 Hi, this is Dr. Don. This short video is going to show you how to do a Chi-square one-way goodness-of-fit test using the XL Chi-square calculator you can download from the website. In this particular problem, we have a manager of a radio station, I'm not sure where, she thinks that the taste of her listeners has changed. Back in 2018, she did a survey, which is labeled here as the historical survey. She got this percentage breakdown of the listeners in her station that participated in that survey. She redid the survey in November of 2019, and these are the counts of the people who responded to that survey, and she wants to know, has something changed? Are the listeners expecting something different? Recall for a one-way Chi-square, the null hypothesis that we're testing is, is the observed frequency distribution, the counts, the same as the historical, the specified in this case? The alternative is, is the observed frequency distribution, is not the same as the historical? So now, let's use this calculator. It is pretty self-explanatory. It's got a bunch of instructions here that can be helpful, but it's really very easy to use. We need to enter the number of categories here in B2, and we've got one, two, three, four, five, six, so I put six there, and that is used to calculate the degrees of freedom combined with the level of significance that I'm going to leave as the normal 0.055%. Now, you can just leave these labels alone, or what I like to do is go over here to my data, and I want to copy those, highlight, copy, and I'm going to go here, click in that cell. I'm just going to paste the values, and that will help me when I put my report together. I need to put the observed counts, so I'm going to go back here to my survey data, highlight that, right-click, copy, and go here and click in the values again, and that gives me my counts. Note that I've got a bunch of decimals showing here. I put this in the calculator because your observed counts have to be integers, and sometimes when you're working with data, you can have something hidden behind what looks like an integer. And doing it this way, if there's something hidden, it will show up. But these are all good. They're all integers. I need to get the expected proportions. In this particular calculator, you enter those, and it gives you the expected counts. So I'm going to go over here and take this data, copy these percentages, control C, and go click in that cell and paste in my values again. And you can see it converts those percentages to decimals, which I said you can enter directly as a decimal or as a percent, or you can enter a fraction by using the Excel formula equal whatever fraction you want there. This calculator gives you the expected counts, and as I said, it gets the degrees of freedom from K up here, minus 1, and that combined with the 5% significance gives us our critical value of 11.07. We've got a chi-square statistic calculator, 63.089. And by looking at that, one of the methods we use to determine to reject the null is, if the test statistic, the chi-square statistic, is greater than the critical value we reject, so that method tells us to reject. But what is this down here? We've got this funky looking number, 2.79 e to the minus 12. Well, if Excel doesn't have room to put all the zeros, it will format your answer as scientific notation. And that means this minus 12, you would move the decimal 12 places to the left. So that will put 11 zeros in front of that 2.79, which is very, very small. And the calculator here tells you, hey, that's scientific notation. Your p-value is very small, less than 0.0001. Down at the bottom, the last thing you need to check is to make sure you haven't violated an expected frequency assumption. And in this case, we have not. We're both okay. I've got a how-to there that will explain what you do if these are violated. The one that's most critical is the no cell less than one. The other one, less than 20% of the cells, less than five. If that is violated, you get a warning, and then you can do some more analysis there. What I like to do if I violate either one of these to see if I can collapse some adjacent categories to give me a better distribution, so you can try that. But in this case, you're good to go. You've got a p-value there that's very, very small, which tells you to reject the no. You've got a very large chi-square statistic compared to the critical value, which tells you to reject the no. So you're good to go. I hope this helps.