GMAT algorithm FAQ, part 3

February 11th, 2010

David Kuntz developed the algorithm for Knewton’s GMAT prep course.  He is one of the brilliant brains behind the accuracy of Knewton CATs.  This is the final installment in his CAT FAQ. For more info, check out parts 1 and 2.

Part 1 | Part 2 | Part 3

How can my overall percentile be higher than both my quantitative and verbal percentiles?

Your overall score is calculated separately from your section scores, so you can score in the 99th percentile on the GMAT even if you didn’t score in the 99th percentile on either of the sections. For example, you could get a 48 on Quantitative (86th percentile), a 45 on Verbal (98th percentile), and a 760 overall (99th percentile).

Are the quantitative and verbal sections weighted equally in the total score?

Technically, yes — the estimates of your quantitative and verbal abilities that the CAT produces contribute the same amount to your overall score. However, the verbal section has a greater effect on your percentile rank because it is generally more difficult. If, for example, you scored a 40 on both the Quantitative and Verbal sections, your percentile rank for Quantitative would be 61st, but for Verbal it would be 91st. Your overall score (650) would be in the 84th percentile.

Why are scores above 51 rare? Why does the scale go up to 60? Can anyone get a 52?

For psychometric reasons, GMAC has truncated the scale at 51 (they do not report section scores higher than 51).

Why is it so difficult to create a good CAT?

A CAT needs to do many things well in order to reliably and accurately estimate your ability. It requires a robust algorithm to estimate your ability, a complex but speedy mechanism to identify the best question for you to see next, a rich pool of questions from which to select the questions, and a powerful scoring algorithm that translates the ability estimate into something meaningful.

Each test question has many characteristics that need to be simultaneously considered in the selection. The statistical characteristics of the questions all need to be determined beforehand through a process known as pretesting. Many, many questions are needed in order to be able to provide accurate assessment for all ability levels. And all of those questions need to be carefully constructed, reviewed, and statistically aligned so that they contribute meaningfully to your ability estimate.

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Disguised subject-verb agreement on the SAT Writing section

February 10th, 2010

Rich is one of Knewton’s expert GMAT teachers, but he’s also a whiz at SAT prep.

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Subject-verb agreement is a fairly simple thing we all learn about early in school:  If a subject is singular, the verb must also be singular.  For example, in the sentence “Thomas sells clothing,” the singular noun “Thomas” is matched with the singular verb “sells”.  It can be confusing, of course, that “sells” has an ‘s’ at the end (since s’s are often at the end of plural nouns). But because “sells” matches with the singular “Thomas,” it must be singular.

Likewise, a verb will be plural if its subject is plural, as in “The salespeople sell clothing.”  Again, even though the word “sell” may appear to be singular, it is plural because it is matched with the plural “salespeople.”

These are fairly straightforward examples.  But of course, the SAT has to make things a little bit trickier.  Interestingly enough, the SAT Writing section tries to trip you up not by making the content itself more difficult, but by changing the sentence structure so it becomes harder to recognize errors in subject-verb agreement.

Here’s an example of a “find the error” question that does just this:

IDSE sample question

Did you find the disguised subject-verb agreement error?  If not, try removing the modifying clause in between the two commas, and then read the resulting sentence:  “Music theory help musicians both understand their artform and appreciate its nuances.”

Pretty obvious now, isn’t it?  The singular “Music theory” is incorrectly matched with the plural “help.”  The sentence should of course read, “Music theory… helps musicians…”

Notice that what makes this question “difficult” is in no way related to content.  All they do is throw in a modifying clause between the subject and the verb, increasing the distance between the two for confusion’s sake.

And notice that in this case, the SAT writers double your fun by ending the modifying clause with the plural “ensembles,” which looks pretty good when paired with the next word, the plural “help.”  The problem, of course, is that even though “ensembles” and “help” appear back-to-back in the sentence, they are not paired together in terms of the sentence’s meaning.  “Music theory” is the thing that “helps,” not “ensembles.”

This happens extremely often on the SAT Writing section.  The test will separate the subject from the verb to confuse you, and it will also conclude a modifying clause with a noun that correctly matches the main verb in number but not in terms of the sentence’s meaning.

Be on the lookout for these types of errors as you work through your SAT practice questions!  Knowing this simple trick will help you tackle many questions on test day.

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February 2010 LSAT survey

February 9th, 2010

Brad McIlquham is Knewton’s Director of Academics. He is really into surveys, but then again, who isn’t?

