 Hi, this is Dr. Don. I have a problem out of Chapter 9 on ANOVA's. This is Section 5, which is on the two-way ANOVA's. And in that section, we have both the regular two-way ANOVA and the repeated measures ANOVA. This is the repeated measures, and I'll show you why. We told that we have a two-way table, which gives a two-by-two factorial, which is a two-way, obviously, with two observations per factor. The factor of the treatment levels, and we have two observations per treatment level. That means this is a repeated measures two-way ANOVA. But to solve this, using stat crunch can be cumbersome. Using pure Excel can be cumbersome. Using a combination of the two, maybe a little bit easier, as most folks, I want to show you that way now. Let's look, and we're going to look at our data. And we've got data that's presented in a matrix rather than in a customary data table format in which you have a column with your IDs of your records and one record in each row. This is a matrix which stat crunch doesn't like. I'm going to click on Open in Stat Crunch, and we've got our information here. And if we look at this, you can see it is kind of funky. If we expand it, you can see that we've got a column with a blank in it, no name, which stat crunch doesn't like. And then factor level A, an underscore, factor A2, an underscore. And then we've got factor B-level 1, and this is B-level 2. So again, we don't have our standard one record per row. And so we need to create that in order to make stat crunch happy. I'm going to go here and relay this first one row variable. And those are our treatments. Next is going to be our column variable, which would be our blocks, or our independent variable if you're looking at it that way. And the third one, I'm going to put our values. Okay. So we're going to start here. We want factor level A, so this is going to be A1, enter, A1, enter, A1, enter, A1, enter. We've got four of those. And then I've got A2, enter, A2, enter, A2, enter, A2, enter. And I probably need to make those all look the same so that stat crunch knows that. Okay. Now I've got my treatments levels in there. And then for my column, I've got B1, another B1, and then B2, enter, B2, enter. And then I'm going to copy those and just paste them so that we've got our two treatments and then our eight observations there, one for each level of B. So then we need to put in our values. And I found the easiest way to that is just if you can be careful, B1, A1, or those two, I'm going to copy those, paste them in. B2, A2, or those two values, copy those, paste them in. B1, A2, copy those, paste them in. And B2, A2, copy those, paste them in. I don't know why Pearson couldn't arrange your data that way. But anyway, now we have the data set up so stat crunch can use it. And most other statistics software likes it this way. I'm going to go to stat, ANOVA, and we're going down to two-way. We're not going to do the repeated measures initially. It's just a funky thing about stat crunch. You're going to do the basic ANOVA first of all. I'm going to click on that. And our responses over here are in the value column. Our row factor is in row. That's our treatment. And our blocks are in the column. We want to plot the interactions. I want to display the means. And I do not want to fit the additive model. I want to see the interaction. If I select that, it will not show the interaction. And that's not what we want. We don't need to key on this particular problem. So I'm going to click Compute. And now we've got the information we can start to answer the questions. I'm going to slide them over here for a bit and close that. The first question, identify the treatments for the experiment. Choose the correct answer. There are four treatments. And if we look in our data here, whoops, I'm going to move this down, we've got our four treatments there. Each treatment consists of two levels of the first factor with two levels of the second factor, which makes sense. And I'm going to go on down there. We need the treatment means. Now we go back to our output there. And if you remember, I selected show the means table. They want X11, which is our A1B1, that's 32, and 44.7 for A1B2. Those are the two values there. And then the 21 and 22, 15.25, 25.6. So we've got that answer. Next, it wants us to plot, whoops, the treatment means using the key level 1 factor A, level 2 factor A. So that means that the A is going to be on the y-axis and the B is going to be on the x-axis. So let's look on our plots here. The first plot has A on the x-axis. That's not what we want. Click on the second plot. And we've got B on the x-axis and A on the y-axis, which is what we want, A1 and A2, which matches what they want. And so then we just need to inspect. The first one shows an interaction because the lines intersect. That's not our chart. That looks pretty much like our chart. That does not match our chart. And these are both flat. That doesn't. So it would be B based on the chart we have. The next thing, it says, do the treatments appear to differ? Yeah, we see a big difference between treatment 1 and treatment 2. On both of these charts, there's a big difference. So they do differ. Do they appear to interact? Again, no. We don't have the lines intersecting there. And we don't have the lines intersecting there. So we don't see an interaction either way. We need the ANOVA table for this experiment. I'm going to click all the way back to the beginning there. There's our ANOVA table, 660 for the row variable, which is B. The column variable, which is, I'm sorry, is A. The column variable, which is B. The interaction is AB. And then we've got the error in the total. We've got all the values we need to fill out this table. The next part is where things go off tracked with stat crunch. We can answer this first part. Test determined whether the treatment means differ at alpha 0.05. Does the test support your visual interpretation from part A? The visual, obviously, was that there is no interaction, but there is a difference in the treatment levels. And so the null and alternative is no differences exist among the treatment means. At least two treatment means differ. Those are the nulls. They want the test statistic and the p-value for that. And unfortunately, when you do the basic ANOVA for the two factor, it does not give you the overall p-value and statistic for the whole test. It just gives you the important parts. But I'll show you how to do that, and that's why we need Excel. So I'm going to pause here, and I'll pick up in another video.