 Suppose a manufacturer of house paint has developed a new formula for their paint, and they want to see whether it will weather better than the current paint formula that they use. In a classical hypothesis testing framework, they would have what are called two hypotheses, a null hypothesis, and an alternative hypothesis. In the hypothesis testing framework, the null hypothesis is that really nothing interesting is going on, so the new paint formula and the current paint formula work just as well as each other. Nothing's there really. The alternative hypothesis, which is what we usually are hoping to show is true, in this case would be that the new point paint formula really does weather better than the existing paint formula, that is it lasts longer. If the null hypothesis is the reality, it means we live in a very, very boring country where there's really nothing to be interesting to be discovered. Nothing's there, and in the video this is called boring land. If the reality is, for example, that the two paints do just as well as one another, that's not really very interesting. We were hoping to find something more interesting than that. On the other hand, we might live in a world where one of the paints really does much better than the other one. The alternative hypothesis states that if we happen to live in that world, then there's something interesting going on. And so in the video we've called this interesting land. The decision that we make after we've gathered data is going to be to try to decide which world we live in. Do we live in boring land and really these two paints work just as well, or do we live in interesting land? I'm going to put the decision in between the two worlds. We might wind up rejecting the null hypothesis, or we might end up not rejecting the null hypothesis. And I'll point out before we go any further that in the end we will never 100% know whether we've made the right decision or not. Whether we've made the right decision depends on which reality we live in, and we just don't know for sure which one we live in. But we could look at four different possible outcomes. What if we live in boring land? So there's really nothing interesting here. There's nothing interesting to be discovered, but we reject the null hypothesis and conclude that, for example in this case, the new paint formula works better than the old. It really doesn't. It really doesn't if we live in boring land. So that would be an incorrect conclusion. It's correct based on our data, but it happens to be leading us to conclude something that's not true. That's called a type one error. It is sometimes called a false alarm. And in the video called SADSEC, this outcome is represented by a character. The character in this video which represents the false alarm is Chicken Little. Chicken Little represents this outcome because in the children's story, Chicken Little, she's the one who screamed the sky's falling, the sky's falling, when really it wasn't. It was a false alarm. On the other hand, if we live in boring land, and so in this context here, the paint formula, new, and old both work just as well as each other. Nothing interesting. There's nothing interesting there. And we fail to reject the null hypothesis. We've made a correct decision. We in fact have correctly concluded that our data really don't support that the new paint works any better than the old. It's a correct decision, but it's not a very interesting one. It's so, in fact, boring that I'm going to write hoe home here. You do not want to land here. You might land here, of course, if, I mean, in a sense you do want to. If you really, if the null really is true, then that's where you want to be. But you wouldn't be doing this research if you really thought the null was true in the first place. The character in the video that corresponds to this outcome is the president of boring land. It's a correct decision, just not a very interesting one. What if we live in interesting land? What if this is the reality? The new paint really does work better than the old. Well, we'd sure love to be able to show that. If we do show that, if our data do lead us to reject the null hypothesis and conclude, aha, this paint formula, this new one works better than our current one. That's a correct decision. But notice how different the character of this is. Correct decision is from this one down here. This was the correct decision to not discover anything. That's pretty boring. This is a correct decision to say, hey, I've discovered something. Aha. This is really where you want to be. You always want to be up here. This is, you do research hoping to reject the null in favor of the alternative hypothesis. And if you do that, and this is the reality, then you're just great. The greatest character of all in this story is called Power Princess. And she corresponds to this outcome where everybody wants to be. You want to be here. You're doing research to try to reject the null. And if you do, and that's the correct decision, then you're happy. But the name of the video is SADSAC. Core SADSAC, the type two error. He lives down here. He lives in interesting land. Type two errors occur when you live in a world where there is something interesting to be discovered, but you've failed to discover it. Think of rejecting the null hypothesis as discovering something. And if you fail to do that, even though it was there to be discovered, then you've made a type two error. And it is pretty much the most pitiful thing of all. Poor poor SADSAC. He lives in this interesting land where there's things to be discovered, but he fails to discover those things. In this case, in our context of paint, this would be, wow, this new paint works better than the old paint formula. And if we could only show it was true, we could make better paint. But our data, perhaps by chance, our data have not provided sufficient evidence to reject the null hypothesis. And so we've just made a type two error and failed to discover something interesting. It would have been helpful if we had.