With no fewer than 20 national-level declared presidential candidates, we are getting all kinds of information about America’s problems and opportunities. Some, maybe most, of it is sincere and honest, but a lot would match up with a picture on Facebook showing a horse trailer marked with the message “Caution Floor Covered with Political Promises.” It’s plenty hard enough to sort out what we think are wrong and right, but there is another concern. Some arguments are simply logically flawed.
Note that I’m not talking about anything debatable, any baseless accusations, or about ideas that we think reasonable people would always reject. I’m not picking on either side, or any candidate, in particular. In the process of getting a Ph.D., I learned a lot about what is and isn’t valid argument. Such knowledge is not common, as I can see by how often even smart, informed sources fall into the traps I will describe. So how can you, too, become aware of them? Here are the first four.
First is what I have long called “Darrell Huff” graphs. Huff was the author of How to Lie with Statistics, a groundbreaking 1954 book which described this gaffe. If we take a trend’s statistical progress, such as, in this example, one view of how many people our country will have in the next 5 to 45 years, and graph it in simple fashion, we might get this:
There is no distortion here. We can see that we might expect a substantial if not massive increase, running from something like 335 million in 2020 to over 400,000,000 forty years later.
But suppose we want to show that this increase is projected to be huge? We can do that by changing the scale of the Y-axis (the vertical one, on the left), which gets us the following:
See the difference? This chart is more likely than the first to prod a reader into thinking that our population is going way up. It even looks better, since the line is in more of the area. And yet I have not changed a single data point. The logical problem is that, in this case, 325 million is not a guaranteed minimum, which the graph implies it is. More than 60 years after Huff’s book, charts with nonzero Y-axes are still commonplace – and fool people consistently. To avoid being one of them, check for a zero in the lower left-hand corner before consciously reacting.
Second, correlation is not the same as causation. As I have written before, that means that when two things seem to go together, one need not be making the other happen. While that rule has been well known in the scientific community for as long as there has been academic research, it still fools many otherwise smart people outside it. When two trends seem to match up, often the second causes the first instead of vice versa, or, most likely, there is what is known as a “third variable problem” – the first and second are both caused by another factor. As before, although studies have shown that girls playing high school sports have lower rates of pregnancy and illegal drug use than their classmates, the games may not be responsible, as lack of interest in drugs may open the door for athletic activity, and the real explanation is probably a third variable – social class, which, for girls, drives not only reduced drug and pregnancy problems but sports participation. As a result, all articles or news stories giving correlations should arouse your skepticism.
The third gaffe is Parmenides’ Fallacy, or the assumption that without someone’s specific actions the situation would have stayed the same. This error is especially common in election seasons, when candidates impugn incumbents about things worsening under their tenure. If American foreign policy has weakened under Barack Obama, we can’t necessarily blame him, since it may have got even worse under Mitt Romney. By the same token, a Republican win in 2012 may have made our unemployment even lower than the latest 5.3%, so Obama does not get automatic credit for improvement from the 8%-plus it was when he took office. It is simply not legitimate to assume that any aspect of the human world is unchanging. As with the correlation and causation gaffe, statements dependent on comparisons with years before should trigger your suspicion.
Fourth is incomplete information. It is almost the same as what people call “comparing apples and oranges,” but is in a way more insidious, since something is missing from only one side. A Washington Post article last month cited two statistics apparently, in combination, supporting gun control, that for every case of a felon being shot and killed in self-defense there were 34 accidental firearm deaths. Those numbers, while believable, are inconsistent, as most people defending themselves or their property with guns do not end up killing their assailants. If the article would have offered that information, we could have used it to help our personal positions on firearm freedoms, but without that key piece, missing only from the second half of the equation, we cannot sensibly go any further with it.
These are the most statistical of the nine logical gaffes I have identified. Going beyond how the numbers are handled, what five other argumentation techniques are less than rational? That will be the subject of next week’s post.