I will explain when it is suitable to perform a Chi-square analysis. And how perform and interpret such an analysis. Let's take a look at a tree diagram that we use for testing influence factors. If you have a Y variable or see the queue that is categorical and an X variable or influence factor that is also categorical, we have to perform a chi-square analysis. Let's take a look at the steps of the chi-square analysis. The first step is to make a cross tabulation. You can either do this by copying a cross table into your worksheet, or by having Minitab make one for you. The second step is to take a look at the p-value. The p-value shows you whether or not the effect you found is significant. Okay, let's take a look at an example from a hospital. Assume you work at the surgical department called A1. Sometimes patients are placed at department A4 because A1 is full. There are three different specialists that work in this hospital department. Let's call them specialists P, Q, and R. In one of the departments, patients stay longer than on the other departments. Could it be that the treating specialist is of influence? Therefore, you want to know if the specialists work equally frequently on both departments, or if they prefer one department over the other. The two departments are your Y variable. This variable's categorical. The three specialists are your X variable, or your influence factor. This is also categorical. So, we have to perform a chi-square test. This is what our measured data looks like. Now pause the video, load your data into Minitab, and then we will continue. Once you've loaded your data into Minitab, you should have three columns, one with Patient, one with Specialist, and one with Department. You see that Minitab automatically detects that these two columns, Specialist and department are text or categorical variables. Let's make a Chi-square analysis. Therefore, we go to Start, and you will find it down in the menu Tables. And there you can go to Cross Tabulation and Chi-Square Analysis. In our rows, you will put your Specialist, and for the columns you can put in the Department. Furthermore, we want to ask for the row percentages, and the column percentages. If you go to the button Chi-square, you can ask for the Chi-square test which will give you a p-value. OK and OK. Your output is displayed in the session window and it looks like this. Let's take a look at the output. Remember that our first step of Chi-square analysis was to take a look at the cross-tabulation. Well, this is a cross-tabulation and it gives us a lot of information. The top rows show us how many of these patients were treated by each specialist at department A1. For example, at department A1, 52 patients were treated by Specialist Q. The row below that shows us the percentage of patients in department A1 that was treated by one of the specialists. For example, 38% of the patients that were treated in department A1 was treated by specialist P. The bottom row shows us the percentage of patients that were treated by specialists on one of the departments. So for example, 82% of all the patients treated by specialist P was treated at department A1. Now that we have interpreted the cross tabulation, we have completed step one. And it's now time to check if the results are significant. That is, whether the division of work for each specialist is equally divided across the department or not this is step two. Let's take a look at your output again. Or no hypothesis is that the department is not related with a specialist. The alternative states that at least one of the specialists, has a preference to visit one of the departments. If we look the p-value, we see that it is much bigger than 0.05. This means that we did not find significant results, and we cannot support our alternative hypothesis, and therefore stick with our null hypothesis. Apparently, the department where you are lying does not affect who treats you. Let's summarize. A Chi-Square analysis is a suitable method if you have a categorical Y, or CTQ, and a categorical X variable, the influence factor. The first step is to make a cross-tabulation. Your second step is to interpret the p-value and check if your results are significant.
