QuikScreen, Part 2 (Plackett-Burman)

In today’s lesson, we continue with our lesson on with QuikScreen Part 2 in QuikSigma. You can watch QuikScreen, Part 1 here.




Okay, let’s work through an example. In this case, I have some data built-in. So let me go get that. So I put all seven of my variables in their low state and observed the output variable, then I put these three in their low state, these four in the high, an observed again and so forth and filled out my matrix. Now let’s then click calculate and what this brings up is what some people call a scree plot. I kinda tend to favor optical f-test. The idea is that usually there’ll be an elbow here. Scree is the rubble at the base a cliff and so we look for the rubble down here and we think, okay it looks like D, F, and B are active and E, A, G, and C are not.

Now, at this point we do not know whether we’re seeing D or one of these two-way interactions. We don’t know what we’re seeing F or one of these two ways or B and one of its. But we will do some detective work based on the structure of the interactions. Plackett and Berman, who developed this, found a very orderly set of interactions or a construction that produce that, and we’ll use that to our advantage. Let’s go to round two. Okay, all my signs have flipped. Note that all the signs at my interactions have flipped. The signs at my main effect have remained constant. So I’ll get another set of data and I’ll click calculate again.

Okay, once again we see D, F, and B above the elbow and we see E, C, G, and A below. Now we’ve seen these weak variables down here in the mud twice. So that’s good enough for me. We will eliminate those. Now, the other thing that has gone on, is we’ve got some things highlighted in yellow and the ones highlighted in yellow are unlikely to be the active variable. So I can highlight those and get rid of them, I can highlight those and get rid of them, and I can highlight
these and get rid of them. How did we arrive at that? Very simple. As I flipped the signs of my interactions, I watched to see if my coefficients flipped and if they flip when I flipped the interactions, well probably they’re interactions. If they don’t, then they’re probably main effects. So I go down here to 3 and there are several different ways to get this into a state that you need, but the one that happens to fit this particular set of data is that I flipped everything except B. What that will do is it leaves BD negative. I suspect that that’s my interaction because I got both B and D’s main effects. It’s more likely than either these other two and I’ll get a new set of data and click calculate and QuikSigma will say yep, you guessed well. It’s not AG, it’s not CE your model is BD and the BB interaction here. So probably my next step would be a 2 to the K factorial as a confirmatory running with just those few variables.

Now the question you might ask is, what will I do if I have only six variables instead of seven? Well the answer is you just take one of these, probably G, and ignore it and then you know in advance that in the scree plot and in the coefficients, G is going to come up with a zero coefficient. Similarly, when we get over here in the 16 run mode, I may only have the 12 variables. So I may leave 4 of these inactive. Now, the nice thing about this particular design is that it will almost always give you a more clear result with less work than doing something like a quarter or an eighth factorial in the 2 to the K factorial table. So this is our recommended way of doing it and the way we set it up in QuikSigma. Better results, less work.

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