statistical guess scenario

[kyriacos01]

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Alright, I have tried to google and sdn search this question, but to no avail; so here is my hypothetical...

While taking the MCAT, or any standardized test in which blank answers are considered incorrect; i.e., there is no inherent penalty for guessing an answer, the exam proctor informs the test taker that there is approximately 1 minute remaining in section 'X'.

The test taker has a substantial number of questions yet to complete, let's say 20 or more. Since there is no reasonable manner for him/her to read each question, the test taker decides that his/her best course of action is to quickly fill in the remaining blanks with a pure guess.

Which of the following options produces the highest statistical probability of correct answers?

1. Randomly choose an independent answer for each question.
2. Choose only one answer and fill it in for each question.
3. Use 4 or 5 consecutive answers from each possibility and block/group the questions.

Thanks,
-ky

 

[gluon999]

Since each random bubble is a mutually independent event of the previous or succeeding bubble, all combinations of answers have equaly probabilities of being right/wrong.

So I wouldn't worry too much about the 'pattern' of your bubbles, since one event doesn't affect another one.

 

[stoleyerscrubz]

if you are guessing and there are 4 answers choices your chances of getting one answer correct is 25% no matter what method you use. You only can make your odds better if you can eliminate some of the choices.

Personally I just pick C if I have absolutely no clue on the 4 choices, but you should be rarely doing that if at all. Narrow it down some how. See if there are opposite answer choices. or choices that don't address the question etc.

 

[SailCrazy]

While statistically correct for a completely random event, I don't know if the "they're all the same" answer applies here. Are all answer choices really equally likely?

Is there a completely even ratio of A:B:C😀 answers? What we need is to have someone (probably in desperate need of new MCAT procrastination techniques) to tabulate the number of A's B's C's & D's on all of the AAMC tests (or at least test 7.) Then we'll know if one shows up more frequently than another.

If so, that's your choice. If not, then it doesn't matter.

Oh yeah - you could also subgroup by quesiton type. Do the quesions with I, II, III, I & II, II & III, I II & III as answer choices have a different answer distribution or the same?

So... you have your task. Let me know what you find out...!

 

[firebird69guy]

Speaking of statistics, I have a question:

About how many people will be taking MY exact test? Just curious.. I guess you'd need to know how many tests will be used, how many test takers, etc. The latter I'm sure we know, but I wonder how many versions are actually used.

Anyone have any insight?

 

[Tinker Creek]

Ok, I counted aamc 7 (yes, I have no life), here it is:
A - 43
B - 53
C - 60
D - 58

Having typed this, I agree with gluon99, and stoleyscrubs about narrowing it down.

 

[SailCrazy]

Ok, I counted aamc 7 (yes, I have no life), here it is:
A - 43
B - 53
C - 60
D - 58

Having typed this, I agree with gluon99, and stoleyscrubs about narrowing it down.

Way to do! I knew someone would come through for us! 😀

Definitely narrowing down any bad choices is a must (if you have time), but when in doubt, I'll go for C. If I've eliminated only C, then I'd guess D & definitely Not A. It represents only 20% of the answers!

 

[gluon999]

Ok, I counted aamc 7 (yes, I have no life), here it is:
A - 43
B - 53
C - 60
D - 58

Having typed this, I agree with gluon99, and stoleyscrubs about narrowing it down.

so there is some truth to the saying, 'when in doubt, pick C'... who woulda known?

 

[Reimat]

I've heard that statistically B and C are more common answers on all standardized tests, and therefore you should pick one and stick with it to maximize points.

That said, if you have a minute left and 20 Q's unanswered on any section, you're screwed regardless

 

[kyriacos01]

...if you have a minute left and 20 Q's unanswered on any section, you're screwed regardless.

lol; agreed.



Thank you to everyone for their input. Big ups to Tinker for tabulating the results; I appreciate your efforts.

Obviously, one should try to eliminate as many incorrect answers as possible; however, the hypothetical I presented did not allow for this option.

This hypothetical came from a debate that a co-worker and I were having. We were assuming a test taking scenario in which there was four possible answers, very little time left, a number of questions yet unanswered, and no possibility of answer elimination. If one had to guess at those questions which remained, how could he/she maximize the probability of guessing the correct answer?

We debated the following:
He: each section will yield an even random distribution of each answer; i.e., 25%. Since there is an even distribution, each question should be considered as a separate event and will have no effect on events prior or future; therefore, one's best option is to randomly select a, b, c, or d. The best one can hope for is a 25% chance of choosing the correct answer.

Me: each section will yield a random distribution of each answer; however, the percentage distribution will not be even; i.e., outliers (a&d) will be closer to 48% with b&c comprising 52%. Since I do not view the events as mutually exclusive, selecting the b or c option increases the probability of a correct by approximately 4%; therefore, one's best option is to select one answer, b or c, and use it for each remaining question.

Based upon Tinker's data, c seems to be the best option with d a close second. So, I guess that if I find myself royally screwed c, c, c, c, c...

Thanks again for the input.

All the best,
-ky

 

[stoleyerscrubz]

🙄 So you are basing your thesis on one exam?

 

[gluon999]

🙄 So you are basing your thesis on one exam?

so much for the scientific method

 

[LukeWhite]

Keep in mind that the AAMC released tests are composites of prior tests. Thus, while the answer breakdown is interesting, it's not a valid reflection of actual MCAT patterns.

Overall, the answer choices tend to average out to even frequencies across all tests. Your best bet if running out of time is to choose one answer and stick wtih it; the time you save in bubble filling would allow you to eliminate at least a few obviously wrong answers in some. Even this very minor improvement in your odds is more than the zero improvement you'll get by trying to scatter your guesses.

Of course, if you run out of time with more than a very few questions remaining, you're in some trouble anyway! Your score will be maximized by avoiding this situation at all costs...it's FAR better to have guessed on some questions earlier than than to be left with twenty guesses at the end; that scenario is so disastrous for the average score as to really not even be worth considering.