 Alright, so what is a p-value? This video shouldn't take too long, it should be very simple, because p-values are simple. There's not much to them, the idea is very intuitive. So hopefully after going through this example, you'll never have to think about it again. It'll just be natural. So the way we're going to go about this is do this beer and water test, where we're looking at if mosquitoes are attracted to beer drinkers versus water drinkers. That's based off of a study that PLOSONE published. So the idea here is that you have a beer drinking group compared to a water drinking group. And the idea is to see if mosquitoes are more attracted to the beer group versus the water group. In this specific study, we had, I believe it was 25 participants in the beer drinking group and 17 or 18 in the water drinking group. I have the data posted, or I'll link to it in the description, you can check the numbers there. And so what you could do is you could take the number of mosquitoes in a certain trap and count them and get an average over the whole group of participants who drink beer before they got hooked up to this, I think it's called a YOLLA factory device. It's not something I know anything about. And they did the same thing for the water group. They'd have participants drink water and then count how many mosquitoes were in those traps. What you can do is you can take the mean of mosquitoes in the beer drinking group and the mean of the mosquitoes in the water group and calculate this difference. And this is a really important number, 4.4. It's our original difference. And so here is where the debate starts and where the statistical question pops up. You have two sides of the story. You might have the skeptic who says, you know, 4.4 mosquitoes on average is just such a small number, there really isn't a difference. If you drink beer, you shouldn't expect to be visited by more mosquitoes. Then you have a alternative argument where someone says, hey, look, this 4.4 is large. It's something that does make a difference. So back to the argument. What you can do is you can just take the skeptics argument and say, look, if you really don't think that there's a big difference between the beer drinking group and the water drinking group, let's run with that. Let's go ahead and take some of these beer labels and some of these water labels and just switch them around because that should be a meaningless tag, a meaningless label. If you switch those, you'll be able to calculate a difference. And you do this 10,000 times. You just take off a whole bunch of beer stickers and water stickers, plop them in different spots, calculate a difference. Do it again. Take off a whole bunch of beer and water stickers, plop them in random spots and calculate that difference. And you do that 10,000 different times or so. And what you'll end up getting is a distribution of differences. So what I have plotted here is just that distribution of differences. There's a red line that is at 4.4 that we originally got. And so what this is showing is that when you kind of shuffle all these different labels around the beer and the water labels and calculate the difference, it's pretty rare to see an event of 4.4 or higher. That's something that just doesn't happen very often. In fact, you can calculate how often this happens. It's something that happens 0.0006% of the time. That value, that 0.006 is the p-value. That's all there is to it. It's just that proportion of times that you actually see an event greater than the original statistic that was calculated. And so the cool thing is that that's all there is to the p-value. It's a really intuitive idea is that you're kind of taking this alternative universe where beer and water just don't really make a difference. And you're simulating this distribution of differences. And you're just counting the number of times that you see something more extreme than that 4.4. So if you've had a statistics class in the past, you might be wondering why we didn't talk about the null hypothesis ritual. That's the idea where we calculate a p-value and see if it's less than 0.05 and reject the null if it is. Well, that was never the original intention of R.A. Fisher when he created the p-value. So we're going to go back in history a little bit, rewind and talk about what the original motivations were for p-values. The idea here is that we have R.A. Fisher, and we'll go into a little history here. R.A. Fisher is seen as a geneticist and the father of modern day statistics. Fisher was born with poor eyesight. And so every picture you see of R.A. Fisher, he's wearing glasses. And it's kind of this neat like origin story. He would not think about things in terms of like algebraic equations. He tended to think of things more geometrically, and so lots of these original statistical ideas came from a geometric approach to statistics. And he would just kind of use those ideas and then come up with the symbols later. But he was a really interesting thinker and kind of the scientist of scientists. And what he was trying to do when this whole idea of p-values came up was to put inductive logic on the same kind of solidity as valid arguments. So we can think of arguments in two large categories. There's the risk-free arguments. These are the valid arguments that you learn in logic 101. Arguments like all men are mortal, Socrates is a man, therefore Socrates is mortal. There's also a whole nother category that usually you don't talk about in undergraduate education that's starting to change a little bit. The idea of risky arguments, this includes things like inference to the best explanation, testimony, and inductive logic. And inductive logic is what we're gonna talk about here. And that's what Fisher was thinking about was this idea of inductive logic. So what makes inductive logic different from the valid arguments like Socrates' mortal argument is that inductive logic relies on just historical facts. So if you were to say the sun's gonna rise tomorrow, your premises would be something like the sun rose today, the sun rose yesterday, and the sun rose the day before. That's all using this idea of induction. You're saying that something will happen just because it's happened in the past. And it's not a bad way to argue. It doesn't have the same watertight properties that the risk-free arguments have. And Ari Fisher recognized this. So what he wanted to do is kind of make this logical disjunct. And the p-value works as a type of logical disjunct or exclusive or. And the way it works is this, is you do these calculations and you come up with a number. And you say either A is true or B is true. And so A would be either we observed a situation if we're taking the null's opinion. Or the skeptic's opinion. Either we observed a situation that only happens, a very rare occurrence of the time of p-value chance. I'm using air quotes, a p-value chance of the time, like 0.005, 0.005, whatever it may be. Either we observed a rare occurrence or the alternative is true. And that's really what the p-value is. And that's how Ari Fisher thought of the p-value, is now we have this tool, we have this logical disjunct where we can put our statistical arguments in a more watertight framework where we can say one of these two things is the case now. And that's all there is to it, really. There's lots of scientific journals now that kind of throw the baby out with the bathwater and say, you're not allowed to even report p-values. My personal view is that that's a little bit silly, it's just a number. And I do think it says something interesting along with many other numbers. And other journals require p-value and you aren't allowed to publish a result unless your result shows a p-value of less than 0.05. Which is also silly because there's cases where maybe that p-value of 0.05 is not really as significant as you might think. So that's it for p-values. I hope this was useful and thanks for watching.