Hello. Welcome back. In this tutorial, we're going to discuss on eye focus time experiment. In this experiment, a human performance analyst conducts an experiment to study eye focus time. There are seven factors; sharpness of vision, distance from target to eye, target shape, illumination level, target size, target density, and subject. So the experimenter decides to run a screening design. They decide to run a 2 to the 7 minus 4, which is a resolution three design. We're going to have main effects confounded with two-factor interactions. So here's the design. It's an eight run design, a 2 to the 7 minus 4, and we see that we can start off with A, B, C as the basic design, and then we're going to let D be confounded with AB, E be confounded with AC, F be confounded with BC, and G equal to ABC. So these are the eight treatment combinations in that design. The experimenter analyzes this first stage of the results and they see that A, B, and D, and of course the alias chains are the largest effects. So one interpretation could be that it's the main effects, A, B, and D, but another interpretation might be that it's the main effects A, B and the AB interaction, since AB is confounded with D. Another one might be the main effects BD and the interaction between B and D are the active effects, because BD is confounded with A. Also it could also be A, D and the AD interaction since AD is confounded with B. So since all four of these are logical possibilities, the experimenter decides to fold over this design. They're going to augment it with an additional eight runs to try and figure out which one of these four scenarios is more likely. So here's the augmented design. We're going to fold over this design and add an additional eight runs. In this design, all of the effect or all of the treatment combinations are completely reversed. So everything that was at the low-level in the first design is now at the high level and vice versa. So here's those eight runs and their responses. In JMP, I'm going to show you how we can augment a design and then of course, how to analyze this stuff. So let's open up JMP. I have the original design here, we could easily create this 2_7 minus 4 by going into DOE and going to classical in screening design and selecting this specific design. I've already done that and entered in this data. So we have this table already to go, but now we know we want to augment it. So I'm going to go to "DOE" and go to "Augment Design". Then once we're in this dialog, I'm going to cast Y into the response role, and I'll select all seven factors and add them in as my X factors. I'm going to click "OK", and now we see that we have this augment design dialogue. There's a checkbox here to group new runs into separate block. This is usually a good idea, I'm not going to do it today, but it's usually a good practice. But then we have some augmentation choices down here, we can replicate, add center points, perform the fold over, add axial points, space-filling, or even finds an optimal augmentation strategy. But since we're going to do a fold over, I'll click that, and it says choose which factors to fold over. I'm going to select them all, we're going to fold over all seven factors, and I'll click "OK". Now, here we see the whole design. The first eight runs are the runs that we've already performed, and the last eight runs, runs nine through 16, are just the fold over of the originally. So I'm going to make this table, and now we see we have a new data table and it has original eight runs, and then added eight runs. So we can go out and perform these additional runs in entering the data. So I've already done that in another table. So here's all 16 runs, the first original design plus the fold over and all of our response data. So I'm going to run this model script over here. The original model just has the main effects. I'm going to add in all the two-factor interactions, just going to use this macro here that says factorial to degree. I obviously I'm not going to be able to fit all of these two-factor interactions, but I'm going to let JMP tell me that basically. So I'm going to click "Run" and we'll see JMP says, oh, AG is confounded with BC and DE, and AF is confounded with BE and CD, and so on. It lists all the relationships between the two factor interactions. I'm going to make half normal plot. So I'll go to "Effect Screening", "Normal Plot" and JMP is saying, hey, I'm not going to be able to fit all those two-factor interactions because a lot of them are confounded, so it's just going to plot the first one, and that's okay with me. So I'm going to say okay. If we look this normal plot, I'd like to switch it to the half normal, we see that B, D, and the BD interactions are significant. So that was one of our original possibilities. So now we know that it's really B and D that are important factors in the interaction. We can screen out the other factors and focus in on these two. So that's how we can augment fractional factorial design with a fold over and also how to analyze it. Thanks.
