GMAT Tip of the Week: Critical Reasoning, Statistics, and Lance Armstrong

With this week’s Lance Armstrong news and this blog’s history of rolling cycling news into GMAT tip posts, it’s only natural that today’s GMAT tip will involve that news. We’ll reserve judgment on the Armstrong case, specifically, but let’s use the situation to talk about GMAT Critical Reasoning and the way that it often uses statistics in arguments to assess your ability to think critically.

Consider an argument such as:

A test to denote the presence of a particular performance enhancing drug is known to be accurate in 95% of its cases. A certain athlete’s sample has tested positive for the presence of that drug. Therefore, by virtue of this test, we can conclude that it is far more likely than not that the athlete used that drug.

Is this argument airtight? That number, 95%, would make it seem so. But let’s examine a hypothetical situation in which there are 1,000 athletes and 20 are drug users. If each athlete takes the test:

* Of the 20 drug users, the 95% accuracy ranking means that one athlete’s test incorrectly said that he didn’t take the drug, and the other 19 were correctly caught.

* Of the 980 who didn’t use drugs, 19 out of every 20 would have been correctly cleared of drug suspicion, and 1 out of every 20 (so 49 athletes) would have been incorrectly “caught,” as their clean samples would have mistakenly tested positive.

So let’s look at the summary – given the hypothetical numbers here, the test results would show:

– 19 athletes correctly identified as drug users
– 49 athletes incorrectly identified as drug users

More than 2/3 of the positive drug tests in this case would have been in error!

What does this show us about Critical Reasoning? You won’t likely have to do this kind of math on a CR question, but you should notice how susceptible we are to making rash decisions when we’re presented with statistics. And particularly with percentages – if someone were to say that there’s a 95% accuracy rating for a drug test you’re taking for a new job, you’d probably feel pretty confident that, as an upstanding applicant, you’ll be fine. But if we just change that to a fraction or ratio and tell you that 1 out of every 20 people tested will experience a false result, you’ll likely feel a little less safe… particularly if there are 20 or more people in the waiting room for that test.

So be careful when making decisions based on statistics. Because these types of arguments will be presented all the time in business contexts (“Our $10,000 service will help you cut your shipping costs by 20%!” – but is 20% of those costs worth more than $10,000?), the GMAT likes to test statistics-based reasoning in both CR and Integrated Reasoning contexts. When an argument includes statistics, set your mind to “skeptical.” There’s a better-than-95% chance that that mindset will help you succeed.

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By Brian Galvin