About Trump’s hands…

Are they really that tiny? We do the stats!

Update: You want the data and code? Here they are!

Update 2: In order to fend off any potential lawsuits, let me point out that an alternative interpretation is that “Donald Trump is very tall for his hands.”

While Donald Trump’s campaign attempts to stop hemorrhaging support, those of us who are interested in data can focus on more interesting things. We got a treat today in the form of an actual measurement of Donald Trump’s hands. Donald Trump’s hands have been a campaign issue for months, and with the election less than 100 days away, it is critical that we get to the bottom of the question everyone is asking: “Are Donald Trump’s hands really that small?

The TL;DR version of this post is “Donald Trump’s hands are smaller than 84% of people of his height. So…yes. They are that small.” As a statistician and educator, I feel the need to tell you how I arrived at that number. Hopefully you’ll stick with me and learn a little something about statistics along the way.

The Hollywood Reporter — where I get all my celebrity anthropometry news — reported that Donald Trump’s hands were 7 1/4 inches long. I wanted to see how that stacked up to the general population. This required that I find a suitable dataset, and, thankfully, I found the 1988 US Army Anthropometry Survey (ANSUR) data freely available on Matthew Reed’s website at the University of Michigan, which includes measurements from 1774 servicemen. This dataset is a convenient choice; after all, we can be sure that Donald Trump isn’t already included in the data set because he never served (those darn heel spurs kept him from getting that purple heart he always wanted).

Donald Trump’s hand compared to the measurement used by ANSUR. Notice that ANSUR measured from a point on the wrist.

I needed to make sure that hand length was measured the same way in the ANSUR survey as Donald Trump’s hand was measured. As it turns out, I had to first correct Donald Trump’s reported hand length by about 6% because ANSUR measured from a point on the wrist. I wanted to make sure I got this right to avoid a libel lawsuit from Trump’s lawyers.

Trump’s corrected hand length is 198 mm (that’s 7.8 inches for my American readers). The Hollywood Reporter reported that the length of Trump’s hands was “slightly less than that of the average man;” so how does Trump’s hand length compare to the men in the Army survey?

Distribution of hand lengths in the ANSUR sample. Trump has slightly above average hands.

The average serviceman has a hand length of 194 mm, meaning that Trump’s hands are somewhat larger than the average serviceman. In fact, Trump’s hands are larger than 71% of servicemen. The Hollywood Reporter claimed that the length of his hands were “slightly less than that of the average man,” but I think this is because they did not correct the measurement properly. Hollywood Reporter, if you need a statistical consultant to avoid these embarrassing mistakes in the future, I’m available at a reasonable rate.

Is that all there is?

Distribution of heights in the ANSUR sample. Trump is very tall.

So, this is the end of the story, right? Donald Trump’s hands are larger than average. Should I expect a call from Trump’s lawyers to serve as an expert witness in a slander lawsuit against Marco Rubio? Well, no. Donald Trump is a tall man; 1880 mm (6 foot 2 inches) tall, in fact. He is taller than 97% of the ANSUR sample. You may have a hunch where this is going: height and hand length are highly correlated; if you’re tall, you would be expected to have large hands. Trump is very tall, but has average hands. Your hunch should be this: compared to people his height, he has probably small hands.

The relationship between height and hand length in the ANSUR sample. Each point is a serviceman.

We can quantify this hunch more precisely. The scatterplot to the left shows every serviceman in the ANSUR sample as a point. It is obvious from the scatterplot that tall people tend to have larger hands. We can actually describe this relationship with a technique called “linear regression,” which allows us to use all the servicemen’s data to work out the the expected hand length for someone of Trump’s height.

The best-fitting linear relationship between hand length and height. Trump is shown as the orange point.

The scatterplot on the left shows the fitted linear regression line (dashed) that best characterizes the relationship between height and hand length. This line has equation:

length = 27 + (0.095 × height)

So for a person of Trump’s height (1880 mm), we’d expect them to have a hand length of about 206 mm. The relationship is not perfect, obviously; for every height, the measured hand lengths vary around the line. However, knowing someone’s height does allow us to make a good guess as to how large their hands are. Trump’s hands aren’t freakishly small for someone of his height, but they are smaller than we expect.

So-called “residuals”, which show how far every serviceman’s hand measurement is away from the linear regression line. The dotted lines are ±1 standard deviation.

To get an idea of how much smaller they are, we look at how far every serviceman’s hand length deviates from the linear regression line. The “standard deviation” of servicemen’s hand lengths around the regression line is 7 mm, marked by the dotted lines above and below. Trump’s hand length is almost exactly 1 standard deviation below what we would expect of someone as tall as he is.

Finally, an answer

The hypothetical population of hand lengths for people of the same height as Donald Trump.

We know we expect of Donald Trump’s height to have a hand length of 206 mm, on average. We also know that the standard deviation around that number is about 7 mm. Trump’s hands are one standard deviation below what we expect. If we make one final assumption — that the spread of hand lengths tends to follow a bell-shaped curve we call the “normal distribution” — then we can say just how tiny Donald Trump’s hands really are. The vast majority of people Donald Trump’s height — about 84%, in fact — would be expected to have hands larger than Donald Trump.

There are, of course, some caveats and assumptions that I will avoid mentioning for the sake of brevity, but also the fact that probably no one has read this far anyway. But in case you are still with me, rejoice! We can finally tell the world:

“Yes, Donald Trump does have small hands, because math.”
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