Wikipedia:Reference desk/Archives/Mathematics/2008 April 7

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[edit] April 7

[edit] F-value and p-value mystery

Hi all:

Thanks for responding to my last question yesterday. I have just one more question that I'm not clear on.

Given the stat output from yesterday, but I have highlighted two different pieces of information this time:

I am asked the following question:

I am wondering, should I be using the F(2, 79) value directly and answer (c)? Or should I use the Prob > F value and answer (a)? Furthermore, is the Prob > F value the p-value for the scenario? If not, how do I determine the p-value from F(2, 79)?

Thanks a million!

L33th4x0r (talk) 16:54, 7 April 2008 (UTC)

Well, let me facilitate your thinking here.
  • What is the interpretation of the symbol F(2,79)? Not it's reported value, but what does he symbol itself refer to?
  • What is the interpretation of the value of 5.81; that is, what does that value describe?
  • What is the relationship between the previous two? Can you make any statements about their relationship by using any other above output?
If you think about these, you will probably figure out your answer. Baccyak4H (Yak!) 17:32, 7 April 2008 (UTC)

[edit] Why is the average verbal score so much lower than the math on GRE/GMAT?

On the GRE the average verbal score is about 100 points lower than the math, so while a 740 translates to the 99th percentile in verbal, even an 800 is only 94th percentile in math. On the GMAT, the verbal average is about 10 points lower (out of 60), and the difference in 99th percentile scores are only slightly dramatic.

Are foreign students a reason for the discrepancy? Are there more math and science students in grad schools than literary types? The GMAT is mainly for business schools even if it also applies to finance majors, though, and I'd assume there are more English majors there. Imagine Reason (talk) 16:55, 7 April 2008 (UTC)

I'm not familiar with these particular tests, but generally the actual mark in a test is pretty meaningless for anything other than comparing the results of two people sitting that test. Comparing the marks in one test to the marks in another is meaningless, unless the tests have been carefully calibrated, which clearly these haven't. What mark someone gets on a test depends both on their ability and on the difficulty of the questions. You can't really say whether or not the questions on one test are as difficult as the questions on another test, other than by seeing if people do equally well at them, which is why people often cite percentiles: the difficulty in reaching the 99th %tile in one test is obviously the same as the difficulty of reaching the 99th %tile in another test, since 1% of the population can achieve each. So, the short answer: The verbal scores are lower because the test is harder (for an appropriate definition of "harder"). --Tango (talk) 17:09, 7 April 2008 (UTC)
I'm going to take a slightly different tack: the math scores are higher on the GRE because the math test is baselined lower. My experience with the math portion of the GRE was that it required virtually nothing I didn't cover in high school (admittedly through AP coursework, but still) -- lots of math-heavy college students are going to ace a math test that can be reasonably administered to an English major. That sort of bias is unlikely with the GMAT. — Lomn 17:39, 7 April 2008 (UTC)
I agree with Lomn. The math portion of the general GRE exam was quite rudimentary. Of course, I was trying to get into graduate school in mathematics, so I was able to ace that test. The math subject test was a different story, however. –King Bee (τ • γ) 18:03, 7 April 2008 (UTC)
It seems like I didn't make myself clear in my OP. What I wanted to know was why students score higher in the math section on both tests. I actually think that GMAT math is easier because its problem solving questions don't include bar and other graphs, and its data sufficiency questions require many fewer calculations than GRE's quantitiy comparison section. Imagine Reason (talk) 22:20, 7 April 2008 (UTC)
Suppose that the distribution of mathematical capability is more positively skewed than of verbal capability, and that for whatever reason the scores in both tests are calibrated to have a predetermined median. Then the average math score will be higher. -- Meni Rosenfeld (talk) 22:48, 7 April 2008 (UTC)
That's what I don't understand. Logically it would seem that in America math skills are positively skewed, but then it should be easier for a person who is good at math to score in the 99th percentile (according to the definition in Skewed distribution), no matter how the median is determined. That is not the case. On the GMAT, I'm not sure two wrong answers can assure you of a 99th percentile score, but even a few more will do for the verbal section. I think people do generally do worse in the verbal section and that is the reason, not the result, for the lower median there. Imagine Reason (talk) 23:20, 7 April 2008 (UTC)
What do you mean by "easier"? Exactly 1% of the population will be in the highest percentile. Having a higher skewness means that there is a significant mass of very high numerical values, thus the highest percentile will have a high numerical value. Are you perhaps mistakenly assuming that the numerical value of the score represents an objective measure of how difficult it is to obtain? -- Meni Rosenfeld (talk) 20:39, 8 April 2008 (UTC)
Percentile is a bit funny on these things, because everything is discretized. A perfect 800 on the GRE math section does not get you a 99th percentile, because more than 1% of people do it. Thus, a perfect score is still not "better than 99%". It's actually just about impossible to get 99th percentile on the math section (I didn't miss any questions, and I didn't get it). However, since the scores are lower on verbal, the 99th percentile includes all scores over 740 or so. Those scores are attainable; they're just hard to get.

