kitchen table math, the sequel: Elizabeth King on guessing

Sunday, February 27, 2011

Elizabeth King on guessing

[T]he SAT is a test designed such that you aren’t rewarded for guessing. If you answer a question correctly you earn 1 point; if you leave it blank you lose nothing. However, if you answer incorrectly, you lose one quarter of a point. Obviously you have a lot to gain by getting an answer correct and so many students use guessing strategies to be successful on the test. Some students have a rule of thumb that if they can eliminate two of the five choices, they’ll guess, because theoretically they have a statistical chance of 1/3 of getting it right. If they guess on 9 questions and get 3 right (which pure statistics tell us they would), that would mean they gain 3 points, lose 1.5 (6 x .25), and net 1.5 (which actually ends up rounding up to a net of 2).

Sounds great, right?

So how come I’m not an avid fan of guessing? How come it’s not one of my primary strategies for my students both in private tutoring and in Outsmarting the SAT? Am I doing them a disservice by not advocating the practice for everyone?

I don’t believe so, and this is why:

A student guessing on a standardized test is not a true random guesser and ETS knows it.

Say I’m working on a sentence completion question and I have confidently eliminated two answer choices, so I’m left with three words: histrionic, cataclysmic, and hierarchical. First, let me point out that the folks reading this post have a better chance of making a statistically random guess than someone who has read a sentence directly related to one of these words. However, even without seeing the question, we’re still not going to be completely random–I may choose the word histrionic because I’m a teenager and my dad uses it to describe me (and though I’ve never bothered to ask him what he means, it may be “a sign”), or I may ignore it because it looks like the word history and I don’t think that’s related to the sentence I’ve just read.

While a student working through the test may not be as long-winded in his rationale for choosing or ignoring a particular word, sometimes a mere “oh yes, I’ve heard that before” can sway a student. Or, if the last two answers were C, a student will usually not select C as his guess (when really the pattern of answers is completely irrelevant.) I honestly believe that ETS knows exactly what they’re doing when they include words that look like one thing and mean another or words that are more ubiquitous than others. They make true random guessing that much more difficult.

The definition of educated guessing is that one makes a guess informed by additional factual information. In these circumstances it is often very difficult for a student to sort through facts and his gut feelings. For some students this is a great boon: they’re the kids whose instincts are usually right on, and after plenty of connoisseurship of their own propensity to guess correctly, I advise them to go right ahead and do so.

And then there’s me. I am the The Worst Guesser On Earth. I categorically do not, no way, no how, ever guess on the SAT. Why? Well ignoring that I usually don’t need to, on the rare occasion that I’m caught without a clue, I guess wrong. It’s like a hex. I don’t know why this is the case, but evidently my own biases and “educated guesses” are way off track.

Educated Guessing, Statistics, and Strategy for the SAT
January 9, 2010
This is a woman who consistently scores in the vicinity of 800 on all 3 sections of the SAT, and she doesn't guess.

I've stopped doing any guessing myself.

Not on reading, not on writing, not on math. If I don't know the answer, I leave it blank.

Outsmarting the SAT

Outsmarting the SAT


gasstationwithoutpumps said...

On the SAT, where random guessing has an expected value of 0, it doesn't make much difference what guessing strategy you use, though being able to correctly rule out one possibility does raise guessing to a positive expected value.

On AP tests, where they have recently switched to counting blank and wrong answers the same, you should always guess, even if you are completely clueless.

On the AMC10 and AMC12 exams, where guessing is penalized more strongly, you only break even if you can correctly rule out one answer and only have positive expected value if you can correctly rule out 2 answers. Those tests are usually hard enough that if you can rule out 2 answers, it's because you solved the problem.


SteveH said...

Nothing stops you from flipping a coin rather than making an educated guess. I do agree that if you reduce it down to two choices, you will probably pick the wrong one with an educated guess.

"I may choose the word histrionic because I’m a teenager and my dad uses it to describe me (and though I’ve never bothered to ask him what he means,..."

This can happen from reading too. There have been lots of words I thought I knew from their use in context. Then I take a word test that tries really hard to find those weak spots.

In math, there is the issue that you can make a common (dumb) mistake, but find the answer as one of the choices. This is worse than making some really bad mistake and not finding that choice.

Catherine Johnson said...

it doesn't make much difference what guessing strategy you use, though being able to correctly rule out one possibility does raise guessing to a positive expected value.

In reality, at least in my experience and also in Elizabeth King's, test-takers don't guess randomly. Steve is right that if you're going to guess you should flip a coin, which may be impossible in the event.

Catherine Johnson said...

Is there a way to make a genuinely random guess while taking an SAT test?

Offhand, I can't think of one.

Jen said...

Pick a system for choosing -- say, an order of letters (cadb) and pick in that order choosing the first non-eliminated one.

Elizabeth King said...

This was great was fun to come across. Thanks so much!

Catherine Johnson said...

Hi Elizabeth -- Love your book!

Anonymous said...

If you score in the vicinity of 800 per section, you don't need to guess. Simple as that. Tricks to help people in the middle ranges dink out a few extra points are irrelevant if you can actually answer the questions, because then you just do it.

Catherine Johnson said...

It's not just that you don't need to guess, it's that you lose more points via guessing than you do leaving the question blank. That's been clear, working through the Blue Book tests with C. (We both take them.)

I'm curious whether high-end SAT test prep works.

People in these parts pay a lot of money for one-on-one SAT prep: $25K to $40K.

SteveH said...

If it's true that you can miss one or two questions and still get a perfect score, then it wouldn't pay to guess at all if you are near that point. In general, it seems that if you convert your raw score into the SAT score or a percentile, then there is a bigger loss on for a error on the low side than there is a gain on the high side.

Is there an official equation showing how a raw score is translated into the SAT grade? Is there an official document showing how SAT scores relate to your percentile?