By Adam Tseng
“There are lies, damned lies, and statistics.” - Mark Twain Statistics is a very unique form of mathematics. You might have learned it in school and found it somewhat boring, but in reality, statistics is extremely powerful. It helps guide decisions in government, finance, education, sports, entertainment, and even daily life. However, while statistics can reveal the truth, it can also lie and distort truth just as easily.
As a prudent citizen, consumer, and general do-gooder, it’s a good idea to learn a few ways statistics can be misrepresented and how to spot them. After all, you wouldn’t want to be deceived into making the wrong decisions by those who want to capitalize on your ignorance, would you? Right. So let’s get into this! Graphical Manipulation
Anybody worth their salt in statistics knows how to read a graph properly. Thus, to deceive the layman with only marginal statistical acumen, a common statistical trick is to toy around with the axes and scales of the graph.
Judging from the shapes of the two graphs, the one on the left certainly seems to show astronomical growth towards the end of 1937. However, if you take a closer look at the labels on the axes to the left, you’ll see that the vertical y-axis doesn’t even begin at zero - it begins at $19 million! Graphical manipulation of the vertical axis magnified the trend because the physical size of the picture is fairly large, even though the range of the y-axis is only around 1.5 million dollars. The graph on the right shows the growth using the appropriate axes, which puts the trend in perspective. It’s linear and uniform, meaning that there wasn’t much change in the government pay rolls in 1937.
Correlation vs Causation
Don’t these two trends look eerily similar? Could the makers of the “500 greatest songs of all time” list be picking many mid to late sixties songs because they were inspired by the oil production boom? Of course not. They simply happened to be coincidences. The song selection and oil production are correlated, but one did not cause the other. After that silly example, one might believe that correlation and causation are easily distinguishable. However, even doctors were duped by a series of medical studies revealing lower incidences of Coronary Artery Disease (CAD) in women who underwent Hormone Replacement Therapy (HRT), and medical professionals began recommending them eagerly to patients. However, the doctors had mistakenly assumed that HRT caused the lower CAD incidence, when it had only been a correlation. In fact, the actual cause of the lower incidence of CAD was the high socioeconomic status and general health of the study population. Evidently, statistics can be tricky. As seen in the previous example, it often requires a bit of doubt. More importantly, it requires us to read between the lines, which can prove especially helpful in spotting the next statistical trick. Texas Sharpshooter Fallacy A man claims to have the best shot in the whole Wild West. His shots are always close to the bullseyes. But is he really? What if, instead of painting a target and then shooting at it, he shoots, and then paints a target around it? Therein lies the Texas Sharpshooter Fallacy, which is a form of confirmation bias - the tendency to seek data and information that supports one’s own beliefs.
This type of trick is often the least obvious because we actually use it to trick ourselves all the time! Have you ever tried to convince your friend to not go to a specific restaurant that you dislike by searching for that one negative review of it? Have you ever felt scared of flying or boating after you read about a terrible accident or crash that seemed to support your belief that those activities are dangerous? That’s the Texas Sharpshooter Fallacy at work in your brain, without you even knowing it. Neil Degrasse Tyson said that, “the Internet is the epitome of confirmation bias.” He could not have been more correct. In fact, the Internet’s tendency to promote confirmation bias and the Texas Sharpshooter Fallacy is likely the reason why many parents now believe that vaccines cause autism. In spite of almost the entire scientific community telling them otherwise, those parents chose to paint their bullseye around one specific study that has actually been withdrawn from all respected medical journals and cite it as evidence that they shouldn’t vaccinate their kids. These are just some of the many ways to be misled by statistics. However, these tricks can be avoided by simply looking at the big picture. By paying attention to the scale and relative size of the graphs, seeking all the information, rather than just a fraction of it, and using common sense, one can easily avoid the three aforementioned tricks. More crucially though, look at the numbers carefully and never take anything at face value. A healthy dose of skepticism is always good to have - you never know when you might need it.
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