SAT confusion

• Testing
I wasn't sure where to post this, so I am sorry if this is the wrong section.

A lot of professional SAT prep books and study guides suggest that if you have no idea of what the answer to a question may be you should not put an answer to that question. But, this doesn't make sense.

The reason is obvious. If there are 5 answers to a question and you only get marked off 1/4 of a point for a wrong answer, then why not just answer every question. By probability you would get 1 out of 5 questions correct. This means you would get marked off 1 point for every 1 point which would equal 0 points and not make any difference.

I was wondering if anyone knows why all the books and what not suggest not to answer a question if you have no idea of an answer? Why would they make a big deal by telling people to not answer a question when it would make no difference? In fact, it would waste time during the test by making people question whether or not they should answer a question...

Also, I thought I would add this in...

"To correct for random guessing, 1/4 point is subtracted for each incorrect answer. Because of this, random guessing probably won't improve your score. In fact, it could lower your score."
-The Official SAT Study Guide by CollegeBoard.

While this quote is true, it creates a very misleading and negative connotation towards random guessing for no reason.

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Something else to go along with that, I recall reading (though this open for being either verified or called out as BS) that your raw score is rounded up to an integer value, so if you miss only three questions, there's no penalty at all.

I greatly approve of guessing on the SAT. Of course, it's also been like 6 years since I took it.

While this quote is true, it creates a very misleading and negative connotation towards random guessing for no reason.

Maybe because they actually want people to know the information, versus how to guess..

Maybe because they actually want people to know the information, versus how to guess..

Thats not true because they are giving advice to a person for a situation in which they do not know the answer. However, like I stated above, there is no reason to not take a random guess at an answer you are unsure of.

Something else to go along with that, I recall reading (though this open for being either verified or called out as BS) that your raw score is rounded up to an integer value, so if you miss only three questions, there's no penalty at all.

I greatly approve of guessing on the SAT. Of course, it's also been like 6 years since I took it.

That is true; the scores are rounded up to the nearest integer. I did not even take that into account, but that is even more reason to guess at questions you are completely unsure of rather then leave them blank. Guessing at 2 questions and getting them wrong would be the same as leaving 2 questions blank, assuming that you missed both questions. However, by guessing at 2 questions you would be giving yourself a 40% chance of getting one of those right.

For the test taker, it may be advantageous to guess, but if the college board wants the SAT to test merit, deviations from the "true" score (student answers only the questions he or she knows or has a very good idea of) due to random guessing would be undesirable, despite the -1/4 point correction. That's just my $0.02. For the test taker, it may be advantageous to guess, but if the college board wants the SAT to test merit, deviations from the "true" score (student answers only the questions he or she knows or has a very good idea of) due to random guessing would be undesirable, despite the -1/4 point correction. That's just my$0.02.

I understand where you are coming from, but I am a little confused. You say that guessing would be advantageous and could inflate the scores which would cause deviations from the "true" score. This is not so. Guessing or leaving a question blank would yield identical scores as I showed in my first post. Guessing is not advantageous nor does it hurt your score like many books seem to suggest.

On the average, you would only get a raw score of 0 if you randomly guess on 5 questions. The chances that a student will randomly guess on a multiple of 5 questions is low. Of course, analysis is complicated by the rounding scheme, and I'm too tired to meditate on that right now .

Guessing may not necessarily inflate scores on the average, but I don't see how it might not inflate scores for an individual. For someone extremely unlucky, it also could bring down their score. Random guessing makes the SAT less effective for testing merit for the individual, although I really haven't completely thought about how the scores would change from the rounding scheme, etc.

As for books not affiliated with College Board that still advocate not guessing, who knows? Maybe it really is advantageous to not guess (proof needed). Maybe they are just jumping on the bandwagon.

Consider for a moment that the rounding scheme is inexistent.
You can not argue the fact that the score of a test with questions unanswered versus the score of the same test with random guesses made in place of the unanswered questions would be identical (on average).

You said above that someone extremely unlucky would have a lower score. Whilst that is true, you can not consider those things when considering probability because the opposite would hold of someone extremely lucky. You also stated that you would have to guess on a multiple of 5 which is not true; that would not make a difference as far as probability is concerned.

You are correct when you say that the rounding schemes would make things more complicated and to be honest I had not even thought of that. But, taking the rounding scheme into account would only advocate guessing instead of leaving it blank.