So, even though the verbal test is "harder", in one sense, it's "easier" to get a top percentile score on it. However, grad schools know what an 800 on the math section means, and what a 99th percentile on the verbal section means: in either case, good work. -GTBacchus(talk) 20:52, 8 April 2008 (UTC)

Perhaps the discrepancy is that the nature of the verbal questions is less objective? I know they're supposed to be written for one "right" answer, but I'm often able to convince myself that several are plausible, and then I start having to guess what the test writer considers "best". The math questions, on the other hand, are quite objective. — Lomn 05:12, 8 April 2008 (UTC)

My 2¢: Very many people who want to be mathematicians, scientists, engineers, computer scientists, etc., spend their undergraduate years doing work that makes them very fluent and comfortable with algebra. On the other hand, very few people who want to be English or Humanities scholars spend their undergraduate years memorizing the dictionary.

The verbal sections of the GRE and GMAT are largely vocabulary tests, and because of the adaptive nature of the tests, they hit you with very, very hard vocabulary words. That's because it's hard to write a multiple choice verbal test that really measures anything useful, except for vocabulary.

The math on the GMAT is harder than the math on the GRE, but most of it is still elementary stuff for someone who's a bit comfortable with calculus. At that point, the hardest math questions become the probability and combinatorics ones. Thus, if you're fluent in algebra - especially if you're conversant in calculus - and if you can handle some tricky counting and probability questions, then you're in pretty good shape to get an excellent if not perfect score on the math section of either test.

A perfect score on the verbal section, however, is quite a bit rarer. That involves having a very strong vocabulary (freerice.com level 45 or better, consistently), a pretty good understanding of how multiple-choice verbal tests "work", and to be quick about it. I teach GRE strategy, and I don't think I can get 800 every time on the verbal. -GTBacchus(talk) 05:34, 8 April 2008 (UTC)

One correction: GMAT verbal does NOT test for vocabulary. There are no tricky words there. It's just sentence correction, a bit of analytic reasoning, and reading comprehension. But otherwise I like your reasoning. Imagine Reason (talk) 16:18, 8 April 2008 (UTC)
Ah, I don't know much about GMAT. It's the GRE that I teach, and I've tutored GMAT math. Thanks for the correction. -GTBacchus(talk) 20:30, 8 April 2008 (UTC)

[edit] Alternatives to GraphViz for drawing graphs

See question at: http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Computing#Alternatives_to_GraphViz_for_drawing_graphics Mr.K. (talk) 18:15, 7 April 2008 (UTC)

See Wikipedia:How to create graphs for Wikipedia articles.  --Lambiam 20:27, 8 April 2008 (UTC)
Not really a helpful answer, since that page is mostly about graphs of functions, and under graph drawing it only says to use graphviz. When I draw graphs, I mostly do them by hand in Adobe Illustrator, or write custom software to draw them, so I suppose this is not a helpful answer either. —David Eppstein (talk) 02:51, 11 April 2008 (UTC)
Thank you both anyway. Instead of Adobe Illustrator you could give Dia (softaware) a try, specially if you are drawing complex graphs. On my side I'll experiment a little with Tom Sawyer software or a combination of CVS and my old graph files (in whatever format). Mr.K. (talk) 12:35, 11 April 2008 (UTC)