## Posts tagged with: guessing

Here is a question that might be simple, though I am stuck on it:)
If you get 1/4 of a point deducted from your score if you answer a question incorrectly, is it worth it at the last few minutes of your test to fill in all of the questions with the same letter because the chances are that 1/4 of them will be right (especially if you can deduct some of the obvious wrong answers)? They tell you not to guess, but to me it seems like it is worth a shot since you will probably get at least 1/4 right.

Well, you have a 1/5 chance of getting a question right when you guess randomly. So if you guess on 5 questions, the likelihood is that you’ll get 1 right and 5 wrong. That’s +1, and –4(1/4), for a grand total of 0. Same as if you left them all blank.

Of course, there’s also a chance you’ll get lucky and gain a point or two, and also a chance you’ll get unlucky and come out behind…

I’ve written a fair amount about guessing and how this math works in the past. See here.

I get asked about guessing on the SAT all the time. All the time. And I’ve written about guessing on this blog often enough that there’s a special label for those posts, so that you can always find them. But I wanted to give a quick tip to aspiring tutors who come to my site looking for advice (judging by the number of hits I get from Ivy League schools, there are many of you). Regardless of what the laws of probability say, you should not be dogmatic about forcing your students to guess.

Explain to your students the way the scoring system works (+1 for a correct response, -¼ for an incorrect one). Explain how random guessing, statistically, is a break even. Explain how, if a student can eliminate an answer, the odds say she should guess. But leave it at that. Because if you don’t, and she guesses, and it costs her, you’ll be Trent from Swingers. You’ll be maligned for giving good advice, because you insisted on it too strongly instead of letting your student make the final call.

There are some things you, as a tutor, should insist on. Writing out algebra instead of doing head math, for example, costs the student nothing although he may resist. This is a good fight, because when you win you’ll probably make an improvement in his score. You’re changing his habits, and causing him to do something that will at worst, make no difference, and at best, drastically reduce his careless errors.

When you have the guessing fight, you’ll often find that even if you win, you’re not making a huge score difference. That’s because guessing has a lot to do with luck. SAT guessing strategy is just a way to make it slightly more likely that a student will get lucky. Once in a while, your student might actually get unlucky and lose points. And then it won’t matter that you’re right. When you find yourself having to defend your guessing strategy to a student who is looking at a 690 instead of a 700 because of guessing, you’re in a bad fight.

I like to run this experiment with students on practice tests. And then, after we’ve done a few tests that way, I shut up about guessing and let them make their own decisions.

I always double down on 11. But I don’t make my friends do the same when the stakes are high.

I just listened to a Planet Money story that I wanted to share with you. It’s a 4:26 long discussion of risk aversion and how some experts see it distorting the American housing market. I’m not recommending it because I think you need to be thinking about the housing market, though. I’m posting this because the whole time I was listening, I was thinking about the psychology involved in guessing on the SAT. To paraphrase one expert in the story, people are afraid to guess because losing feels more intensely bad than winning feels good.

I actually think the SAT is a better application of the theory in question than the housing market, since home buyers and sellers generally don’t get to buy and sell often enough for the “if you flip the coin 1000 times” argument to really make sense.

On the SAT, you lose 1/4 of a point for an incorrect answer, and gain a whole point for a correct one. Since there are 5 choices per question, if you are deciding whether to guess or leave a question blank more than a few times per test, you’re in a position where, statistically, random guessing is a complete wash (thorough explanation here). From there, if you feel like your guess is even a little bit better than random, the “rational” move is to guess, since the scales tip slightly in you favor once you eliminate even one incorrect choice.

I’m not saying you need to guess, but listen to the story, and see if any of it resonates with you. It may or may not inform your future guessing strategy on the SAT.

Because there’s a penalty of ¼ raw score point for incorrect multiple choice responses on the SAT, many students experience extreme trepidation about guessing when they aren’t sure about an answer. I’ve stated my general advice on guessing before, but the truth is that while I almost always find that my students benefit slightly from guessing more, I’m open to adjusting that advice if it doesn’t seem to serve a particular student well. If you’re not comfortable just taking blanket advice from a stranger on the Internet, there’s actually a very simple experiment you can perform to help you settle on a guessing strategy that works for you.*

Here it is: always, ALWAYS, ALWAYS GUESS on practice tests, and make little marks on your answer sheet to remind yourself which choices were guesses. When you’re done, score your test twice: once with your guesses in there, and once with all your guesses replaced by blanks.

What you’ll probably find is that there isn’t much difference either way, but once you’ve done this on 3 or 4 tests, you’ll start to get a sense of how guessing works for you. By the time the real test comes along, you’ll be comfortable in your guessing strategy, knowing that it’s based not on superstition or blind faith, but science.

If you want to get really crazy and add a bit of granularity into this, that’s possible too. Replace the little mark you were using to signify a guess with a number. Rate your guesses on a scale of 1 (no idea whatsoever) to 3 (got a good feeling about this), and score your test first with all the guesses, then with only the 3-rated guesses, then with the 3- and 2-rated guesses, etc. You could similarly use numbers to note how many choices (if any) you were able to eliminate before you guessed. I wouldn’t go so far down the rabbit hole though; I’m just spitballing here.

