http://en.wikipedia.org/wiki/Simpson's_paradox

It’s not the best explanation I’ve seen and the examples are a bit simplistic, but it’s free, and my statistics textbook isn’t. :-)

Conjecturally, however, there’s likely to be random variation even within a census when the response is binary on an issue with fine gradations of opinion. Consider typical 1-5 survey questions along the lines of Strongly Support, Support, Neutral, Oppose, Strongly Oppose, etc. Presuming some fraction of the population is Neutral but might vote anyway (out of say, sense of democratic duty or peer pressure), particularly since votes could be changed many times (encouraging the ambivalent to vote!), I think it quite probable there would be significant variation in popular opinion (potentially more than 39 votes) every time this identical survey were to be put to the campus.

…but, given that Bwog still hasn’t mastered the concept of a sample versus a population, I think advanced concepts like Simpson’s paradox is beyond them

Given that the NROTC initiative came out of SEAS, and reciprocally, NROTC is most interested in SEAS engineers at Columbia, it’s conceivable NROTC would benefit SEAS students disproportionately at Columbia. So, we shouldn’t we at least know what SEAS students think about NROTC return?

Especially, if the senators were going to view their school’s vote as a recommendation, if not an obligation, it doesn’t make sense that we only know the aggregate total for CC, SEAS and GS. With only a 39 vote spread among 3 colleges, it’s conceivable 2 of the 3 college student bodies actually voted in favor of NROTC, which would change the entire viewing dynamic of the results.

Statistically, nonresponse is considered part of the sampled population. The portion of the 7441 who did not respond were still sampled because they were given the option to express an opinion, and they abstained from voting. This is different from contacting 2965 out of those 7441 and polling this smaller sample population to figure out the opinions of the 7441 students as a whole. Their lack of response must be considered part of the experimental results, and any attempt to ‘correct’ the results for their opinions would be counting theirs twice.

Think of it this way: you have a bag of M&Ms, and you want to figure out how many red ones there are versus how many blue ones. One crude method would be to take a random sample of 43% of them and extrapolate the proportions to the rest of the bag. Every single one is red or blue, in this case, because every single on of those 43% of people who answered said ‘yes’ or ‘no’ (ignore the six idiots who didn’t respond – it’s insignificantly small).

Now, suppose you count every single candy in the bag and find that 21.1% are red, 21.5% are blue, and the rest are yellow. You are only trying to figure out how many reds there are in proportion to blue in this experiment. Thus, the 57% of M&Ms that are neither red nor blue make no difference. You cannot extrapolate the 21.1%/21.5% ratio to the ‘rest of the candies’ in the bag, because you already know that they are neither red nor blue (or, in the NROTC case, not opinionated enough to vote).

There is no margin of error for the candies in the bag, because every single piece of candy has been counted.

I understand that we’re talking about an online poll and not M&Ms in a bag, but sometimes, it’s easiest to see statistical principles when you make them physical like this.

You can’t have a margin of error if the sample size is the same as the population size.

If this is truly the way that students feel, then a legitimate vote will have the same results.

I support the outcome, but not if it was dertermined in a false manner.

Both sides presented their arguments to me numerous times.

I debated both sides and brought up their flaws.

Both sides failed to convince me that they were correct.

Hence I did not vote. I see no apathy in this progression.

The only need for the survey was to help the senators vote. This isn’t a binary win/lose issue.

Now, pending the release of a by-school breakdown without which this survey really is meaningless and the councils really would have screwed up:
1 CC senator will have to vote Yes, 1 CC senator will have to vote no. The third may choose her position.
SEAS senators may choose abstain because the graduate SEAS students who they also represent were not counted despite demands to do. Otherwise 1 will vote No and the other will have a choice in votes between Yes, No or abstain.

The GS Senator must vote no.

UPDATE: BC senator must vote No after a 62% vote against.

All but BC is contingent on the by-school breakdowns being exactly what this poll showed.

However, if GS had a margin of 70-30 the GS Senator should vote Yes but we’ll see. The same applies to local populations in CC and SEAS. Only CC, SEAS, and BC senators have pledged to represent their constituency (again this is a slight issue for the SEAS guys but we’ll work it out soon with the EGSC).