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Most common answers on the SAT

PWNtheSATPWNtheSAT Posts: 232Registered User Junior Member
edited October 2013 in SAT Preparation
So I saw someone on Yahoo! Answers suggesting that C was the most common answer choice on the SAT. I hear people say this all the time and it drives me batty, mostly because I'm afraid students will actually consider such misinformation actionable and fill in a bunch of C's. You deserve what you get when you do that, I know, but still I worry.

Anyway, I decided to spend some time this morning counting up all the choices in the Blue Book (leaving out Grid-Ins, obviously) to prove a point, and ended up proving the point much less firmly than I had hoped to. There's actually a fair amount of variability over what seems to me to be a big enough sample to mitigate most of the noise.

Here's a link to the data.
https://spreadsheets.google.com/pub?hl=en&hl=en&key=0Agar2-EatDDSdGZPeUI5UE9mSEtEcnBrWVRzbnpmSkE&output=html

I don't really expect any of this to be useful information, but I did want to solicit your opinions on this, since this is a community of people who seem to think about the SAT as much as I do.

Also, I know there are some people on this board who are at university and still poke around here. I'm interested in hearing from someone who's taken a stats class more recently than me about statistical significance of, say, the infrequency of A. So, you know, if you wanna nerd it up with me, I'm up for that. PM me.
Post edited by PWNtheSAT on
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Replies to: Most common answers on the SAT

  • EAsoccer10EAsoccer10 Posts: 71Registered User Junior Member
    lol do you have any hobbies, sports, or friends to entertain you? sorry but this is kind of extreme hahahaha ;)
  • PWNtheSATPWNtheSAT Posts: 232Registered User Junior Member
    A fair question, to be sure. I get paid pretty well to be very good at the SAT, though. This is work, but I also kinda enjoy it.
  • EAsoccer10EAsoccer10 Posts: 71Registered User Junior Member
    ya i was going to say this is kind of interesting though :)
  • fignewtonfignewton Posts: 1,412Registered User Senior Member
    A little while ago, I did a study of this question using 13 past (QAS) exams (math only).

    The results are consistent with a uniform random distribution of answers, i.e., p(A) = p(B) = p(C) = p(D) = p(E) = 0.2.

    For a total of 572 multiple choice questions, here were the letter frequency numbers and corresponding z-scores:

    A 108 -0.67
    B 116 0.17
    C 119 0.48
    D 120 0.59
    E 109 -0.56

    (expected value for each: 114 to 115).

    You would need a z-score of more than 1.96 or less than -1.96 to say with a decent level of confidence that these letter frequencies are NOT uniformly random.
  • BillyMcBillyMc Posts: 7,753. Senior Member
    Actually, little do most people know, each SAT has a secret code built into the answers. If you get the first 5-6 right in the section, it should only take you 10-15 minutes to crack the rest of the code. In June 2007, they used the Fibonacci Sequence (alphabetical with the usual encoding exclusions, of course) for most of the Writing section, but it was too obvious; that's why so many people got 760-800 on the June 2007 Writing. But there is suspicion that people knew ahead of time because a North Korean stole the code.

    I was able to crack my last Reading one (ha, and who says Tuvaluan history never came in handy), but screwed up the code on one of the math sections. For the essay, I went with the ol' binary bypass, but the computer picked up the 874th 0 as an O, so I didn't get a 12.
  • fignewtonfignewton Posts: 1,412Registered User Senior Member
    Wait, I thought the code was the digits of pi (mod 5)!
  • BillyMcBillyMc Posts: 7,753. Senior Member
    Wait, I thought the code was the digits of pi (mod 5)!
    Nah, they tried that November 2008, but just once; nearly as obvious as the whole Fibonacci fiasco.
  • buffalowizardbuffalowizard Posts: 337Registered User Member
    I don't know stats, but I just had some fun at random.org asking for sets of 1600 integers from 1-5 (link: RANDOM.ORG - Integer Generator)

    Here were my results:

    1st Run:
    1: 326
    2: 311
    3: 336
    4: 305
    5: 322

    2nd Run:
    1: 315
    2: 338
    3: 309
    4: 314
    5: 324

    3rd Run:
    1: 294
    2: 323
    3: 322
    4: 328
    5: 333

    4th Run:
    1: 329
    2: 321
    3: 360
    4: 291
    5: 299

    The first three runs were fairly even, but the fourth was even more lopsided than the Blue Book analysis, and it was generated by completely random atmospheric noise!
  • BillyMcBillyMc Posts: 7,753. Senior Member
    Atmospheric noise isn't random; the aliens are trying to contact us.

    Unless... College Board... is... Oh my God.



    Run.
  • PWNtheSATPWNtheSAT Posts: 232Registered User Junior Member
    I guess I deserve the ribbing for going so aggressively public with my nerdery this morning. Thanks, though, fignewton, for admitting that you've also done something similar before.

    I wasn't expecting any surprising results, but the difference of 50 between A and D raised my eyebrow a tad. After having a look at buffalowizard's post...not as surprising as I thought. :)

    Thanks guys!
  • pckellerpckeller Posts: 809Registered User Member
    Nothing too nerdy about this at all! Some related nerdery: pick up any section, look at the answers and you will find things like: 12 in a row with no 'd', only 2 e's in an entire section...other similar weird stretches -- and these are all completely normal. People just don't expect weird sequences as often as they come up.

    I forget where I read this, but it seems related: ask half the students in a class to flip a coin 100 times and record the results, while the other half just pretends to flip coins, but actually just makes up a random string of 100 h's or t's. Then examine the data. You can usually tell who did the experiment vs who faked it. The fake data doesn not have as many weird strings: runs of lots of h's in a row say. For example, 5 in a row seems unlikely, but in a random set of 100, it is actually more likely than not to have at least one such stretch.

    Of course, that leads to a probability question, too hard for the sat: you flip a coin 100 times. What is probability that you do not get at least one stretch of 6 h's or 6 t's in a row?
  • mrprez29mrprez29 Posts: 1Registered User New Member
    Is this a joke?
  • MITer94MITer94 Posts: 1,104Registered User Senior Member
    Fibonacci numbers mod 5 would be interesting :) except that every fifth Fibonacci number is 0 mod 5.

    This reminds me of the 2012 AMC12A, where the answers to #22 through #25 were all C.
  • QuantMechQuantMech Posts: 5,679Registered User Senior Member
    PWNtheSAT: Great analysis--I think it's quite interesting to look at the data, and it's perfectly valid as a hobby.

    If I were an evil SAT test designer, I'd make the answers to the Level 5 questions more likely to be A or E than anything else--the theory being that those who were just guessing would go with B, C, or D. Bwa ha ha! (Oops, kind of a give-away)
  • malkovichiomalkovichio Posts: 39Registered User Junior Member
    Hey, you're that guy who's the reason I did so well on all the sections! YOU ROCK!
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