katie's coke® vs pepsi® doe
TRANSCRIPT
This past year my youngest daughterKatie challenged me to a blind taste-testof Coca-Cola® versus Pepsi-Cola® softdrinks. Her 7th grade social studiesteacher had done something similar inher class that day to illustrate howadvertising influences consumer per-ceptions. I was tired after a day of teach-ing DOE and figured a good dose ofcaffeine might help me stay awake tomoonlight on a new book titled, "RSMSimplified" (due out 2004). Katie helpedme experiment on spring toys for a gen-eral factorial design featured in the firstvolume, "DOE Simplified" (Productivity,2000). She also participated in a similarDOE on flying disks that we publishedin one of my prior columns for thisnewsletter (September 2002, Stat-Teaser).Therefore, Katie fancies herself quitethe experimenter and wanted to diginto the business herself.
While Katie prepared in our kitchen forthe cola challenge, I settled at my homeoffice (really just a broken-down oldroll-top desk) and sat staring at my com-puter screen. I chuckled to myself whenKatie paraded in with two glasses —onemade of white foam and the other ofblue plastic. She explained that, althoughI and other taste testers in the householdshould not be told which cola was which,she needed to keep them straight. Beforewe get to the "lessons learned" part, let'sgive her credit for replicating the test,rather than just doing it once on me!
"Katie," I said, "Do you realize that
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May 2004 • 1
you've made the fundamental error ofconfounding my treatment of Cokeversus Pepsi with my preference forwhite versus blue and Styrofoam versusplastic?" She gave me this look. I'veseen it before from my other daughtersand sons and even more powerfullyfrom my wife. It's not good, but it wasworth taking a hit to defend the sancti-ty of unaliased experimental designs. Ifone cola is always in white styrofoamand the other cola is always in blue plas-tic, there is no way to tell if my prefer-ence for one over the other is due to thetype of soft drink or the type of cup—these factors are aliased. For instance,perhaps in general people prefer drink-ing pop in a plastic cup rather than aStyrofoam cup. Then whichever cola isin the plastic cup would get the mostfavorable reviews.
In the end, both Katie and I came out ofthis experience with positive thoughts.My daughter got her revenge later thatevening when she confronted me withthree cups of cola all in foam containersthis time. "OK Dad," she said with agloating look, "Taste these and tell me if
Katie’s Coke® vs Pepsi® DOE
—Continued on page 2.
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Mark’sMark’sExperimentExperiment
2 • May 2004
there's any difference." I knew it must bea trick, but I tossed all three caffeinatedbeverages down the hatch. Since I'dalready drank so much of the stuff, thisnew round of drinks all tasted the same—sickly sweet and bubbly. I said asmuch to Katie, "You are trying to foolme by putting the same brand in all theglasses." "Ha!!! I did fool you Dad—oneglass is Pepsi, the other is Coke and thethird is a mixture of the two!" "Youwin," I said and preserved the self-esteem of my daughter and avoided themarital discord that would've resultedotherwise by Dad being a statistical bullyaround the home.
Why was I happy? Because Katie's poorDOE on Coke versus Pepsi provided anideal example for illustrating the con-cept of aliasing, especially for peoplewho don't normally perform experi-ments. I presented this case at a gather-ing of non-manufacturing trainees forSix Sigma at the Ohio State University'sFisher School of Management and theydrank it up (pun intended).
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tions run from scratch, or were theysimply replicated measurements on asingle setup of that condition?Replicates that come from independentsetups of the process are likely to con-tain more of the natural process varia-tion. Look at the response measure-ments from the replicates and ask your-self if this amount of variation is similarto what you would normally expectfrom the process. If the "replicates"were actually run more like repeatedmeasurements, it is likely that the pureerror has been underestimated (makingthe LOF denominator artificiallysmall). In this case, the lack of fit statis-tic is no longer a valid test and decisionsabout using the model will have to bemade based on other statistical criteria.
If the replicates have been run correctly,then the significant LOF indicates thatperhaps the model is not fitting all thedesign points well. Consider transfor-mations (check the Box Cox diagnosticplot). Check for outliers. It may be thata higher-order model would fit the databetter. In that case, the design probablyneeds to be augmented with more runsto estimate the additional terms. Thismay be the case when, for instance, theFit Summary screen shows that the lin-
ear and quadratic models have signifi-cant lack of fit, but the aliased cubicmodel has insignificant lack of fit.
If nothing can be done to improve the fitof the model, it may be necessary to usethe model as is and then rely on confir-mation runs to validate the experimentalresults. In this case, be alert to the possi-bility that the model may not be a verygood predictor of the process under cer-tain conditions. (To learn more about lackof fit and basic DOE, sign up for Stat-Ease’sExperiment Design Made Easy workshop.)
FAQ - Interpreting Lack of Fit A statistically significant lack of fit(LOF) value often worries experi-menters. This article is meant to giveexperimenters a better understandingof this statistic and what could cause itto be significant. The formula is:
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Figure 1—The centerpointshave less variation than themodel points, causing signif-icant lack of fit.
