Test Strategy/Argument

[WCGRider]

Two people i live with are having an argument over which of the following cases is correct. Please vote in the poll which side you agree with and explain if possible, thanks. (And they will be each typing up a paragraph from their own point of view)

Both me and my roommate agree that on the SAT, you gain 1 point for a correct answer, and minus 1/4 a point for an incorrect answer. There are 5 possible answer choices. This information is all agreed in the premise of the argument. My argument is that you should always guess on any question, because its neutral EV if you have absolutely NO IDEA, and you are going to have at least the slightest idea of at least one answer, and thus positive EV. Additionally, just from the fact that answers appear very slightly less twice in a row, you become positive ev. Not significantly at all, but even as low as 18%, and then answers very rarely go 3 in a row, and actually never 4 in a row. Even if your decision is less then a tenth of a percentage point increase in your net ev, then you should take, as basically we build our entire lives on as poker players, right?

First of all there are 5 possible answers and one wrong gives you minus .25 while one correct gives you 1 point, this by itself means you will always break even(this assuming of perfect probability). Apart from that, bias is a great part of the answering process as there is a predetermined answer and as you read a question you already make up your mind on an aspect of the question which will always affect your answer. This meaning that as one makes a choice even over a question which one has no idea about there will be an aspect of the question which will affect your answer, meaning there is a greater probability of getting an answer wrong from a question you don't even know. My whole argument is that your own mind will automatically put you as an underdog when guessing on a question. You will never gain from guessing.

[ncray]

Let's just say that having absolutely no idea is the same as randomly guessing (pick each of the 5 answers with probability 1/5). So, by randomly guessing your expected score is going to be 0. Why are you assuming that people are going to have the 'slightest idea' (probability > 1/5 of getting the correct answer)? This assumption obviously bumps us up to > 0 expected score.

This might be true for poorly designed questions, but it's very easy to come up with trick questions or more difficult questions where fewer than 1 in 5 get it correct.

[jay_shark]

If you have absolutely no clue what the right answer and there are 5 equally likely choices , then the probability you make the right guess is 1/5 .

You win 1 point one-fifth of the time . You lose 1/4 , four-fifth of the time .

1*1/5 -1/4*4/5 =0 . Neutral EV .

You don't win or lose anything from guessing .

On the other hand , you would have to be close to brain dead to consider not guessing . If you were studying for this exam , you should certainly do better than picking the right answer one fifth of the time .

[Some9]

obv #1 but

Guessing increases variance. So if you need a score X to get to the college you want and you think X is easily achievable you should not guess, whereas when you think X is pretty high you should guess. makes sense?

(also guessing takes time which is -EV compared to skipping it. )

[filsteal]

I see both sides of the argument.

And if the SAT were set up to have a lot of "trick" questions (i.e., questions where fewer than 20% of people get the right answer, because the question is deceptive in some way), the Argument 2 might very well be correct.

However, I very strongly doubt that's the case. I find it extremely unlikely that, after reading and thinking about a question, you could have less chance to get it right than if you hadn't read it in the first place and had picked an answer at random.

So I'd take argument 1.

Some9's argument about variance is a very good point. However, I don't think most people taking the SAT have a good idea of what scores are easily achievable, unless they've already taken it multiple times before.

[pokercurious]

I happen to have taught SAT test prep for several years now, so here's my $.02:

1st, I'm curious about where the 'answers never come 4 in a row' comes from, as I'm pretty sure that's not true.

Second, the argument in 'case 2' has some merit. The SAT includes an experimental section in which they test new questions on unwitting test-takers. They choose the wrong answers that were chosen the most to be the actual 'wrong' answers on the real test. They call these answers, bastardly enough, 'distractors'.

However, if you truly randomize when guessing (i.e. using a watch face etc.), most of that bias can be overcome.

That said, maximizing your score must involve actually taking the test. As in any game, knowledge is power. Knowing that math questions increase in difficulty over the course of each math section allows you spend more time worrying about accuracy and precision on the front half, where you can be more sure of your correct answers, and focusing on things like eliminating wrong answers on the back half (which makes guessing +EV if you can remove on incorrect choice).

The problem with guessing for most students is the variance issue that some0 mentioned. It's a complex game that involves an ultimate goal of getting a college to admit you. Almost everybody is going to be more risk-averse than normal, and reasonably so, as the SAT, unlike poker, isn't played out over the long run for a student - they take it at most 3 or 4 times.

So in the discrete short run, completely random guessing (having no idea whatsoever how to deal with the problem) comes into play (for the average+ student) infrequently enough that guessing in these cases is more likely to be detrimental to his/her score than 0 effect, so skipping those problems is better, also because he/she can spend more time increasing EV on problems that will yield to a bit more brainwork.

[sandman-54]

[ QUOTE ]
and actually never 4 in a row.

[/ QUOTE ]

I always assumed that the letters of an SAT answer were decided at random by the test-makers. If I'm correct, then the probability of this occuring for a randomly selected sample of 4 questions is:

1/5^3 or 1/125

There's two ways that I can think of that you would be able to know that the occurence of 4 same-letter answers in a row happens less than 1 time for every 500 questions:

1) You know or your own intuitive probability suggests that the makers of the test are more likely to want to make a last minute adjustment if there is an occurence of 4 same-letter answers in a row.

2) You have amassed (at least) thousands of questions (in their original order) and have not yet seen 4 answers in a row

I really would like to know what evidence you have that suggests this.

[PantsOnFire]

Assuming I have a decent shot at a good score, I would want to perserve that score. Thus, I would not do something like randomly guess in a 0 EV situation. I would want to limit my variance.

If I had very little hope of doing well by not studying and getting blind drunk the week before, I would take a different approach. I would quickly move over the questions until I hit one I could do. When I had done all those, I would go back and randomly finish the test and cross my fingers (we all know guys who got into college this way right?)

So I think your arguement needs to be qualified with the motivation of the person being tested. I would suggest most normal students who have a decent chance of getting a good score should refrain from blind guessing and probably only guess on questions they can eliminate at least one answer and hopefully two.

[pzhon]

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I would not do something like randomly guess in a 0 EV situation. I would want to limit my variance.

[/ QUOTE ]
Your expected submitted score increases if you might take the test multiple times and submit the highest score. Adding variance tends to be good.

[PantsOnFire]

[ QUOTE ]
[ QUOTE ]
I would not do something like randomly guess in a 0 EV situation. I would want to limit my variance.

[/ QUOTE ]
Your expected submitted score increases if you might take the test multiple times and submit the highest score. Adding variance tends to be good.

[/ QUOTE ]
Hey, you're changing the rules.

If you only get one shot, then I think my way is pretty good.

If you get multiple shots and the best score counts, then another approach may be better.

If you get successive shots (and again your best score counts) but know your score after each one, then you may want to take another approach which depends on your best current score.