How Statistics Got to the Root of My Turnip Problem

Technical training specialist Lou Johnson needed to find the best way to turn a garden full of turnips into soup. With several good ideas, but a limited amount of time, he realized that he could apply design of experiments (DOE) to his turnip problem, and enlisted a group of his Minitab colleagues as taste-testers to help. This article discusses his experiment—and reveals the results!

by Lou Johnson

Turnip Soup DOE

Turnip-soup tasting at the Minitab kitchen!

I love sautéed turnips and turnip soup, especially when the roots are plucked fresh from the garden. But turnips, much like the poisonous Japanese blowfish, can be deadly to your culinary reputation if not prepared correctly. Most cooks have a story about how a batch of bitter turnips spoiled the dish. On the other hand, turnip lovers extol their unique, slightly peppery flavor; their use as a low-carb potato alternative; and how easy they are to grow.

So, how do you cook turnips without getting burned? With a garden full of turnips on the way, I needed to know. Fast. You’d think someone already figured it out, but scouring our cookbook library and the Internet brought no easy answers.

I did, however, find several promising ideas to remove their bitterness:

  1. Peel the turnip about ¼" down, below the yellow bitterness line you can see when you cut the turnip in half.
  2. Boil the turnips in salt water.
  3. Add a few potatoes to the boiling water.
  4. Add cream.
  5. Use spices such as nutmeg, bay leaf, and basil.
  6. Get some new turnips because, as one Internet site put it, “You got yourself some bitter turnips,” and there’s nothing you can do to fix that.

But how could I determine which of these promising ideas would really yield a tastier turnip soup? I realized that I could apply my experience with design of experiments (DOE) to my turnip conundrum.

Why Use Design of Experiments (DOE)?

Design of experiments is a statistical tool that lets you evaluate several factors simultaneously, reducing the number of experimental “runs” needed, as compared to one-factor-at-a-time (OFAT) experimentation. In addition to saving time and resources, a well-designed DOE experiment will also reveal if synergies between two or more factors might lead to an even better outcome than any one by itself.

The basic recipe for my soup experiment included sautéing garlic and onions, boiling the turnips in salt water for 15 minutes, and cooking with a small amount of carrots and chicken stock.

I identified four experimental variables as well:

  • The inside color of the turnip (White or Yellowish)
  • Adding potato (2-to-3 potato-to-turnip ratio)
  • Adding cream
  • Adding nutmeg

I then used Minitab Statistical Software to create a 24 – 1 fractional factorial design, as shown in the table below.

Turnip Soup - DOE Layout

As you can see, this designed experiment has eight runs, each with a different combination of variables (or factors). The first run used white-fleshed turnips, and included potato, cream, and nutmeg. The second run used yellow-fleshed turnips, and included potato and cream, but not nutmeg. And so on, as shown above.

So how did I choose this 24 – 1 fractional factorial design?  First, I needed to consider the 6 possible factors I could study. Idea 6—get new and presumably better turnips—could lead to conflicting opinions about the best way to cook out bitterness, because starting with great turnips would make any recipe look good. Therefore, I used suspect yellowish turnips as well as what were thought to be sweet white turnips. I also decided to include the nutmeg, cream and potato factors.  However, I decided to incorporate idea 2 in the entire experiment: by boiling the turnips used in all recipes in salt water and removing the water, I would be reducing the amount of runs needed by half while putting this idea to the test.

If all 8 recipes received favorable scores, we could conclude that boiling in salt water was a good solution. Ideally, I wanted to include all possible factors in the experiment, but a 5-variable experiment would have required 16 recipes, a number beyond both my budget and one’s ability to discern between that many soups. (Wouldn’t you get tired of tasting soup well before the 16th bowl?) My 4-factor, 8-run experiment is a resolution IV design, which means that all two-way interactions are confounded with other two-way interactions. This was a bit of a risk since I wouldn’t be able to distinguish between significant two-way interactions, but it was one I was willing to take, and will address in more detail later.