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The February 2010 LSAT was this past weekend (at least for those who managed to avoid the massive snow cancellations). Just like we did in September and December, we polled our hearty Knewton students to get their feedback on the exam.

Most students who responded were from our full-length LSAT prep course, but a handful were from the first run of our 2-week Total Access program — their study program was abbreviated and largely self-directed, so we were interested to hear their feedback as well.

All told, the majority of respondents (70%) found the Logic Games section to be the most challenging. This majority wasn’t as overwhelming as it was in December — when over 80% agreed that AR was the toughest — but it still dwarfed the next runner-up. Only about 30% found Logical Reasoning to be the most difficult, while close to no respondents thought RC was the hardest.

Full results after the jump:

Read the rest of this entry »

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February LSAT cancellations: what to do if your test center closed

February 8th, 2010

If your LSAT administration was canceled this weekend, you should be getting another email from the LSAC in the next few days; when weather gets in the way of an exam, they try to schedule a make-up test within two to three weeks.

Here are some things you should do if your LSAT was canceled:

  • Hang on to your admission ticket; this will get you into the make-up test when it’s scheduled.
  • If schools are waiting on your LSAT score, give them a call to explain that your test was delayed.
  • Keep practicing! A postponement is disappointing, but it’s a great chance to take a few more practice tests.

For students whose Knewton LSAT prep memberships were set to end last weekend, we’re extending your courses until the make-up exams are finished. Next weekend is a holiday, so chances are most re-tests will be the weekend of February 19th or 26th. In the meantime, keep up the hard work!

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The latest February LSAT cancellations

February 5th, 2010

A storm’s a-brewin’, and the LSAC has already canceled a number of tomorrow’s LSAT administrations. Before you head out tomorrow, check to make sure your test center is open! The LSAC is keeping of running list of centers that are already closed, and that list is sure to grow today and tomorrow.

Here are the closings so far, state by state:

Delaware

Center 1330 – University of Delaware, Newark, DE

Maryland

Center 1364 – Towson University, Towson, MD
Center 1381 – Towson University, Towson, MD (overflow)
Center 1382 – Towson University, Towson, MD (overflow)
Center 1369 – University of Maryland-Eastern Shore, Princess Anne, MD
Center 1371 – University of Maryland-College Park, College Park, MD
Center 1372 – University of Maryland (Overflow)-College Park, College Park, MD
Center 1386 – Montgomery College, Rockville, MD
Center 1393 – Hagerstown Community College, Hagerstown, MD

Ohio

Center 4528 – Cedarville University, Cedarville, OH

Pennsylvania

Center 2012 – Villanova University, Villanova, PA
Center 2019 – Lebanon Valley College, Annville, PA
Center 2025 – Millersville University, Millersville, PA

Virginia

Center 1582 – Washington & Lee University, Lexington, VA
Center 1594 – Hampden-Sydney College, Hampden Sydney, VA
Center 1597 – University of Mary Washington, Fredericksburg, VA
Center 1598 – Northern Virginia Community College, Springfield, VA
Center 1609 – Liberty University, Lynchburg, VA

Washington, DC

Center 1556 – Howard University, Washington, DC
Center 1569 – Catholic University of America, Washington, DC

It can be a drag if your LSAT administration is canceled, but don’t fret. The LSAC will usually contact you with rescheduling information within a week. Silver lining: more time for LSAT prep.

Read more:

What to do if your test center closed

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February 2010 LSAT: some last-minute tips

February 5th, 2010

The February LSAT is tomorrow, and it always helps to get a little last-minute advice. This post comes from Kristen Kennedy, who taught a great exam-day seminar back in December. All you February test-takers should check it out! The link is below, as are some tips to remember once you’re in the exam.

One last thing: It looks like weather may affect a number of test centers tomorrow, and the LSAC has already issued some cancellation notices. Check their site regularly to make sure your test center will still be open.

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For all of you taking the LSAT tomorrow, good luck! By now you’ve done your practice tests, run through your drills, and gotten yourselves in optimal LSAT-taking shape. How should you spend your last precious hours before the test? Here are some tips.

I’m posting a link to a workshop we ran for our Knewton LSAT prep students. Anyone can view it, so check it out! We’ll break down how to approach the writing sample, how to prepare for test day itself, and what you should do for last-minute prep.

To watch the archive video, click here.

A minor note on test-taking strategy. One of the best tricks (and the simplest) is to make sure you have your answer-bubbling strategy in place. There are strategies! You can bubble in answers a question at a time or wait until you finish a page, RC passage, or logic game. All methods work, just choose the one you like best beforehand so you’re consistent.

