Scatterplots: Two Variables at Once

Full transcript

Word for word what is said in the video — the same text as the subtitles. Times are minutes:seconds into the video.

0:00Two numbers, one dot ▶

Twenty-four students, and two numbers for each of them: hours on the phone, hours asleep. Here is the first student: four point seven hours on the screen, six point seven hours in bed. Those two numbers make one dot, and twenty-four dots make a picture neither list could give you. By the end of this video: four steps to read a cloud like this. And you will know the one question it can never answer.

0:35Two averages are not the class ▶

Ask about a class and you get averages: four hours on the phone, seven and a half asleep. Two numbers, and most people stop there, because it feels like knowing the class. Here is the crack in that promise. A second class can match the average, the spread, even the histograms, the bars you get when you stack one column into groups. And even with all of that matched, the second class can still be nothing like this one. Stay with me and you get three things: what a cloud shows, four steps to read one, and what it hides.

1:13What a dot really is ▶

To see what a dot really is, start with two lists: twenty-four screen times and twenty-four sleep numbers. Take one student, walk out along the screen-time edge to four point seven, then along the sleep edge to six point seven. Where those paths cross, a marker drops, and that marker is the student. Do it twenty-four times, lift the camera, and the floor is a scatterplot. Nothing was averaged and nothing was grouped: every student is still in the room.

1:48Direction and form ▶

A cloud only ever tells you a few things. First, direction: dots that climb together, dots that trade places, or dots with no direction at all. Second, form: the dots keep to a straight band, or they bend. Our class falls, so students further right tend to sleep less, and you can see the ones that do not. Step three is the one that people read wrong almost every time: they look at how steeply the band falls.

2:21Same numbers, second class ▶

Now the second class, with exactly the same twenty-four screen times and the same twenty- four sleep numbers. All I changed is which sleep number belongs to which student. So the average is the same, four hours and seven and a half. The spread is the same too: s, the one number for how spread out a list is. Even the two histograms are the same, bar for bar. Before you look: does that second class have to look like the first one?

2:59The pairing is the difference ▶

Class B's histogram is identical to class A's, of course, because all I changed was the pairing. The averages are identical as well, four hours and seven and a half in both classes. So here are the two clouds. Class A is a band you could almost draw with a ruler; class B is a shapeless blob. Count it out: in class A the twelve lightest phone users sleep eight point two hours a night. The twelve heaviest sleep six point eight, which is one point four hours of sleep less. In class B both sides land on seven point five, so there is no gap at all. Everything a one-column summary could see was equal, and everything that mattered was in the pairing.

3:51Step three: how strong? ▶

So here is step three: how strong is that link? Here are two more classes, on exactly the same axes. Class C's band drops two point four hours from left to right, and class D's drops only one hour. Steeper looks stronger, but steepness on its own will not tell you. Look at the dots instead: in class C, two students with the same three hours on the phone are ninety minutes apart in sleep. In class D that same gap is eighteen minutes. Strength is how tightly the dots keep to the band, compared with how far the band itself travels. One warning: widen the axes and the same cloud looks tighter, though no dot has moved. And some dots do not sit near the band at all.

4:45Step four: the odd ones out ▶

Step four: look for the dots that do not fit. Here is another class of twenty, and one student sits far off the band. Now find that student in the two histograms: both of them call this student perfectly ordinary. Only the pairing shows that they are not, and that dot is worth a question.

5:09What a cloud cannot say ▶

And then there is the question a cloud can never answer, because it shows a pattern and never a reason. Our band falls, but nothing in the picture says the phone took the sleep away. A week of heavy homework, or a house with no phone rules, could be pushing both of them around.

5:29One look back ▶

One look back before we finish. Last video you measured spread with s; the one before that, you stacked numbers into bars. Both of those summarise one column at a time. So here are class A and class B again as histograms only: which one is the tight cloud? You cannot tell, and that is exactly why the scatterplot exists.

5:56In one picture ▶

Here is the one picture to take away. A dot is one person with two numbers, and the pairing is the whole point. Read the direction, read the form, and read how tightly the dots keep to the band. Then look for the dots that do not fit, because those are the interesting ones. And remember those two classes, sharing every single number and sharing nothing else —

6:25Next: one number for a cloud ▶

— which leaves one obvious question: can you put a number on how tightly a cloud holds together? You can, and it is one of the most quoted numbers in statistics, and one of the most misread. You will meet that number next time. And if a picture ever showed you a link that was not really there, tell me in the comments. And if you want to keep learning, subscribe, the next video will find you. Until then: happy learning.