Turnip Soup Testing  

I cooked eight batches of soup following the order of the recipes shown in my Minitab worksheet, and asked 10 volunteer taste-testers drawn from the population of Minitab employees to try each soup and give it a score of 1 to 10 (“Yuck” to “Excellent”). Taste-testing was conducted in random order, and testers had no knowledge of each other’s scores. 

Data Analysis

The raw scores for testers, shown below, revealed that each had their own pattern within the 1 to 10 scale. These differences were emphasized during the tasting with comments like “These all taste great!” and…well, I can’t say what some of the other comments were, except that they were equivalent to “I don’t think I like this very much.” 

Turnip Soup Individual Value Plot

Since one tester’s 8 could be another tester’s 5, the data had to be normalized based on the mean score of each tester in order to combine the scores for all 10 individuals. The average of each tester was subtracted from each of their raw scores to create a normalized score. The average of the normalized data for each recipe was then used in the analysis.

Now I used Minitab to analyze my experimental data, trying a model that included all the main effects and the interactions of Color with Potato, Cream, and Nutmeg. Based on those results, I removed the insignificant Color*Potato interaction from the model, and reran the analysis. Next, I removed the insignificant Color*Nutmeg interaction, leaving a model with all main effects and the Color*Cream interaction as shown below.

Turnip Soup Pareto Chart of Effects
 
Factors that extend beyond the red line on the Pareto chart are significant, and include all remaining factors except nutmeg. After rerunning the analysis one last time to remove the insignificant Nutmeg effect, I arrived at the final model for my turnip soup experiment.

Turnip Soup ANOVA Table

When Nutmeg is removed from the analysis, the White*Cream interaction is no longer confounded with the Potato*Nutmeg interaction. When selecting the resolution IV design with each two-way interaction confounded with another two-way interaction, we can rely on the principle of sparsity of effects to assume that at least one factor and its interactions will commonly drop out and the resulting analysis will not have an issue with confounding.

The main effect for each of our four factors is shown below. On average, using white turnips, adding potato and adding cream resulted in a better tasting soup. The graph also indicates that adding nutmeg may have caused the scores to drop a little, but we can’t be sure since this factor was not statistically significant.

Turnip Soup Main Effects Plot

Since there was a significant interaction between the turnip color and cream factors, I also created an interaction plot, shown below. The Color*Cream interaction plot illustrates that the main effects plot doesn’t tell the whole story!

Turnip Soup Interaction Plot

The effect of adding cream is not what I expected. I suspected that the cream would improve the flavor of an otherwise bitter (yellow) turnip, but it didn’t quite work out that way. The red line representing the yellow turnips indicates that adding the cream didn’t compensate for the lower quality turnips. The yellow turnip soups received poor scores regardless of whether or not cream was added. On the other hand, adding cream did enhance the flavor of the better-quality turnip (white) as shown by the black line.

From Soup to Nuts

Turnip Soup - Sliced Turnips

Do white or yellow turnips make better soup?

Let’s pull it all together. It seems that all but one of the ideas we started with were true, but none alone tells the full story. Only through this designed experiment and statistics could I draw clear conclusions about the factors that contribute to a great turnip soup.

First, you need to start with good quality turnips, which means the outside peel should be smooth and soft and the inside pulp should be as white as possible. (See the comparison photo at right.)
 
Second, boiling turnips in salt water first did make some great-tasting soup, but it isn’t a silver bullet. The tasters were able to identify better and worse recipes even though they all started with this first step.

Third, adding potatoes and adding cream to white turnips will result in the best tasting soup, while nutmeg will not! Just spice to your own taste.

On the other hand, if your garden or Community-Supported Agricultural Cooperative provides you with some slightly bitter roots, boiling in salt water and adding potatoes will enable you to make some pretty darned good soup. However, adding cream is not going to help.

After our experiment, some local organic farmers came up with some interesting ideas for growing the best possible turnip, and I’ll be putting those factors to the test when I start my garden next spring. Once again, one good experiment has led to another!

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