October 8 is National Pierogi Day. Not only is this a great opportunity to nosh on those cheese-and-potato-filled dumplings, but it’s also a good time to offer a simple kitchen-based example of what makes the statistical method called Design of Experiments so cool.
Let’s say you want to make pierogies that are as good as grandma’s, but yours are too mushy. You don’t know why. With so many inputs (or variables), how can you quickly determine which ones really make a difference?
That’s where Design of Experiments comes in. In a designed experiment, you can change more than one factor at a time, then use statistical analysis to get meaningful results about all factors simultaneously. That means you can quickly screen many factors, determine which are most important, then adjust the process to get the desired results—in this case, pierogies that are neither too hard nor too soft.
Minitab can easily create and analyze many kinds of designed experiments. We’re going to design a two-level fractional factorial experiment, a class of factorial designs that lets you quickly identify the most important factors in a process. (You don’t need statistical software to design an experiment, but a tool like Minitab makes it a lot easier. Which will leave you more time to fine-tune your pierogi recipe.)
The first step is to identify your variables and the result you wish to influence. In a two-level experiment, we also need to select a high and a low value for each variable. For our pierogi mushiness experiment, let’s use the following variables and values:
|Variable||High Value||Low Value|
|A. Dough casing||Thick||Thin|
|B. Amount of filling||Bountiful||Miserly|
|C. Filling cheese/potato ratio||Cheddarific!||Ultra-starchy|
|D. Amount of butter & onions used in cooking||Ample||Sparse|
|E. Temperature of cooking pan||Super-hot||Just hot enough|
Now we choose Stat > DOE > Factorial > Create Factorial Design… to get started in Minitab. We need to set the Number of factors to 5.
Next, clicking the Designs... button reveals our options for a five-factor, two-level factorial experiment:
Now we need to choose the best experimental design for our situation. In industry, experiments can be very expensive, so we seek to minimize the number of runs needed to get usable information. In this case, each “run” is a batch of pierogies. I like pierogies, but I can’t eat 32 or even 16 batches. So our best option is the ¼ fractional factorial design.
The dialog box above tells us this is a Resolution III design, which means our results won’t let us draw conclusions about the effects of interactions among variables. An experiment with more runs would give more detail, so if we were concerned about those interactions—and we had bigger appetites—we could choose a ½ fractional or full factorial. Since we don’t care about the interactions, we can use this design to get usable information about our main factors with just 8 batches of pierogies.
We choose “OK” to select our design, then “OK” again to actually create the design, which Minitab puts in a worksheet:
The A, B, C, D, and E columns represent our variables, while each -1 represents the low value and each 1 represents the high value for the variable. So the variable settings for our first run (i.e., the first row) would be:
A. Thin casing
B. Bountiful filling
C. Ultra-starchy cheese-potato ratio
D. Sparse butter and onions
E. Super-hot pan.
Following that through for the remaining 7 rows gives us the settings for each run in the designed experiment. Now all we need to do is cook (and eat) eight batches of pierogies, and evaluate and record the mushiness of each batch.
In my next post, we’ll discuss how to use Minitab to analyze the data we gather in our 8 experimental runs.
Pierogi photo by cwisnieski, used under Creative Commons 2.0 license.