[QUOTE=InvisibleWombat]
I think I understand what’s going on now. You and I are speaking of two very different things.
You’re speaking of the number of negative scores, and I’m speaking of the overall score on the test.
If I can narrow every question down to two potential answers and then I guess, I’ll get half of them wrong, but my average score will be 0.75 points per question. If there are three potential answers, I’ll get 2/3 of them wrong, but I’ll still average 0.5 points per question. With four, I’ll get 3/4 wrong, but I’m still going to average 0.25 points per question.
So, you are quite correct that guessing will get you many more negative scores (on individual questions) than leaving questions blank.
I am also correct, in that even .25 points per question beats the heck out of zero points per question (what you get if you leave it blank).
[/QUOTE]
I suppose he wanted to take this hijack outside the thread, but, judging from the PMs I’ve exchanged with him, I don’t believe that’s what ArizonaTeach’s point is. His claim is still that the probability of getting a negative score overall is significantly greater than that of getting a positive score overall, randomly choosing 1 out of 4 possibilities for each question. His claim is grounded in the assertion that the probability distribution of answers to distinct questions are not independent; that is, there are certain statistical patterns linking them. For example, he asserts, the probability of four answers in a row being the same letter is extremely low, much lower than would be expected if separate answers were independently distributed. In fact, he believes, this has only happened twice in the last 30 years of the test. Similarly, he has also been told that the test designers ensure that answers are approximately equal in number, each letter being constrained to a frequency of 20% plus or minus 3%. If separate questions’ answers are not statistically independent, then, I agree, it is mathematically possible for the probability distribution over answer keys to be such that random guessing to be very probable to hurt overall.
However, I find such claims about the lack of independence of separate answers hard to swallow, as they suggest the tests are susceptible to being “gamed” in unfortunate ways, through more “sophisticated” guessing (have three answers in a row that you know are As? Don’t even look at what choice A is for the next question; strike it out. Filled in all the answers you know? Find the letter you used the least often, and fill it in for everything else, guaranteeing (or almost guaranteeing, thanks to the 3% wiggle room) a score at least high as you would receive had you left them blank, and very probably much higher). But I lack authoritative information from the test designers on what exactly they are doing, and some people in the business of test preparation seem to be passing these claims along.
Though I continue to be skeptical of what ArizonaTeach has been told about the design of the tests, it is not my intent to badger him about this, which I fear I may be doing by continuing to voice my disbelief/skepticism/argument, particularly given the view that it is a hijack of this thread. He did give me some links, though, for others making similar assertions about the distribution of answers; for example, here and here. Quoting that last link may be informative, in seeing once again the kinds of premises he has been taught on which his claims about guessing can be grounded:
[QUOTE=satscore.us]
The SAT test writers ensure that there is a relatively equal number of correct answers corresponding to each of the multiple choice letters. That does not mean, however, that you should mark 20% of your answers As, 20% Bs, …, and 20% Es. The distribution is not that even. In a section with 25 questions, there may be 4 As, 5 Bs, 7 Cs, 3 Ds, and 6 Es.
You can count on certain patterns, though. One of these is that you will not find more than 3 consecutive multiple choice questions with the same answer. If you find you’ve answered 4 or more consecutive questions with “A,” for example, you will know that at least one of your responses is incorrect. Of course you will not know which one of them is wrong - but at least you’ve got a starting point.
If you find yourself in this situation, we advise you to remain calm. Just make a notation in your test booklet (not on the answer sheet), and revisit this series of questions at the end of the section, if you have time. Otherwise, don’t worry too much about it. Chances are good that you got 3 of the 4 answers right.
[/QUOTE]
The particular SAT preparation company which he has experience with uses slightly different numbers, but the same basic idea. Anyway, there you go.