Lack of Fit F - test = Lack of fit MS
Pure Error MS
where MS = Mean Square. The numer-ator in this equation is the variationbetween the actual values and the val-ues predicted from the model. Thedenominator is the variation within anyreplicates. The variation between thereplicates is meant to be an estimate ofthe normal process variation. Significantlack of fit means that the variation of thereplicates about their mean values is lessthan the variation of the design pointsabout their predicted values. Either theruns replicate well and their variance issmall, or the model doesn't predict well,or some combination of the two.
Figure 1 is an illustration of a data setthat had a statistically significant model,but also had a statistically significant lackof fit. Believe it or not, there are actuallysix center points on the graph. They areso close together that they overlap andsome are hidden below the responseplane. Now look at the other modelpoints. Many are positioned off theresponse plane. Although the predictedresponse surface fits the model pointswell (providing the significant model fit),the differences between the actual datapoints and the response plane are greaterthan the differences between the centerpoints. This is what triggers the signifi-cant LOF statistic. The center points arefitting better than the model points. Doesthis significant LOF require us to declarethe model unusable?
When there is significant lack of fit,check how the replicates were run—were they independent process condi-
Optimize Mediums with Mixture DOE
(DX) software, they then took the topthree of these six and conducted a mix-ing assay via a simple mixture design.Almost all of the new formulationswere found to improve cell growth andproduce high levels of recombinant pro-tein production.
Assay data can be analyzed by one oftwo methods: 1. Separately analyzingthe data for each response [cell growth(Fig. 2, left) and recombinant proteinproduction (Fig. 2, center)] and rankingit in order, or 2. Doing an in-depthanalysis using Design-Expert software(which allows the optimal media mix-ture for a particular CHO clone torapidly be found). Using Design-Expertsoftware, Sigma-Aldrich discovered theparticular combination of the threemedia that was the most desirable (Fig.2, right). The result was a medium thatprovided their CHO cell line with theoptimal nutritional requirements formaximum cell growth and recombinantprotein production. Tests of the recom-mended media mixture verified theresults from Design-Expert software.
Design of experiments is tailor-madefor optimization applications such asthis. Traditional one-factor-at-a-timeanalysis can be useful, but it is unlikelythat the best combination of mediawould be found in this manner. DOEcreates predictive models that can inter-polate to all of the combinations ofmedia that have not yet been tested.Based on this interpolation, the best for-mulation can be predicted, and then
validated via a confirmation run. WithDOE, Sigma-Aldrich can develop anoptimized medium for any givenrecombinant CHO clone.
For further information, contactSigma-Aldrich Biotechnology, 3050Spruce St., St. Louis, MO 63103,USA.
(Figures courtesy of Sigma-AldrichBiotechnology.)
May 2004 • 3 Stat-Teaser • News from Stat-Ease, Inc.
The following study by the cell cultureR&D group at Sigma-Aldrich (St. Louis,MO) is an example of a unique applica-tion of design of experiments (DOE) tooptimize a biological process. We'vedescribed the case study here in generalterms for those of us who are not biolo-gists. For technical details, please referto the article, "An Efficient Approach toCell Culture Medium Optimization—aStatistical Method to Medium Mixing," on Stat-Ease's web site atwww.statease.com/pubs/cellculture.pdf.
Chinese Hamster Ovary (CHO) cellsare used extensively by researchers inindustry and academia for recombinantprotein production. Grown in mediacontaining all of their nutritionalrequirements, these cells vary greatly inthe specific amounts of amino acids, vit-amins, salts, etc. they need for maxi-mum cell growth and recombinant pro-tein production. This presents a chal-lenge for researchers because each par-ticular CHO cell line is unique.
As more and more recombinant CHOclones have been developed, it hasbecome increasingly important tostreamline the medium optimizationprocess. Sigma-Aldrich has taken thisprocess to a new level with their CHOMedium Optimization Kit 1. This kitallows the researcher to quickly screensix different media formulations (whichrepresent the wide range of nutritionalrequirements found in CHO clones) forcell growth and recombinant proteinproduction. If optimization is desir-able, it then leads researchers to thedevelopment of an optimized mediumthrough mixture design and analysis.
For this case study, Sigma-Aldrichresearchers started their creation of a bet-ter medium by screening the six primarymedia in their kit against the targetCHO cell line. Using Design-Expert®
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Using DOE Software for a More Precise Data Analysis
Figure 2—Data from the mixtures assay can be analyzed using Design of Experiments (DOE) software for precise analysis and optimization.
BA C A: C5467
B: C8862 C: 9737
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Prediction 0.625 X1 0.29 X2 0.34X3 0.37
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B: C8862 C: C9737
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Production
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18.2997
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30.315433.2224 34.8671
34.1988
33.2224
2.25335E+006
2.40348E+006
2.70374E+006
2.55361E+006
2.40348E+006
2.85387E+006
A: C5467
B: C8862 C: C9737
1.00
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2 The Optimum
Mixtures Triangle with Respective Media Mixes
Figure 1—The three-point mixtures diagram and corresponding media mixes.
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Media Mixes: 1) 100% A 2) 100% B 3) 100% C 4) 50% A, 50% B 5) 50% B, 50% C 6) 50% C, 50% A 7) 67% A, 17% B, 17% C 8) 67% B, 17% C, 17% A 9) 67% C, 17% A, 17% B10) 33% A, 33% B, 33% C
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