Remember that guessing *is* advocated, but only if you can eliminate at least one answer. I think the reasoning is this:

-if you can eliminate no answers, as previously mentioned, the guessing penalty is set to average out to no benefit to guessing

-if you can eliminate at least one answer, then the odds tip in the guesser's favour

Telling students to guess only in the latter case (and, I might add, guess *randomly* once you've eliminated choices) is a strategy that, in theory, has a chance of raising their scores. Why guess in situations when guessing is expected to give you *no* advantage when you could simply guess in situations where you *do* have an advantage?

It would seem to be a waste to tell students to guess if we expect, on average, no benefit to doing so, which is the case if they can't eliminate any answers.

And, for what it's worth, whenever I've given students practice tests and they haven't known about the guessing penalty (I used to do a lot of intro seminars, and in Canada a lot of students don't know much about the SAT at all), their scores tend to be lower because of guessing. If I told them to go back and leave blank answers for the ones they had no idea about, they usually do end up with a slightly higher score.

Just a bit of personal experience.

Just to prove that the plural of anecdote is not data, I've also tutored students in SAT prep and have found that if I have them leave blank everything they are unsure of, then do a second pass of guesses, in general they make enough correct guesses to offset the penalty of the incorrect ones (and incorrect ones they thought they knew!)

Just to prove that the plural of anecdote is not data

Yup! :D

But I'm curious, do you differentiate between guessing when you can eliminate answers and guessing even when you are unable to do so?

Ah, very good point! I should have been more specific; I tell them to guess if they can eliminate even one - the second pass is for the ones that they have no intuition whatsoever.

It would seem to be a waste to tell students to guess if we expect, on average, no benefit to doing so, which is the case if they can't eliminate any answers.

And, for what it's worth, whenever I've given students practice tests and they haven't known about the guessing penalty (I used to do a lot of intro seminars, and in Canada a lot of students don't know much about the SAT at all), their scores tend to be lower because of guessing. If I told them to go back and leave blank answers for the ones they had no idea about, they usually do end up with a slightly higher score.

Just a bit of personal experience.

If it is a waste to tell students to guess if we expect, on average, no benefit of doing so then surely it is a waste to tell students not to guess if we expect, on average no benefit of doing so.

I don't see how the scores would be lower on average because of guessing in place of leaving an answer blank. Perhaps it was just an unlucky coincidence, because mathematically it is the same.

Sheneron, I think I'm agreeing with you. I was only trying to determine what motives College Board may have for telling students not to guess if they cannot eliminate any answers.

Sheneron, I think I'm agreeing with you. I was only trying to determine what motives College Board may have for telling students not to guess if they cannot eliminate any answers.

Yeah that is the part I am unsure of as well. I just can't figure out why they would make a point of telling people that. I hear it from alot of sources, and it has no mathematical truth.

In fact I feel as if it would be better to tell people to always put an answer no matter what. Most of the time people should be able to narrow it down at least a little, in which case, it would be beneficial to guess. Doing this would also cut down the time people spend deciding whether they should answer a problem and risk losing a fraction of a point.

I don't see how the scores would be lower on average because of guessing in place of leaving an answer blank. Perhaps it was just an unlucky coincidence, because mathematically it is the same.

Do you think it matters that, *in theory,* you'd need to guess at 5 questions in order to practically expect the zero-sum game?

Perhaps it's the difference between EXPECTING to get 2.8 questions correct if you randomly guess at 14 of them, and the fact that on any one test, you can only get a finite number of correct answers . . . and this number on any one test may very well be 2, and you'll lose a whole raw point. Of course, it may also be 3, which gives you your +.25 advantage.

Certainly using P ( x out of 14 correct) = C(12,x) * (.2)^x * (.8)^ (14-x) separately for the just a few integer values of x (ie the number of correct guesses in the neighbourhood of 2.8, the calculated expected value, one might reasonably expect to get out of 14) will give you a smaller expected advantage than the the theoretical expected value (since, of course, you're ignoring the slight chances that you may in fact guess many or all of them correctly).

But, if we think about any one typical student at any one test sitting, perhaps it's illustrative to compute the expected value of correct questions (in this case 2.8 out of 14), then determine an expected value based on getting anywhere from say 0 to 6 questions correct and see whether this result alone is close enough to the zero-sum game to say that guessing shouldn't hurt.

Maybe in finite cases, the advantage gained by random guessing might be a little less for individual test score scenarios than in our theoretical model.

Just wondering aloud.

