In this lesson, we discuss Design of Experiments, or DOE, which allows you to simultaneously test the effects of multiple input variables on output variables. QuikSigma makes the investigation simple.
We’re back to the simulator to start to learn about one particular kind of designed experiment. This is the 2 to the K factorial experiment. Now, the key to that is down here in this matrix. It’s set up for 8 input variables. I’ve stripped out five of them so that we can have a simple example. What we have here is a matrix of minus ones and ones and if you look down this column, I’ve got -1, 1, -1, 1 and so on down. Here I’ve got -1 twice and then +1 twice and then I’ve got
0:49-1 four times and +1 four times.
In a 2 to the K factorial, we use two states for each input variable, a high and a low. Minus 1 represents the low and plus 1 represents the high. So what this says is that I’m going to put variables A, B, and C in their low state, and then I’m going to measure the output which is going to be my Y. Then I’m going to put A in the high state and B and C in the low state, and I’m going to do the same thing. I’m going to measure Y. Well, if you think about it a little bit, if you’ve got two states per variable, and three variables, then the maximum number of unique combinations that you can make is 2 to the 3rd power or 8. So you notice I’ve got a set of eight combinations, unique combinations, of input variables here and so this is a full factorial. That is, that I’m using all possible combinations.
There are some nice fractional designs, we’ll get to those and in due course, but for right now, this is the one we want to look at. It’s very illuminating. Up here in my settings, I can set up a low and high for each of the eight variables. Well I don’t have to worry about D through H, and I don’t have to worry about Y for the moment, and I can set my nominal value. Then the factor, I want that moved by to create my low and my high. So 300 + 4 is 304 and 300 – 4 is 296. So this is my high value. This is my low value. Here’s my high for B, and my low, and my high and my low.
Now, if we look over in this matrix, I can just ignore D through H because I’ve set you up a simple three-factor design. This is the same thing as this matrix. Here we go, low, high, low, high, and if you look over here, low, low, high, and then four lows, and four highs. So these two are the same thing, except this is in coded units and this is in native units. The strategy then is I’m going to put my A variable at 296, my B variable at 50, and my C variable at 1.7, taken observation.
The nice thing about this structure is that it’s a very robust structure and it will allow you to simultaneously test easily up to five variables and all of their possible interactions for the same number of observations that it takes to do a t-test. When we get about five variables there are some other things that we like to do, but 2, 3, 4, 5 variables a full factorial 2 to the K design is an excellent choice.