There’s no penalty for guessing on the LSAT, so also make sure you fill in every answer choice before time runs out. If you have a few minutes at the end of the section, use it to review questions you were unsure about and double-check that you’ve taken a stab at every answer.

Remember that the goal for tomorrow is accumulating points, not achieving perfection. These small tips can lead to big gains over the course of the test.

Good luck everyone!

Kristen

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Future lawyer? Take our Facebook quiz

February 4th, 2010
That's right. Venturing into the wide, wide world of Facebook quizzes.

That's right. Venturing into the wide, wide world of Facebook quizzes.

Wondering about what kind of lawyer you would be? This quiz makes it crystal clear. Fair warning: there may be a Johnny Cochran reference.

Once you find your true calling, we’re also happy to help with your LSAT prep. Happy quizzing!

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GMAT algorithm FAQ, part 2

February 4th, 2010

David Kuntz is Vice President, Research at Knewton, where he builds the CATs for its online GMAT course. He is one of the brilliant brains behind the accuracy of Knewton CATs. This is part 2 in a series of posts about the algorithm behind the GMAT.

Part 1 | Part 2 | Part 3

How is the GMAT actually scored? Here are some more questions that students frequently have about its algorithm.

1. My score doesn’t seem to match my performance: I only got a few questions wrong, but my score isn’t as high as I thought it would be / I got a bunch of questions wrong, yet my score seems higher than it should be.

Most exams are linear assessments, like the SAT or your 10th grade history final. These are scored by counting the number of questions you answer correctly, and sometimes by penalizing for each question you answer incorrectly. The result, a raw score, is then converted to a scaled score, like the 600-2400 range for the SAT.

A computer-adaptive test (CAT) works very differently. It doesn’t really care as much about how many you get right or wrong, but rather which questions you get right and wrong. The CAT algorithm estimates your ability based on a variety of criteria, including the difficulty of a question. After each question, it evaluates your response and updates this estimate. When the test is over, the algorithm converts your quantitative and verbal ability estimates into the quantitative and verbal scaled scores, and then separately combines your quantitative and verbal ability estimates to calculate the overall score.

2. Do the first X number of questions matter more?

Many variables that come into play when the CAT selects your next question. One of them is the CAT’s current estimate of your ability. It uses this estimate to select questions that will be most useful in refining that estimate (if you’re a high performing student, giving you low difficulty questions isn’t usually as useful in discerning your true ability as giving you harder questions, and vice versa). What is important to remember is that you should not try to guess how you are doing by whether the question in front of you seems easy or difficult; every question deserves your full attention. With that understood, unless you have completely bombed the test, it is usually the case that missing a couple of very hard questions late in the test will have a smaller effect on your final score than missing a couple of very easy questions earlier, not because of their position within the test but because of their levels of difficulty.

3. How severe is the penalty for not finishing a section?

The penalty is significant. You can expect your scaled score to decrease by roughly 1 point for every question that you don’t answer. For example, if you correctly answer every question you encounter but fail to answer the last five, you generally won’t score higher than a 46.

4. I took the GMAT and got a 710, 44q/44v/6 AWA. A friend of mine happened to take the test 6 days later and get the exact same quant/verbal scaled scores but he got a 720. How this could happen?

Both the individual section scores and the overall score are calculated using an estimate of your Math and Verbal abilities derived from your performance on the CAT. Your overall score is not calculated from your section scores. Because your underlying ability estimate might be slightly different from your friend’s, your overall scores might be different.

For example, there are a range of ability estimates that translate into a Verbal score of 40, and there are a range of ability estimates that translate into a Math score of 42. Depending on which specific estimate is calculated for you, your overall score could range from 660 to 680. Please note that the Standard Error of Measurement (SEM) on the overall score for GMAT is 29 points, so scores of 660 / 680 all fall within the standard error.

Check back next week for part 3. Until then, do your homework!

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Law school admissions tip: Banish common, boring openings

February 3rd, 2010

This is the first in a series of  posts from our friends at Accepted.com. Stay tuned for inside tips on the law school and B-school admissions process.

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What are the most boring, non-starters for your personal statement? Openings that use wording from the question, or in the case of general questions, are so common that they will have a narcotic effect on any admissions reader wading through mounds of files.

