 Our final chapter, chapter 12, is called Chi-squared. And aside from introducing you to a new Greek symbol, Chi, this is the only chapter we have that allows you to work with categorical outcome variables, like yes, no. That makes it useful. It makes it very flexible. So in terms of what we're going to learn in this chapter, we're going to learn, again, the difference between quantitative outcomes, which we've had with everything else, and categorical outcomes, which is what we have right now. We're also going to look at something called contingency tables or cross tabulations, where you take two variables, for instance, whether somebody graduated from school or not, and whether they have a job or not, and look at the association between those two things. There's also a kind of Chi-squared that's called a one-way or one-factor, where you're simply looking at how common things are in categories and to see if they match what would be your expected outcomes. How many people do we expect at random to fall into each of these categories? And is it different from what we would have otherwise? So this makes it a very flexible procedure. And in terms of why you would learn this, it's because this is one that you can actually calculate by hand. It is the only one that works with every level of measurement as an outcome. And if you have nominal, it's your only choice. And in a lot of situations, it's the preferred method. If you're looking at an outcome that is yes, no, then this is gonna be your best bet. So if you're looking at something like in marketing research, did somebody click on a site or not? Did they make a purchase or not? Did they come back or not? Any one of those would be great for a Chi-squared analysis. And if you wanna look at associations between categorical variables, you wanna say are people who come to our website on mobile versus desktop computers more likely to make a purchase, yes or no? And those are useful questions in terms of what you can use it for. Well, think about, for instance, if you do a favor for somebody, yes or no, you did one, are they more likely to do a favor for you in the future? So those are both categorical. And you can look at the association. Hopefully people understand the principle of reciprocity and they'll do. The favor for you. Or you can think about graduating with your degree and employment. You have the degree, yes or no. You've got a job that in your field, yes or no within a few years. Or you can think about something if you have children, I do. Did you go to parent-teacher conference? Those are inconvenient. I don't like going to them. But I know I learn important things. And then does your child pass the class? And so there's an association between those two categorical variables. That's an intuitive version of Chi-squared. Something that you'll find is very flexible and that you can apply to any time that you can take the outcome that you're interested in and break it up into categories. And with that, this is our final chapter. And hopefully the whole course will have been something useful for you either explicitly because you maybe are gonna do some research in the future. But the general principles and the concepts, you will see how you use them in an implicit process every single day.