As Twitter has confirmed, the real winner in this week’s U.S. Elections was Nate Silver, the statistician behind fivethirtyeight.com and the prognosticator who called nearly every national race correctly, save for one senate race in North Dakota. Famously, he predicted each state’s presidential race correctly and he’s risen to prominence with a role on the New York Times and with his new book “The Signal and the Noise.” So with Nate Silver taking statistical analysis to heights that Moneyball only hoped to, it’s only fitting that we close this week by summoning our inner Silver and taking a statistical dive at GMAT questions.
Polling isn’t new, nor is statistical analysis. So why is Nate Silver so much more successful than others when it comes to using statistics to project outcomes? If we understood completely, we’d be writing a different article for a lot more money on a more-heavily-trafficked blog, but the layman’s answer is largely that he takes time to determine which statistics are most relevant to the outcome, and focuses his energy on those. And that’s what you should do when you analyze your GMAT practice tests and consume information about the GMAT – cut to the most meaningful statistics and focus your energy there.
Here are some of the statistics that Nate Silver wouldn’t bother with, or would at least make sure to investigate skeptically, related to the GMAT:
– “My accuracy on Sentence Correction questions is around 70%”
– “The 13th edition of the Official Guide for GMAT Review has 15% more statistics problems than the 12th edition”
– “My last two practice test scores were 20 points lower than my previous test”
– “Both of my geometry mistakes were on triangle questions”
Why are these stats less than actionable? Well, the GMAT cares more about “how difficult the problems were” than “how many did you get right”, so the first stat can be misleading without further context. And the Official Guide isn’t designed to reflect proportionality of what you’ll see on test day, so small fluctuations in question allocations really can’t tell you anything. Your practice test scores will probably vary anyway, let alone if you took one late at night or after an awful day at work or with your roommate listening to loud dubstep in the next room. And “triangle questions” aren’t really what the GMAT is testing – the reason you missed one could be entirely unrelated to the reason you missed the other.
What statistical analysis is more important? Where would Nate Silver spend his time?
In our Tales from the Question Bank series, launched yesterday, we begin showing you statistical analysis of wrong answer choices. Why are people making the mistakes they’re making? What types of traps tend to appear in the hardest questions?
For example, let’s take a “triangle question.” If a Data Sufficiency question were to ask:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees
(2) Angle F measures 96 degrees
The stats will show on this one that anyone who picks the wrong answer picks C. (The correct answer is B – if one angle of an isosceles triangle is 96, that means that it cannot be the “matching” angle, so the other two must match and the trio must add to 180) And what you can learn from the stats is you missed this one is not just “I don’t know about triangles” (to pick the trap answer C you do still have to know most of what you need to know about triangles) it’s that you didn’t leverage all the given information. When you pick C but the answer is A or B, the reason usually isn’t “poor content knowledge” but rather that you didn’t dig deeply enough on Data Sufficiency. This question will have similar statistics to the following question:
Tyler sells two types of milkshakes: chocolate and Oreo. Chocolate milkshakes cost 52 cents each and Oreo milkshakes cost 58 cents each. How many Oreo milkshakes did Tyler sell?
(1) Tyler sold 9 milkshakes total
(2) Tyler’s total revenue from milkshakes was $4.92
The stats on this question are similar, with a more-pronounced “C Trap” because the question is slightly more involved. But the reasons are the same – statements 1 and 2 pretty obviously solve the problem together (C + O = 9 and 52C + 58O = 492 gives you two equations and two variables). The answer, again, is B (for a full debrief check out this article about essentially the same problem), and the lesson to be learned is that if you pay attention to the reasoning behind your wrong answers, you learn a lot more than if you just study the “surface stats” like content area or overall percentage.
So back to Nate Silver – where would Nate Silver spend his time on GMAT stats?
– When you have access to stats like those in our Tales from the Question Bank series, you can learn a lot about what truly makes GMAT questions hard.
– When you analyze your own mistakes (as you won’t have nearly as much data as GMAC or Veritas Prep do) go deeper than just “geometry” or “algebra” – try to find patterns that are more meaningful, such as “most of my sentence correction mistakes come when the key word that signals verb tense is outside the underline” or “I tend to miss Data Sufficiency questions when the trap answer is C but one of the statements alone is sufficient”. Try to find the “signal” statistics and spend less time on the “noise”. With our newfound Nate Silver love we’ll try to point you in that direction in the Tales from the Question Bank series, but be mindful yourself of the reasons behind wrong answer and not just the surface-level descriptions of them. Focusing on meaningful data helps you be a lot more Nate Silver (nearly 100% correct) and less 538 (about the average score on the GMAT).
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By Brian Galvin