Experiments 2A - Analysis of experiments in two factors by hand

Videos used in the Coursera course: Experimentation for Improvement. Join the course for FREE at https://www.coursera.org/learn/experimentation These videos are also part of the free online book, "Process Improvement using Data", http://yint.org/pid Full script for the video: http://yint.org/scripts/2A -------------------- Remember that term "factor" from the last module? Well, our main goal with this module is to achieve confidence, to run and analyze data from experiments when there are two factors. We are only going to use pen and paper only, and everything is going to be done by hand. It's actually a whole lot easier than you think. But, if you already understand the concept of factorial experiments in two factors, feel free to jump ahead; check out the last video, which is a 3-factor example, then try the quizzes for this module. If you do well, move ahead and start the material for module three. In that next module we are going to introduce computer software to analyze the experiments and visualize the data. But for now, get out that pen and paper and let's get started. -- So we are considering a basic example; an experiment with 2 factors. In the previous module we had said factors can be either numeric or categorical. In this example we will consider one factor of each type. So we're going to make popcorn! And in this experiment, the outcome is the number of popped kernels. It might be our objective to maximize that number of popped corns. Most of you will be able to try this one at home, which is why this is such a great example to start with. We're going to apply the same amount of heat each time and use the number or raw kernels to start with. From prior experience, I know that between three to four minutes are required, on medium heat, to pop most of the corn. So our first factor is going to be the time on the stove. And I'm going to use 160 seconds and 200 seconds. Notice that we use two levels, or two values, for this factor. Just under 3 minutes, and just over 3 minutes. Figuring out these numeric values for your experiments takes some practice. You will make mistakes, but we give general advice in coming classes. One quick tip though is don't use extremes. For example, you wouldn't use 30 seconds and 10 minutes for this experiment. You know in the first case that nothing happens in 30 seconds, and for 10 minutes you are going to burn it all. So let's recap: we use 160 seconds and 200 seconds. In later modules you'll learn how to either increase or decrease that cooking time, in order to improve our objective. The second factor we will consider is the type of popcorn. You could buy either white popcorn or yellow popcorn. Notice that this is a categorical variable, and there are two levels. We will assign the low level for white corn and the high level for yellow corn. So let's start planning the experiments next. We have two factors: cooking time, and type of corn; and each factor has two levels. From this we know that we will have four total combinations. This comes from the mathematical rule that two to the power of "k" tells us how many experiments we will have. Now "k" is the number of factors, and in this experiment we have 2 of them. So in other words, there will be two to the power of two, or in this case four, experiments in total that we have to run. We will write them in a table first, as follows. Let's pick cooking time and call it factor A, then call the type of corn factor B. So there are two columns, one for A and one for B. We use minus signs to indicate a low level for a factor, and a plus sign to indicate a high level. You will hear me say this a few times, but I hope you believe me: I promise it will be clearer by the 3rd module why we use minuses and plusses. The standard approach is to vary the signs for factor A the fastest, so put "minus", "plus", "minus", "plus", in the four rows for column A. These signs tell the experimenter what levels to operate that factor at. For factor A in this experiment that means we will have two experiments at 160 seconds, and these other two experiments will be run at 200 seconds. For numeric variables, the "minus" corresponds most naturally to the smaller numeric value, and the "plus" to the larger numeric value. Now let's consider factor B,. This is a categorical variable. There isn't a natural assignment for the "minus" or "plus" signs. In this case, we allocate the signs arbitrarily. For example, let's put white corn as "minus" and yellow corn as "plus". We could have flipped this allocation around. But, as you will prove to yourself in a quiz during this module, you will still get the same results. So, complete the table, now, by adding column B, and vary that one step slower than you varied column A: "minus", "minus", "plus" and then "plus". Now we are ready to implement the experiments. Here's a bit of advice and, in this course, when we give some practical advice, we will show it with this icon. The most ...