[MUSIC] So in the last slide we said that comparing two groups, the control group and the experimental group, is the name of the game. And we said that we're trying to take some test statistic and measure the difference between those two groups. But how different is different enough to be significant. In other words, how do we know that the difference that we saw in the experiment is not attributable to just chance. Well the answer is, we don't. But we can calculate the probability that is attributable to chance. And that's what the p-value is. Okay, so the p-value is the following. If you were to repeat the experiment over and over and over again at the same sample size, what percentage of the time would you see results that were at least as extreme as the ones you got in this experiment? And this is all assuming the null hypothesis is true, so let me say that again. Assuming that there is no difference between the groups, the control group really is the same population as the experimental group, the treatment has no effect. If I were to do the same experiment over and over again, what percentage of the time would I see a difference in the treatment group, anyway, just by chance? Okay, and that's what the p-value is. Fine, so, more terminology, you may think about two-sided versus one-sided. So, two-sided is if we're measuring something in terms of the absolute value, right? So the p-value is two times the probability that X is greater than the absolute value of the measured value. And if the test is one-sided, it's either greater than or less than, and here the notation that we're using is Mu, which is the mean and Mu sub-zero, which is the mean of the population of the null hypothesis. So this screenshot is taken from a nice applet that you can find online and play with here. But here if the null hypothesis is that the mean is 325, and we're doing a two- sided test where mu is not equal to 325. We're saying it must be something different than that, either higher or lower, right? And the sample size is 10 and the observed sample mean is 328. Then when you click the show P button on the applet, what you get is, it computes the P-Value for you, and shows these colored regions. And so these colored regions, the area to that curve is the P-Value. Okay? So, that's the probability that it's at least as extreme as the measured value. Here the only change I've made is that the sample mean was 329 instead of 328, which means it's even less likely that you would see this by chance, and so the area into those curves is even smaller. And you notice the P-Value changed. The P-Value went from 0.0574 to 0.0114, okay. So, in order to make some sort of a decision, did this treatment work, right? Do we invest in this treatment? Do we move on to the next stage of trials? We need of some sort of threshold, some sort of a cut off for the P-Value. So what is that cut off? Well, it's 0.05. Why? No good reason. It makes the math work out. So this is a 1 in 20 chance. If you can show it's more rare than a 1 in 20 chance, then that's deemed to be good enough, okay? This is the subject of a lot of controversy depending on what sort of literature you're reading. And we'll talk a little bit more about this in a few segments, but that's all I'm gonna say about it right now. So 0.05 is what people are looking for. All right. [MUSIC]