Statistics have always been used to obscure the truth. There’s the famous quote by British prime minister Benjamin Disraeli, and popularized by Mark Twain: “There are three kinds of lies: lies, damned lies, and statistics.” Sadly, nothing has changed. In fact, it’s gotten worse.
The problem is that statistics isn’t a popular subject, and many people happily avoid taking any classes that cover the topic. (It was affectionately known as “Sadistics” when I was in college.) We’re easily led astray by official-sounding numbers, especially if the conclusion is one we already agree with. While we (thankfully) don’t need to worry about Chebychev’s Rules, Probability Distribution Functions, or Stem and Leaf Diagrams, we should know how statistics work, and how they can be used to fool us. There are numerous ways in which statistics can be misleading. I ran into one of them while reading the news this week.
You may have seen the widely published headlines about a majority of Americans in favor of President Trump being impeached. CNN reports, “A clear plurality of Americans approve of the House’s impeachment inquiry into Trump….” USA Today proclaimed “A plurality of Americans now support impeaching Trump and removing him from office.” And a CBS poll reveals: “Majority of Americans favor an impeachment inquiry into President Trump,” 55 percent to 45 percent.
Do the facts support these articles?
Let’s take a look at the CBS poll, conducted by YouGov. You’d expect a fair poll to survey equal numbers of Republicans and Democrats. This wasn’t the case. In fact, out of the 2,059 people surveyed, there were 124 more Democrats—who could be assumed to be more likely in favor of the inquiry. This is a statistically significant figure, 6%. If instead there had been 6% more Republicans, the majority would have be reversed, with 49% favoring the impeachment inquiry, and 51% opposing it.
Also important in a poll’s results is what questions are asked, and how they are asked. In this case, consider Question 4: “Do you approve or disapprove of Congressional Democrats starting an impeachment inquiry into Donald Trump?” Note that the question itself might be considered to be a bit misleading; although the constitution doesn’t address the details, traditionally the entire House votes to open an official inquiry (as with Nixon and Clinton). As I write this, there has been no vote. Therefore, some may disapprove simply based on the fact that the way the current inquiry is being conducted is unprecedented.
Finally, the article states: “A slim majority [of Americans] feel the Democrats are trying to politically damage the president with the inquiry.” This “slim majority” is actually 53% to 47%. That’s not a whole lot different from the 55% to 45% that the press is calling “unprecedented,” and “a clear plurality,” and well within the 2.3% margin of error.
These reports are an example of a statistical fallacy. Biased Sampling is defined as “polling a non-representative group.” In addition, the language used is intended to sway both those being polled, and you the reader, in a particular (anti-Trump) direction. Regardless of where one happens to stand on Trump’s presidency, we need to have unbiased reporting on which to base our opinions and, eventually, votes. This poll does not qualify.
We’ll be looking at more statistical fallacies in the months to come. In the meantime, I want to recommend a little book written more than 50 years ago: How to Lie with Statistics by Darrell Huff. It remains the best-selling book on statistics ever written.