Thinking about variation

Variation is at the heart of statistics.  It’s everywhere, and without it, data are not very interesting.

Understanding this is central to the tasks we carry out in visualising, summarising and analysing data.  Our goal is to understand patterns in data.  Underlying random variation makes that challenging; we must meet this challenge in applied analytics.

In the video below, a pool player is asked to reproduce the same result repeatedly.

Watch and see how difficult it is to avoid variation.

Transcript

Ian Gordon: Today, we have Ben playing a few break shots for us at the pool table. For all of his shots, he'll be playing from the centre of the D and aiming to hit the front corner of the triangle of balls. We're gonna look at where the balls finish up. Will the black eight ball, for example, always finish in the same spot? What about the other numbers? So, over to Ben with his first break. Nice break. Now, if we just look at the 8 ball with respect to its starting position, it's ended up towards the right-hand side of the table. Most of the balls have finished up in a scatter at the far end, but the blue 2 ball has rested up near to where Ben played his shot. Now, over to Ben, and see whether he could predict where the 8 ball would end up on the table.

Ben: No, certainly not. I mean, really, when I'm trying to break, it's just trying to get a good spread of the balls and you get lucky with where the eight's gonna land. Very sensible response there.

Ian Gordon: Now, let's see if that can be done again. OK, so straight away we can see that the 8 ball didn't even move much from its original position this time. Although a few other balls have made their way up closer to where the shot was played. Over to Ben again and see what made the difference in the resting place of the balls.

Ben: Suppose in my mind it, it, I didn't really have a lot of influence, it's uh, it's just each break is gonna be different, like you try to do the same thing, you try to apply the same sort of force, but every time you actually hit the balls, the, the way it reacts, they're all gonna spread out differently.

Ian Gordon: Fair enough. Now, for good measure, let's see a few more breaks. So, after each break, the balls ended up in different positions. Well, if you've played pool or watched it being played, you won't be very startled by that. That's what we expect. But think for a moment, what causes this variation? Why is it so unpredictable? It's the same table, the same balls, arranged the same way to start with, the same queue, the same player operating with set instructions and making a sincere attempt to reproduce his break shot with the same force and direction and angle. And yet we get major chaotic variation. What are the causes of this? There are several. Two major ones are the slight variation in the brake shot, despite the best intentions. And small differences in the positions of the balls pre-break. These lead to a cascade of different forces delivered to the balls as they collide and disperse each time. Well, this is quite a controlled situation. Many interesting contexts of systematic inquiry are much more complicated and less structured, involving events over time, years sometimes. Human behaviour, the weather. Natural processes and so on. Variation is the big characteristic of most things we want to study and analyse. Learning about variation. How to describe it, how to model it, how to reduce it if possible, how to allow for it in analysis, is central to applied analytics.