Design of Experiments (DOE) with Pierogies, Part II: Analyzing Results

A few weeks ago, on National Pierogi Day, I explained how you could use Minitab Statistical Software to design an experiment that would let you assess the impact of different factors on the mushiness of pierogies. 

We created a 1/4 fraction factorial design, which let us look at the effects of five factors. We had to make a trade-off: this design would not let us look at how interactions between our factors affected mushiness, but we could evaluate the main effects in only 8 runs.  

1/4 fractional factorial Designed Experiment

The A, B, C, D, and E columns represent our variables. 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  

So assume that we followed the settings laid out in the next seven rows, or runs, of the experiment.  We cooked (and ate) eight batches of pierogies made under different experimental conditions, and evaluated and recorded the mushiness of each batch. Assume that we asked all family members to sample the pierogies and assess their mushiness on a 100-point scale, and then we averaged the responses to form our final mushiness rating. We record our data in a new column in our Minitab worksheet, giving us something like this:

 DOE Data Entry in Minitab

Now let's look at what we can learn by analyzing the data we collected.  (First, a word of caution: my grandmother would have my head if I gave out any real information about her pierogi recipe, so all the settings and results related here are for demonstration purposes only. The data have been falsified. Therefore, we cannot be held responsible if you make and eat 8 batches of pierogies under these experimental conditions!) 

To see what our data say, we'll choose Stat > DOE > Factorial > Analyze Factorial Design in Minitab. We enter the name of our data column, "Mushiness," as the response:

DOE Dialog Box

We'll also click on the "Graphs" button in this dialog, and ask it to give us a Pareto chart of the factor effects. When we analyze the data, we get the following graph: 

DOE Pareto Chart of Effects

The chart reveals that of the five factors we varied in our eight batches of pierogies, only C (cheese/potato ratio of the filling) and B (amount of filling in the pierogi) had a statistically significant relationship with the mushiness result.  

But how can we use this information to adjust our settings so we get pierogies that are less (or more) mushy?  Go to Stat > DOE > Factorial > Factorial Plots.  Choose "Main Effects Plot" and click "Setup..." to bring up this dialog: 

Factorial Plot Dialog

Since B and C were the only significant factors in our experiment, we select those as the factors to include in our plots.  Minitab gives us the following: 

DOE Main Effects Plot

The graph shows us the relationship between each factor and pierogi mushiness. If we want pierogies that are less mushy, we want to choose the lower amount of filling (B), and the higher cheese-potato ratio (C).  

I hope this light-hearted experiment gives you a sense of what a powerful tool Design of Experiments is, and why it's so valuable across industries and professions.  

But this simple experiment barely scratches the surface of what can be done with designed experiments in Minitab.  For instance, Minitab's Response Optimizer tool can let you fine-tune the settings for several factors simultaneously to get the best settings for a process.  That's invaluable in manufacturing, where even minute changes in settings can make a difference in product quality and/or the amount of materials used in the process...but that's a topic for a future blog post!  



Name: sreedher • Tuesday, July 31, 2012

Plesae note that under the graphs option in this dialogue box, there are no options for - normal plot and pareto diagrams etc. I am using minitab 16 version.

Please help


Name: Eston • Wednesday, August 1, 2012

Hi SK -

Perhaps I didn't describe it quite clearly enough above, but if you actually click on the "Graphs" button in the Stat > DOE > Factorial > Analyze Factorial Design... dialogue box, the top row of the "Analyze Factorial Design - Graphs" dialogue consists of checkboxes for Normal, Half Normal, and Pareto effects plots. You are correct that those options do not appear directly under the Graphs button itself, but rather in the sub-dialog the Graphs button calls up.

Hope this helps!

Name: Marly • Friday, February 7, 2014

Eston, very good, material, but I did not find the Pareto effects plot option in the Graphs button, I am also using 16 version... The options are residual for plots: regular, standardized and deleted. What is going on?

Name: Eston • Monday, February 10, 2014

Hi Marly, thank you for reading. When you click the Graphs button in the DOE > Factorial > Analyze Factorial Design... dialog box in Minitab 16, the first row you'll see is for Effects Plots, with the options for Normal, Half Normal, and Pareto. Immediately below this is the box in which you'd enter your alpha value. This is directly above the options for residual plots.
Hope this helps!

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