Educated Guessing, Statistics, and Strategy for the SAT

I can never say enough about how much I loathe what the idea of needing "strategies" to tackle standardized tests has done to the psyches of American high school students. The worst is an emphasis on guessing strategies. In this post, we look at why guessing strategies, the machinations of some Ivy League grads trying to imagine how "the average person" guesses, are useless. 

Let’s start at the beginning. Before we even talk about guessing on the test, you have to understand a little bit about probability.

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OK. One of the things you need to know about probability is that it calculates the likelihood of independent events. Independent events are exactly what they sound like: events that happen without outside influences. Let’s imagine I’m about to flip a coin and I’d like to know the odds of it landing on heads because I’ll win a prize if it does so. Given the absence of any other influences, all things being equal, the odds of my landing on heads is 1 in 2, or 1/2. It doesn’t matter if I have a feeling it’s going to land on heads or if it’s landed on tails the last two flips. No matter what, the odds are that landing on heads are 1/2, or I have a 50 percent shot at winning the prize. There is nothing I can do to influence the outcome of the flip.

If you’ve ever taken a stats class, you’ve probably seen a chart like this one before. It’s a random number table, used by statisticians for ensuring absolute randomness in research. Imagine some researchers want to do a survey and will be using the phone book to call people up and ask them some questions. Without getting into it too much, it’s important that you understand that they can’t just flip open the phone book and “randomly” point at names and get an official sample. There are all sorts of factors that can influence selecting folks to call: where their names are on the page, if the names are listed next to each other, or if I am drawn toward phone numbers that are eye-catching (like 353-7777).

To get around accidentally influencing who they call, researchers will use a chart like this to guide their calls, perhaps by counting to the 8th person on the list, then down 3 more, then 1 more, then 3 more, then 7 more, and so on. Just as I use a completely fair, outside deciding agent–a coin–in my first example to see if I win a prize, so also must scientists use randomly generated directions (like a number chart) to guide their randomness.

What does this have to do with your SAT score?

Well, as you probably know, the 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 try to 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: histrioniccataclysmic, and hierarchical. First, let me point out that anyone reading this post has 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 because I’m pretty darn good at the test, 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.

The sad fact is that as much as we’d like to believe that stats will come to our aid and boost our SAT scores, we’re never randomly guessing at the testing center.

Guessing on the SAT is a bad idea.

It’s also why you may want to be wary of any tutor that relies on guessing strategies to help you prepare for the test. Remember, everything on the SAT can be learned. However, if you still struggle here and there, your best bet is to track yourself–in your practice work, note when you’ve guessed and note how often you guess correctly. If it’s working for you, go with it. If you’re anything like me, you’ll probably prefer to leave answers blank.