 Now, most people are going to appreciate that Jane and Billy, in this case, are going to perform on average on day two. Now, what do we mean by that? Again, 100 people who took the exam in the first place, most of them are going to perform by guessing alone at 50%. Jane and Billy had a lump in their performance at 65% and 35%. The next time around, they're going to behave like the rest of the class at 50%. The correct response would have been 50%, which is the average. Remember, they're regressing back to that mean, back to the average. The best predictor would be 50%. That's right. The best predictor would be 50%. Now, I think it's really important to consider this idea of regression to the mean when it comes to not just a toy example like this, when we're dealing with random responses to a multiple choice test, but taking it outside into everyday sort of life. And imagine then that you are feeling really terrible. You walk into a clinic because you're just feeling bad. You have all sorts of symptoms. You have a sore throat. You have a runny nose. You haven't had any sleep. Everything, the world just seems to be against you. And you walk into a clinic and somebody hands you a vial of water. There's not a single drop of medicine in this thing. And as a result, as a result of taking this vial over a period of a few days, maybe you start to improve. You feel like, hey, I feel fantastic. My runny nose is going away. But it might not be causal. It might just be the regression to the mean. They might just have, their bad luck has run out in a sense. Their symptoms have gone away as a result of the random lumpiness that we just talked about in the last episode. So just like Jane, who performed better the next time around. So she was at 35%. Now she's at 50%. You have the person who walked into a clinic at day one. They took a vial of water. And on day two, you test them again and they improve just by statistical chance alone. And this is really common. And this happens all of the time. And if that happened to you, if that happened to me, I'd be very tempted to attribute that experience to that whatever happened in the interim, to that vial of water and feel like it has healing properties when it's just water. It's completely neutral. Well, let's take this and move it back to the previous example. So we have 100 people taking a true or false exam. The 100 people can't speak a word of English. And again, they take this exam. Now, on average, we expect people to perform at 50%. But again, Jane performs poorly on this exam. And Billy performs well. Now, before we separate Jane and Billy and we go on to the testing on day two, let's do some interventions. Let's give them a vial of water. Or let's give them some brain training or ask them to close their eyes and jump to hop on one foot. And now we go to day two. And then they take the exam again. What do we expect? We expect Jane to regress towards the mean and do a little bit better on the exam. And we expect Billy, the second time, to drop back to regress towards the mean and do a little bit worse. Now, exactly like you said, if that happened to me, if I was Jane or Billy, I would attribute the change in their performance to the thing that I introduced. So I imagine that Jane would think, wow, brain training is amazing. It improved my performance out of sight from last time. And Billy's going to think that vial of water is cursed. It made me do worse. It's formerly, it's called, post hoc ergo proctor hoc. After this, therefore, because of this, we attribute that intervention, that thing in time, to the outcome. That's right. And I think it's really important as one of the goals of this course. I mean, most people who are taking this course might be quite willing just to dismiss people who fall into these tendencies as just being silly or stupid. But that's not enough. I mean, if we can figure out why people tend to believe these things, I think we're getting a lot further in figuring out when they're operating and what we can do about them in that particular case. And so just to make that concrete, let's ask people at home just to answer a few more questions about regression of the mean before we move on.