9 Nov 2014

How Many Points is Your Name Worth on the SAT?

Submitted by Karl Hagen
Topic: 
TL;DR: Your name isn't worth any points.

The question comes from the flip remark that, because the minimum score on the SAT is 600 (200 each for the Critical Reading, Mathematics, and Writing components), you get 600 points for just for filling in your name. In point of fact, this claim is untrue on several levels.

First, if you merely fill in your name on an SAT score sheet and submit it with no questions filled in, College Board interprets the lack of answers as a request to cancel your scores, so you will get no results at all.

Second, we have to ask what we mean by a point. SATs are scored in a two-stage process, and the points that you actually earn comprise your raw score, which is calculated based on the number of questions you answer correctly and incorrectly. The 200-800 point scale is derived by transforming your raw score through a function that changes slightly for each test. But the presence or absence of your name doesn't change the raw score in any way. As a result, to think of being "awarded" 200 points for each section is rather misleading. This score scale is an arbitrary range. If you wanted, you could transform each component to a scale of 0 to 600 (or 0 to 1800 for the composite) with no loss of precision, and you can see how bizarre it sounds to say "you got 0 points just for filling in your name." Even though the minimum score is a positive number, it doesn't make much sense to think of achieving this minimum as earning anything.

Third, to get the minimum scaled score of 600 actually takes some work. Suppose you did the minimum necessary to avoid having the College Board cancel your scores, and deliberately answered exactly one question incorrectly. Based on the way that College Board calculates raw scores, you will still have raw scores of 0 in each domain. But your scaled score would be higher: picking an arbitrary test (and the numbers will be slightly different from test to test), raw scores of zero on all three domains translates to a composite scaled score of 670.

The reason that a raw score of zero doesn't always give the minimum scaled score is that College Board uses formula scoring (deducting 1/4 of a point for incorrect answers and rounding the result), and so a raw score of 0 is not the lowest possible raw score. The theoretical minimum, if you deliberately set out to miss every question, would be -17 for critical reading, -11 for math, and -12 for writing. To get a 600 on the SAT for the scale I referenced above, you would need to answer 11 critical reading questions incorrectly and 3 math questions incorrectly, with none right.* As long as you skip the essay, a raw score of 0 on writing = 200, so we can ignore that section.

In short, the notion that you get points on the SAT for filling in your name should be taken as an attempt to be humorous. Taken seriously, it misrepresents the way that scores on this, or any other standardized test, works.

* For the detail-obsessed, I should note that I picked these numbers to be sure of my answer. In the scale I'm looking at, a raw score of -3 on critical reading and -1 on math equal scaled scores of 200 for each section.How many problems you need to answer incorrectly to reach these scores depends on what rounding rule is used. For positive numbers, the SAT always rounds up. For example, a 10.5 rounds to 11. For negative numbers, though, I've never seen any evidence to indicate whether the SAT is using symmetric rounding (i.e., rounding away from zero, in which case -0.5 would round to -1), or rounding up (in which case -0.5 would round to 0). If the SAT turns out to round negative numbers up, you would only need to miss 10 critical reading and 2 math questions on this test.