Monday, April 28, 2014

SAT tips -- the opposite of the worst test you ever took

[This is part of an ongoing series of posts designed to help students, parents, teachers and other interested bystanders learn about and prepare for the SAT]

A message for perspective test takers...

No, really. Think back over the tests you've taken over all the years. Now think about the ones that caught you completely off guard. The ones that covered material you hadn't expected, asked questions completely different than what you expected. If you've ever had a test like that you probably still remember that feeling of being surprised, unprepared, even lied to, and worst of all, helpless.

If you're like me, those were probably the worst test-taking experiences you've ever had.

What would the opposite of a test like that be? What about one where the teacher gave you a stack of all of the old tests over that section going back ten years? On top of that, what if the teacher promised to keep the test as similar as possible to all those old tests, same material covered, same format, same type of questions, same difficulty? Wouldn't that pretty much be the opposite?

That's what we have with the SAT. The company that makes the test has been releasing its old tests for decades. You can buy collections of old tests in almost any book store. Better yet, you can get them for free from your school library.

And you usually don't have to worry about the new tests throwing in a lot of big changes. This next year might be an exception (there's been lots of talk about 'reforming' the test), but in general the SAT changes very slowly. This next year might be the exception, but other than that if you get a collection of old tests and work through them, asking your teachers for help whenever you get confused, you'll find that the SAT is exactly the test you expected and prepared for.

And that's a very good feeling.

Friday, April 25, 2014

The SAT and the penalty for NOT guessing

[I'm about to start a major SAT thread, so I thought I'd lay some groundwork by reposting something I wrote a few weeks ago on the analytics blog West Coast Stat Views. I'll be elaborating more on the widely misunderstood correction for guessing in future You Do the Math posts.]

Last week we had a post on why David Coleman's announcement that the SAT would now feature more "real world" problems was bad news, probably leading to worse questions and almost certainly hurting the test's orthogonality with respect to GPA and other transcript-based variables. Now let's take a at the elimination of the so-called penalty for guessing.

The SAT never had a penalty for guessing, not in the sense that guessing lowed your expected score. What the SAT did have was a correction for guessing. On a multiple-choice test without the correction (which is to say, pretty much all tests except the SAT), blindly guessing on the questions you didn't get a chance to look at will tend to raise your score. Let's say, for example, two students took a five-option test where they knew the answers to the first fifty questions and had no clue what the second fifty were asking (assume they were in Sanskrit). If Student 1 left the Sanskrit questions blank, he or she would get fifty point on the test. If Student 2 answered 'B' to all the Sanskrit questions, he or she would probably get around sixty points.

From an analytic standpoint, that's a big concern. We want to rank the students based on their knowledge of the material but here we have two students with the same mastery of the material but with a ten-point difference in scores. Worse yet, let's say we have a third student who knows a bit of Sanskrit and manages to answer five of those questions, leaving the rest blank thus making fifty-five points. Student 3 knows the material better than Student 2 but Student 2 makes a higher score. That's pretty much the worst possible case scenario for a test.

Now let's say that we subtracted a fraction of a point for each wrong answer -- 1/4 in this case, 1/(number of options - 1) in general -- but not for a blank. Now Student 1 and Student 2 both have fifty points while Student 3 still has fifty-five. The lark's on the wing, the snail's on the thorn, the statistician has rank/ordered the population and all's right with the world.

[Note that these scales are set to balance out for blind guessing. Students making informed guesses ("I know it can't be 'E'") will still come out ahead of those leaving a question blank. This too is as it should be.]

You can't really say that Student 2 has been penalized for guessing since the outcome for guessing is, on average, the same as the outcome for not guessing. It would be more accurate to say that 1 and 3 were originally penalized for NOT guessing.

Compared to some of the other issues we've discussed regarding the SAT, this one is fairly small, but it does illustrate a couple of important points about the test. First, the SAT is a carefully designed tests and second, some of the recent changes aren't nearly so well thought out.