Buix0065 wrote:
Ian--your reference of cause & effect vs. correlation logical errors, as well as population bias, are there good online resources I can take a look at to ensure I'm aware of this? I definitely have not consciously thought about these concepts.
I only teach high level Quant these days, so I'm not the best person to ask about Verbal resources. I've generally disliked the approach to CR taken by every book I've read (I particularly dislike the distinction books draw among Assumption, Strengthen and Weaken questions, since in each case your task is really just to identify a 'gap' or flaw in an argument), but perhaps you'll find good recommendations elsewhere.
If you've answered 97% of OG CR questions correctly, you're surely aware of common logical errors even if you don't use the same labels for them as a prep book might. To perhaps save you the trouble of seeking out a book, I can give a partial list of the types of issues I was referring to. The first three are all variations of the same cause/effect idea:
Correlation does not imply Causation: Just because some correlation exists between two things (i.e. when one thing goes up, the other goes up), it does not mean that one thing causes the other. There may, for example, be a third phenomenon which produces both observations. A researcher might observe that people reporting high levels of stress tend to sleep less per night than people who report low or normal levels of stress. It would not be correct to conclude that stress causes people to sleep less. It may be that people mostly suffer stress when they have an overwhelming quantity of work, and it is this overwhelming quantity of work which produces both observations: high stress and a lack of sleep.
Did A cause B, or the reverse?: When someone concludes that one thing causes a second thing, there is an assumption that the second thing did not cause the first. In the example above about stress and sleep, if one concludes that stress causes people to lose sleep, one is assuming that the reverse is not true: that losing sleep causes people to suffer from stress.
Post hoc ergo propter hoc ("after this, therefore because of this") : just because one event follows another, it does not mean the first event caused the second. The events may be completely unrelated. For example, if I wake up one morning, then the sun comes up, I can't conclude that by waking up I caused the sun to rise. Or to give a more GMAT-like example, if a question read "Country X imposed a year-long trade embargo on Country Y at the end of 2009. In 2010, Country Y's exports were down 20% from the previous year". It would be a logical mistake, without further information, to conclude that the trade embargo was responsible for the decline in exports. Perhaps Country X is some tiny nation like Tuvalu, and the trade embargo was almost irrelevant to Country Y's economy. There may be all kinds of other explanations for Country Y's loss of exports - a manufacturing decline in Country Y, for example.
Population/Sample Bias: When you conduct an experiment on a sample from a population, you can only generalize your conclusion to the entire population if your sample is 'representative' of the entire population. If the sample is somehow 'special' or different from the general population, it is a logical mistake to draw a conclusion about the entire population from the sample. This error is often called 'sample bias', and is a particular issue in real-life polling (it's why most internet polls are unreliable). To give a GMAT-like example, if a polling company surveys 1000 people from a list of cell phone subscribers in a certain country and learns that 60% of these people intend to vote for Party A in tomorrow's election, it would be a mistake to conclude from this (without more information) that Party A will win tomorrow's election. It is very possible that the group surveyed, cell phone subscribers, is not representative of the population at large; people owning cell phones might tend to be wealthier overall than the population at large, and might therefore have different voting preferences, and it may be that Party B is heavily favoured among people who do not have cell phones.
A ratio is not a number: Many CR questions test misapplications of mathematics, almost always misapplications of percentages or ratios. For example, just because a percentage goes up, you cannot conclude that an actual number increased. If you were told that the percentage of employees at Company X who are men increased from 60% at the end of 2009 to 70% at the end of 2010, it would not be correct, without further information, to conclude that Company X's hiring practices favoured male job applicants in 2010. Company X may not have hired a single person in 2010; it may instead be the case that several female employees retired during 2010.
That's just a partial list, but if you already have an 'intuitive' understanding of the logical issues above, you certainly don't need to learn labels to describe them, which is what you'd pick up from a book.
You are on the way to a good CR part in your test, I am sure!
