Quality Progress - October 2014 - 46

STATISTICS ROUNDTABLE BY CHRISTINE M. ANDERSON-COOK AND LU LU Divide and Conquer Understanding trade-offs by studying separate relationships IN HIS BEST-SELLING book, David and work for anything and feeling entitled. Goliath: Underdogs, Misfits, and the Art Hence, a plot of income (the x-axis) exaggerate advantages and disadvantages when looking at competitive situations. of Battling Giants, Malcolm Gladwell versus ease of child rearing (the y-axis) has The idea is an important one, and it presents examples in which benefits for a bell (or inverted U) shape with a peak at can lead to improved thinking about daily many desirable attributes don't follow about $75,000, according to sources quoted choices we make. An important question, the assumed ever-increasing pattern, but by Gladwell. Through examples-including however, is how we can find the best solu- rather can be described by what he calls how school class size relates to the effec- tion to achieve the optimal gain-that is, an "inverted U-shaped curve." tiveness of teaching, and how alcohol con- the peak of the inverted U-shaped curve. sumption affects people's health-Gladwell This requires an accurate and precise us might assume that having more money describes a common principle that applies quantification of the true relationship of the would make parenting easier. We might to many things in life: Having too much of a outcome and the input factor-that is, the think that having $200,000, instead of good thing can actually be less desirable. inverted U-shaped curve. sure off of child rearing. To dispel this idea, Competitive situations to help further unravel the complexity of he describes how having too much money These examples speak to the primary mes- finding the optimum. At the heart of all of can lead to children lacking motivation to sage of Gladwell's book of how we tend to Gladwell's examples, and many others that 1 He describes, for example, how many of There is, perhaps, one more step to take $50,000 or $100,000, would take some pres- we can think of for ourselves, is the idea of Choosing the number of production lines / FIGURE 1 competing relationships between the driving factor and the result for different objectives. In the child-rearing example, more Approach one: inverted U money always will allow parents to offer 1 2 3 4 Number of production lines is no natural maximum on the opportunity Desirability Productivity their children more opportunities. There scale, but perhaps diminishing returns. What pulls the inverted U-shaped curve down after the peak, however, is a different 1 2 3 4 Number of production lines relationship. We might call it the "entitlement scale," which suggests that children lose motivation to achieve things or strive 1 2 3 4 Number of production lines 3 2 More relationships With the example of classroom sizes, the two competing relationships might be 1 Product variability These are two approaches for choosing the best number of production lines for maximizing productivity and minimizing product variability. Approach one uses a desirability function to combine the two objectives with the integrated relationship matching Gladwell's inverted U-shaped curve to summarize. Approach two identifies a Pareto front consisting of all the superior solutions and examines their trade-offs and robustness to subjective choices. 46 QP * www.qualityprogress.com for excellence on their own. 4 Productivity Product variability Approach two: Pareto front labeled "attention from teacher" (in which smaller class size is more beneficial for attention) and "diversity of opinion and group learning" (in which opportunities to hear from differing views and to develop cooperation skills) are lost with smaller classroom size. When both aspects play important roles in influencing teaching, http://www.qualityprogress.com

Table of Contents for the Digital Edition of Quality Progress - October 2014

Up Front
LogOn
Expert Answers
Perspectives
Keeping Current
Mr. Pareto Head
Step It Up
Strength in Numbers
Take Care of Your ‘Ugly Baby‘
Getting It Right the First Time
Career Corner
Statistics Roundtable
Quality in the First Person
Standards Outlook
ASQ's Quality Resource Guide
QP Toolbox
QP Reviews
Back to Basics

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