?

  6. Anonymous  

    The calculations that are up there are for a scenario that doesn't exist--that a random sample of 2971 people were polled and we expect 7411 people to vote in the actual survey. Whereas in reality, 2971 people just voted.

    Along with everyone else, I'm confused as to why you put any calculations in this post at all. The right answer is "there is no margin of error."

  7. Academic Advisor

    BWOG, based on your recent collection of posts, it appears that you are far more talented in the natural sciences (ornithology, nutrition, biology) than mathematics and statistics. I would recommend pursuing a course of study in one of the former fields, potentially in conjunction with pre-med. A specialty in ob/gyn does appear quite promising.

  8. Bwog...

    The calculations done in this poll are both meaningless and useless. Here is the only relevant sentence to this story, which for some reason the reader must get to the jump to read:

    "because this survey is not a random sampling by any means, there can be no true margin of error calculated."

    This shouldn't be in the last paragraph of the story. Perhaps you should have gone with a headline with the phrase "NO Margin of Error" as opposed to one that leaves this possibility of a margin of error open.

  9. pfsh  

    I *totally* figured this out on the back of an envelope. Thanks, David!

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