Time to practice. Suppose you have two types of printers. Printer AX-2 and printer AX-4. You would like to know if one of these produces prints of higher quality. And you measure this as uniformity, which is categorized into good, dubious or bad. You do that in a visual inspection. Now, pause the video, load the data into Minitab and try to answer this question before you continue. Good luck. Okay, did you manage to find the answers? The first step before doing anything is to find your Y-variable and your X-variable. The Y-variable or the factor that is being influenced is quality. Measured in terms of uniformity. The X-variable here is printer. The Y-variable is categorical. And your X-variable is also categorical. Now, let's take a look at the tree to see which method we should use to analyze this data. Since both variables are categorical we should perform a chi-square test, do you remember the steps of a chi-square analysis? The first step is to copy across tabulation into Minitab or have Minitab make one for you. As you can see, the data is already in the correct form, so you can simply Copy and Paste this table into Minitab. The second step, is to perform the main analysis and calculate the p-value. This is to find out whether there is a statistically significant relationship between your two variables. We want to know whether the type of printer affects the uniformity of the print. So, our null hypothesis states that there is no relationship between the type of printer and the uniformity. And the alternative hypothesis is that, the type of printer influences the uniformity of the prints. Let's take a look at how to let Minitab calculate this p-value for us. I have copied my data into Minitab with Printer in the first column, AX-4 and AX-2 and a number of Good, Dubious, and Bad prints in the next three columns. Let's make a chi-square analysis. We go to the menu Stat > Tables. You can find a Cross Tabulation and Chi-Square test here. Now, you have to select do we have raw data or do I have a summarized data in a two way table. Which is of course here the case. Now Minitab asks you which columns contain the table? Well that's Good, Dubious and Bad. You have the option to give your table labels. Well, want to have label would arose which are the printers. Lets go to the chi-square test. You ask for a chi-square test and also ask for expected counts which I'll show you what they are. OK, OK. And Minitab gives you this session window output with a table with all the different values in there. Let's have a look. We have 10 good prints from AX-4. That's just the data and it says here for cell counts that's the count. Underneath it gives you the Expected count which is 14.50. And the expected count is the number of good prints you would expect from the printer AX-4, if the quality of a print or uniformity of the print was unrelated to the type of printer it was made on. So the expected count is the number of prints we would expect if the two variables are unrelated. The session window shows us the cross tabulation with expected counts. As you can see, the p though used smaller than 0.05. Which means, that the effect statistically significant and the alternative hypothesis can be supported. This means that the difference in quality of prints is not due to random fluctuations and it can be attributed to the printer. Now, let's have a look at the data. Printer AX-4 was expected to print 14 good prints, if the quality of the prints is not related to which printer you take. It was also expected to print only 11.5 bad prints but it printed 17 bad prints. So printer AX-2 performed much better than And it should perform when the quality of the prints is just due to random chance. And printer AX-4 printed worse. In summary, the Chi-squared analysis showed us a p-value of 0.017. Which means, that we found this statistically insignificant relationship between printer and uniformity. Printer AX-2 performed better than we would've expected and printer AX-4 performed worse.