As for motives:

1. One possibility could be related to the fact that the CB assigns the difficulty of questions based on how many students answer it correctly vs. incorrectly. Perhaps in their algorithm, they assign a question as being most difficult if it's left blank (therefore, they can conclude that the student has NO clue because they've been instructed not to guess in that situation) and less difficult if it was attempted (so, the student had some idea of either what a reasonable answer might look like, or had an idea of how to work through the question, albeit indirectly.) Maybe random guessing messes up this process for them somehow.

2. I think it's an easy enough call to say that the CB wants to ascribe meaning to their results, something that is much harder to do when advocating a "guess randomly" strategy. Yes, they have the correction factor worked into their scoring so that people who do guess won't throw the results off too much one way or the other. But, given that this is such a high stakes test, I think it opens themselves up to a lot more criticism if they advocate a total random guessing strategy. At least by saying "guess if you can eliminate" it gives the impression that students who can make *some* sense of the question will have an advantage over students who can make *no* sense of the question, which is what test-taking students and their parents want to hear. I just think, from a PR standpoint, it's a lot more palatable.

The reason is obvious. If there are 5 answers to a question and you only get marked off 1/4 of a point for a wrong answer, then why not just answer every question. By probability you would get 1 out of 5 questions correct. This means you would get marked off 1 point for every 1 point which would equal 0 points and not make any difference.

Your "obvious" reasoning is wrong. There is an implicit assumption made when you reasoned that that the average score would be zero by random guessing-- and that is that the number of questions is infinite (you're thinking huh? so let me tell me the 1 in 5 correct is an average only true as the probabilities for the other choices goes to zero, which only happens when the number of questions becomes infinite)

The number of questions is finite, then your average sub-score from the questions you guessed on will actually be negative. Intelligent guessing is the strategy that you should use. If you can eliminate down to three choices, then even for finite number of questions you will be more than 90% likely to have a positive average score.

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I think you guys are over-analyzing.

Many years ago, there was no penalty for wrong answers, and students were encouraged to guess, as there was an advantage to guessing. This was changed, and the instructions now reflect that there is no advantage.

Think of it this way: If you can't eliminate any answer choices, you have a 20% chance of getting the question right by guessing, and if you don't, you don't earn any points and instead lose 25% of that question.

If you can eliminate one answer, you have a 25% chance of getting it right, 33.3% for eliminating two, and 50% for eliminating three. You should compare the probabilities with the points that will be deducted should you get it wrong and decide for yourself how often you will guess.

Your "obvious" reasoning is wrong. There is an implicit assumption made when you reasoned that that the average score would be zero by random guessing-- and that is that the number of questions is infinite (you're thinking huh? so let me tell me the 1 in 5 correct is an average only true as the probabilities for the other choices goes to zero, which only happens when the number of questions becomes infinite)

Perhaps I was wrong in thinking the way I did, but I never assumed the questions were infinite. There are 170 total multiple choice questions on the test. If you guess randomly on every question would the average score not be 0 (the same as if you left every question blank)? Also you are not taking into account the rounding scheme. In the case I just mentioned it would be beneficial (although very minute) to randomly guess because they round up to the nearest integer.

After taking a couple of practice tests, I noticed its most efficient if you skip 1, 5, or 9 questions on each section. Because, if you get 2 wrong, you'd get .5 taken off, and since the score is rounded, it would be the same as having 1 point taken off (getting 4 wrong).

I don't see anything wrong with the current instructions. They clearly say random guessing "could"--not will--lower your score. It's up to the test taker to decide if they're willing to take a chance that their score will be brought down in the hopes that it might be brought up. It does emphasize the negative aspect, but I feel this is better than getting people's hopes up by saying "in fact, it could result in a higher score." You don't want students to randomly guess, after all. Two minor reasons, but reasons enough for me.

If you truly believe that the results will average out to 0 (something that simply, as stated, will not happen in many cases), then why should students guess? It's just a waste of time anyway. Given two equally ineffective actions, I would suggest the easier one. But the fact is that many students that guess will suffer from a lower score for guessing. Is it worth the equal chance of getting a higher score? I guess that's up to the student to decide. I assume more students would rather play it safe than hope for a higher score. I'd imagine that if all test-prep companies say this, they find students largely feel that way.

If I ran a test-prep company I would simplify the situation the same way the Princeton Review does and tell students to guess if they can narrow it down. No need to get into a debate about two ineffective actions--it's better for those books to focus on the effective actions!