Recently, Accepted editors discussed a client’s response to the question, “How have you experienced culture shock?” The applicant began her response with “I experienced culture shock when…” How many applicants responding to this question start similarly? Too many. However, if the applicant from the first word contrasted the culture she comes from with the one that engendered the shock, she would be immediately painting a picture of the situation, differentiating herself from her competition, and making maximal use of each word in an essay with a tight word count.

Another common opening: “I want to be a lawyer because…” or “I was born in…” or “I come from…” Start with an opening that portrays your vision for the future, reveals your preparation for your chosen path, or depicts an illustrative and impressive experience from your background. Then swing back and tie this opening to your desire for a legal education or the theme of your personal statement.

Your opening needs to immediately grab your reader’s attention, introduce your topic, and make effective use of the space. You all have word or page limits. Your readers have limited attention spans and a pile of other applications staring at them. Don’t bore them from the get-go. Begin with an opening that engages and grabs attention. Start your essays with an anecdote, a description of a scene, a startling statistic, or an appropriate quote.

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Accepted.com’s staff has been checking clients’ work for the essentials of great law school personal statements since 1994. Visit accepted.com/law for professional advising and editing services as well as sample law school personal statements, tips, free ecourses, webinars, and more.

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Fun with probability and combinatorics on the GMAT

February 1st, 2010

Rich Zwelling is one of the expert teachers in Knewton’s GMAT course. “Combinatorics” is  a word he throws around casually.

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I was recently discussing a particular GMAT problem with a friend, and as so often happens with standardized-test nerds, the discussion turned into an extended analysis.  We can’t help ourselves, I suppose.

The question went something like this:

Jim and John are workers in a department that has a total of six employees.  Their boss decides that two workers from the department will be picked at random to participate in a company interview.  What is the probability that both Jim and John are chosen?

Now, with many GMAT problems, there are multiple ways to skin a cat.  As it turns out, my friend and I chose completely different strategies that arrived at the same answer.  But interestingly enough, our different strategies got us to hit upon some key distinctions between probability and combinatorics.

1. My friend chose to go strictly with probability:

There is a 1/6 chance that Jim will be selected first.  Then, there are 5 workers left, so the probability that John is chosen next is 1/5.  Therefore, the probability of Jim being chosen first, then John being chosen second is simply 1/6 * 1/5 = 1/30.

However, we also have to consider the possibility that John is chosen first and Jim second.  That still leads to the same number:  1/6 * 1/5 = 1/30.

So, because we are interested in each of these possibilities (and nothing else), we must add the two probabilities to get the final answer:

1/30 + 1/30 = 1/15.

2. I chose to bring combinatorics into the picture:

There are 15 possible combinations of 2 people that you can choose from a group of 6.  You can find this using the combination formula:

n! / [k! * (n-k)!]

In this case, n = 6, since there are six people total, and k = 2, since we’re finding a subgroup of two.  Therefore:

6! / (2! * 4!) = 6 * 5 / 2 = 15 total combinations.

Now, out of those 15 combinations, we are interested in only one — Jim and John.  And recall that this is a combination (where order does not matter), as opposed to a permutation (where order does matter).  Jim and John is the same combination as John and Jim, since the same two people are involved.

(For clarification, it would be a permutation if, say, John and Jim were running a race, and we awarded different prizes for 1st and 2nd. In that case, Jim finishing first is different from John finishing first.  But in our problem, we’re not concerned with who is picked first; we only care about who’s in the group of two).

Back to the problem:  We’re interested in only one combination (Jim and John) out of a total of 15.  Therefore, the final answer is 1/15.

“But wait,” said my friend, “It’s a combination, so that means order shouldn’t matter.  Jim and John is the same combination as John and Jim.  So how come in my solution, we added two different probabilities for Jim-John and John-Jim?  Order shouldn’t matter, but in my solution, it did.”

What we realized is that order mattered in my friend’s solution because he was considering two different events, not two different combinations.  Jim and John is the same combination as John and Jim, so if we were restricting ourselves to finding information solely about combinations, then order would not matter.

However, we were not only finding information about combinations; we were also interested in probability.  The situation of Jim and John being chosen first and second, respectively,  is a distinct event from that of John and Jim being chosen first and second, respectively.  So even though both events involve the same combination of people, the events themselves are different.

What makes problems like this a little bit tricky is that they can involve both probability and combinatorics, and it might be easy to confuse the two.  But always remember, combinatorics on their own deal solely with finding the number of combinations or permutations in a given set of data, while probability deals with finding the likelihood that an event or events will occur.

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