 Hi, this is Dr. Don, and I want to spend a few minutes showing you how you can use the chi-square test, the one-way chi-square test, to answer some questions about categorical data. Categorical data is data that is counts. We have a question in which we have counts. And here the information is about opioid deaths in the United States in 2017. It's broken down according to age groups, and there are seven age groups there, and we have the counts, the number of people who died in each of these age groups in the United States from opioids in 2017. And I have a few states here as well. Now I'm going to focus on Florida, which I have highlighted in green. And I see we have these counts, but I have two questions that I want to answer. First of all, is there a significant difference in the frequency distribution for Florida and a uniform distribution? That's a way of saying, are these really significantly different than just an equal number of counts for each of those categories? The second question is, is the Florida distribution significantly different from the United States distribution? So we can answer those two questions using the one-way chi-square. We're going to, first of all, start by getting the fractions for Florida and the uniform distribution. If you think about it, we've got seven categories. So we should have one seventh of the Florida total count in each of those cells. So let's calculate that fraction just equal one slash seven. And so I get that particular fraction, about 14.3%, and I can highlight that and then drag it down. And you can see that the total, which is important for quick counts, is one. Now I'm going to do the same thing in a slightly different way for the U.S. fraction. Here I'm going to hit equal. And I'm going to go over here and get the count in that first category and divide it by the total United States. And I'm going to use Excel's lockdown function here, F4, to lock down that denominator. And it's 0.17. I've got a little formula there which just multiplies this times 100 to convert that 2%. So you can see the percentages. And I drag that down, and you can see that we have, again, critically, one for the fractions of the U.S. and 100 for the sum of the percentages. You have to have that in order to use quick count. So let's go to quick count. Okay, I'm at quick count, our one-way calculator, and we're interested in this part down at the bottom. So I'm going to scroll down to there. And there are two ways to enter data. I've got a more detailed video showing you this. I'm just going to click on the second option, which allows me to paste in my information, and that moves a lot faster. I'm going to go back. And the first thing I want to do is to copy my categories, highlight those, right-click, copy, go back to quick counts here. And I'm going to go into my categories, right-click, paste. Now I'm going to go back to my Excel there, and I'm going to get my Florida observed copy, go back to quick count, and I'll paste in the observed. And now I'm going to use the fraction that works best, I think, when you have an odd number of categories. So I'm going to click on fraction, expected. Go back to my Excel, and get my Florida fraction, the uniform fraction, copy, go back to quick counts, paste it in, and then click calculate. And we have our results. And this is what you need to get a screenshot of and paste into your report. You've got our car score statistic in which, unfortunately, quick count doesn't give you the critical value, so that doesn't help you a whole lot. But we do get our two-tail P-value, which is less than 5%. So this means it's statistically significant. There is a difference between the uniform distribution that was expected down here. You can see there's the expected percents, and there is the expected counts. You can see those little extra digits there, and there is a significant difference. So the Florida distribution is different from a uniform distribution. So let's go back now, and let's look at the comparison with the United States. This time I'm going to go back to our table in Excel, and just to make it easy for me, I'm going to grab the U.S. fraction, copy that, go back to quick counts, and then I'm going still in the fraction expected. Go here and replace that with these new expected fractions, and hit calculate again. Okay. Here we also have a statistically significant result, less than 5%, a different chi-square statistic. And here are our expected counts and frequencies. You can see there's a big difference there between Florida and the U.S. distribution. So I hope this helps you. It shows you two ways you can use a one-way chi-square to test your hypothesis.