Hello. In this tutorial, we're going to talk about the filtration rate experiment. This experiment is a two to the four factorial, and it use four factors to investigate their effect on filtration rate of a resin. The four factors were temperature, pressure, mole ratio, and stirring rate. This experiment was performed in a pilot plant. You'll notice one thing special about this experiment, if we look at this data table, is that there are only 16 runs, and this was a 2_4 factorial. So that means that there are no additional replicates. So we call an unreplicated design. So I'm going to show you how we can analyze an unreplicated design. By doing that, we'll use normal and half normal plots to help us figure out which factors are important. So let's check out this experiment. I have this 2_4 or 16 run experiment, all ready to go. In this table, all of the factors are coded at negative one and one. So I don't need to tell JMP to change anything, this data table is already coded for me. We have a response filtration rate. So if I go to "Analyze" and "Fit Model", and I enter filtration rate is my response, and I select all four factors and use my sorted macro factorial sorted here, I'll get all four main effects, all six two-factor interactions, all three three-factor interactions, and a one four-factor interaction. So I've entered them all into the model effects. If I click "Run", it turns out we're not going to get much here. That's because with a full model and an unreplicated design, we don't have enough degrees of freedom to estimate error. So I can come up with parameter estimates and sums of squares for my factors, but I can't do any statistical testing on them because I have no estimate of standard deviation. So what we're going to do is look at half normal plot to try and help us figure out which factors are active. So if I go to the red triangle, and go to "Effect Screening", and go to the "Normal Plot", we'll see this normal plot pop up. We'll have some parameter estimates that we use links method and get a pseudo p-Value from a pseudo estimate of error. But if we look at the normal plot, I always like to switch this to a half normal plot. It helps me to see how big things are in magnitude. We see that the A, AC, AD, D, and C effects are pretty large on this plot. JMP's somewhere highlighting this A, B, D interaction, although if we look at its pseudo p-Value, it's not very big. So if I wanted to, I could just look at these large effects and notice that there's no B in these effects. So we could rerun this model without B and collapse a 2_4 onto a 2_3 with a replicate. This would give us enough degrees of freedom to estimate error. So I'm going to hit "Recall" and bring up my last analysis, and I'm just going to select B and remove it. Clicking yes will remove all effects with a B in it, and that's exactly what I want. So now I just have my 2_3 where my three factors are A, C, and D. If we click "Run", we'll see now, I can estimate error and I can perform some statistical tests and see that ACD and CD are not very large, whilst A, D, and C, and AC and AD look big. So we could even reduce this model if we wanted to by removing those insignificant terms and checking out our new model. That's how we analyze an experiment an unreplicated 2_k by using half normal or normal plot to help us figure out which affects are active. Thanks.
