Guessing and Average PGRE Scores

I'm sorry if either of these have been discussed before.

1) It seems to me that if you don't know the answer to a problem but are able to eliminate at least one of the 5 choices, then it would be better to guess instead of leaving it blank. That's because with each problem wrong you lose 1/4 a point and each problem right, you gain a point. Thus, on average, you would gain and lose one point every 5 problems if you just randomly guessed. So, if you can eliminate even one choice, the odds would be in your favor to guess. Does this sound correct?

2) Are there any lists/tables anywhere that show the average PGRE and GRE scores for the students who were accepted at various schools? I know they had this for the SATs back when applying to undergraduate schools.

No you cant say anything about the state your going to be in 5 questions later. If youre guessing with 4 choices and a quarter point off all you can say is that it is very likely youre not going to gain any advantage. It is not a guarantee and its still possible to get screwed over by guessing even if you have only 3 choices.

for your 2) no not really, there are a few statistics in gradschoolshopper although programs really should have to report average PGRE.

The expected value from guessing is positive if you can eliminate 2 or more answers (it is 0 if you can only eliminate 1). When I take standardized tests of that sort I don't guess if the expected value isn't positive (i.e. if I can only eliminate one on the PGRE I would not have guessed). I will say that it is pretty common in my experience to be able to eliminate ~2 answers by dimensional analysis/asymptotic behavior and such.

As cato88 says, the AIP has data for quite a few schools. For instance, in 07/08 Berkeley had a 890 average PGRE among accepted students (I think this is one of the highest averages).

What's wrong with my calculation? Let x be the number of points you get per question.
If you don't eliminate any choices and just randomly guess, P(correct) = 1/5 and P(incorrect) = 4/5.
Thus, <x> = P(correct) * 1 + P(incorrect) * (-1/4) = 1/5 - 1/5 = 0.

Which is why I thought the expected value was zero if you don't eliminate any answer and positive if you can eliminate at least one.

AIP data at:
http://www.gradschoolshopper.com

average gre/pgre scores for many schools

Whoops, you're right. For some reason I remembered it being calibrated to be a penalty for random guessing instead of break even. That teaches me to actually do the fractions in my head before asserting something

Keep in mind how skewed the averages will be. International students generally have to do a lot better on the GRE than their American counterpart, regardless of school, to be accepted. Which means that the numbers are not very acurate indicators for both international and domestic students.

A much more useful statement are cutoff scores, which only a few schools give.

I would say for his second question the decisive answer would be that there is not much useful PGRE information available to prospective graduate students.

If you can attempt around 70~80 questions confidently, then it is a good option to guess intelligently, the remaining 30~20 questions. I had attempted 89 questions in which around 10 where guesses after some eliminations. I do feel if I had attempted remaining 11 question I might have aced the exam. At least it would not have harmed my score too much. While guessing it is important to use dimensional analysis, intuition about range of values, other techniques etc.

I ran across this article on guessing.

This article makes a very good point. When I was taking the practice PGRE tests, I would make a little tic mark by a question when I eliminated as many options as I could and then guessed on it, so that afterward I could see if the way I was guessing helped or hurt my score overall (that is, I would calculate the score I would have gotten if I had left everything I guessed on blank, versus the score I got by guessing on some). When I eliminated the answers I was absolutely sure were wrong, I found that my score was helped the most when I randomly guessed from the remaining choices without even looking at what they were, versus looking at the options and guessing which one I thought might be right.

You'll have to see what works best for you.

Expected Value on guessing is actually positive even if you can't eliminate ANY answer choices. That's because they round up to the nearest integer.

.25 gets rounded down
but .5 and .75 get rounded up

You might as well guess on all of them

That fact doesn't give any structural advantage to guessing except in very specific situations (for example if you've answered 98 questions that you're certain are correct and have no idea on the last 2). More realistically the spread on the number of questions you may have gotten wrong is large enough that fractional part of your score is essentially random, so getting an additional question wrong has effectively exactly a 1/4 chance of dropping your rounded raw score by 1.

Still it's not really ever strictly worse to guess than not.