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* Of course, the best guessing strategy is to never have to worry about guessing because you have prepared so well for the test that nothing can surprise you. But you knew that already, right?

Note: This post is about the old SAT (pre-2016). The “new” SAT does not have a penalty for incorrect answers.

In short: almost always.

(Note: This is generalized advice; if it doesn’t sit well with you, read this.)

I’ve encountered a lot of misinformation about the SAT in my travels, but the single subject that generates the most confusion and rampant speculation is The Guessing Rule.  So here it is, as plainly as I can put it: If you have read a question and thought about it for more than 5 seconds, you should not leave it blank.

Here’s how it breaks down:
Every incorrect answer in a multiple choice section* costs you 1/4 of a raw score point. Every correct answer, of course, gives you a whole raw score point. A blank has no positive or negative effect on your score. Fractional points are rounded to the nearest whole number when scores are compiled.

Imagine two ne’er-do-wells, Johnny and Morrissey, are taking a much shorter test with the same scoring scheme. Johnny doesn’t give a damn about the test, and guesses C for every question without even looking at it.  Morrissey cares even less than Johnny, and just leaves the whole thing blank, opting instead to stare out the window dolefully.

 Question # Johnny Morrissey 1 C [blank] 2 C [blank] 3 C [blank] 4 C [blank] 5 C [blank]

When you guess completely randomly, like Johnny did, what are your statistical odds of getting a question right? Well, there are five choices, A through E, so that’s a 20% chance (or 1 in 5 odds) that you’ll get any particular question correct. Since our test had five choices on it, Johnny will get one of them right, and the other four wrong.

 Question # Johnny Morrissey 1 C +1 [blank] +0 2 C -1/4 [blank] +0 3 C -1/4 [blank] +0 4 C -1/4 [blank] +0 5 C -1/4 [blank] +0

Note that when you total up Johnny’s score, it’s the same as Morrissey’s! Both get a grand total of 0 raw score points. Now, it makes sense that they both would earn a goose egg — they both did about the same amount of work. It would be unfair to give Johnny a better score simply for picking up his pencil and bubbling randomly (note: this is what the ACT does).

It might be clear by now why the SAT’s scoring system works the way that it does. It’s not to penalize you for wrong answers; it’s to prevent people from gaining an unfair advantage. Say your proctor calls time at the end of a section that neither you nor the person next to you has finished. You put your pencil down like the obedient student that you are, but your conniving neighbor hurriedly bubbles in random guesses for the last few questions. That person shouldn’t have an advantage over you, and the SAT’s scoring system (on average) ensures that she doesn’t.

So the obvious implication is that random guessing doesn’t pay. Why, then, am I arguing that you should guess whenever you’ve had time to read and consider a question? Simply put, because then you’re not randomly guessing anymore, so you’re tipping the scales slightly in your favor. You will still get more questions wrong than you will right when you’re guessing, but even if you only eliminate one bad choice before doing so, the math says your score will slowly go up.

Let’s look one more time at Johnny, but change his strategy a bit. Let’s say now that he’s still randomly guessing, but before he does so he’s putting in the minimal effort of eliminating one choice he knows is wrong before doing so (so his odds of a correct answer are 1 in 4). Let’s also say the test got a little longer…say it’s 8 questions now. That means, statistically, that he’ll get 2 right, and 6 wrong.

 Question # Johnny 1 C +1 2 C -1/4 3 D -1/4 4 C -1/4 5 C -1/4 6 B +1 7 E -1/4 8 A -1/4 TOTAL POINTS +2/4 = +0.5

When it comes time to calculate final scores, that half a point will round up, and Johnny has just (amazingly) helped his score.

I want to be clear here: this is not going to net you hundreds of points. This might get you 10 points on a test, or it might get you none. Since it’s purely theoretical, it might even cost you points on a particular test if your luck is worse than average (remember, even though statistically you have a 50/50 shot when you flip a coin, sometimes in real life you can flip heads 10 times in a row).

This guideline is kinda like the rules a Vegas blackjack dealer has to follow. I know you’re probably not in casinos very often if you’re worrying about the SAT, but maybe you’ve been to a charity casino night at your school? At my school that was one of the attractions of the post-prom party. But I digress. The object of blackjack is to get as close as possible to 21 without going over. If you’ve got 18, but you’re feeling lucky, you can take another card to try to get closer. It might not be smart, but you can do it. The dealer, on the other hand, cannot. He has to stop if he’s got 17 or higher, even though he can see your hand and therefore might know that 17 is a losing hand for him. Why? Because someone very smart at a casino a long time ago figured out that if he always does that, always, then the house will slowly but surely win money, even though some individual players might walk away from the table with more money than they came with.

So it is with you and guessing on the SAT. If you always guess when you’ve read a question and thought about it for more than 5 seconds, you’ll win more points than you lose, even while you’re getting more questions wrong than you’re getting right. It might take some getting used to, but that should be your new guessing rule.

One last note that should be obvious: guessing is for emergencies only. The better way to improve your score (and the only way to improve it more than a minuscule amount) is to learn some techniques to help you actually get the questions right. Hopefully I can be of service there too.

*There’s no penalty for guessing on a grid-in in the student produced response part of the math section. Why do you think that is?