The gentlemen referred to as “Pareto” long ago advocated that 80 percent of the world’s wealth was controlled by 20 percent of the world’s population. This phenomenon is also called the “Pareto Principle,” and will be designated as “PP” for our discussion. For the case just given, it should be noted that the 80 percent (per se) is related to money – a continuous variable at the ratio level of measure. The 20 percent is related to the count of people – a discrete variable at the nominal level of measure.
For the aforementioned circumstances, the dependent variable is continuous, whereas the independent variable is discrete. Must this hold true for all cases in which PP is applied? Does the rule of 80/20 hold when both the dependent and independent variables are discrete? What about when both variables are continuous – does the rule still hold? How many categorical variables must be considered before the true ratio is revealed? Is it a “hard rule” or just a “guiding principle”? To such pondering, my thoughts take me to the dreaded phrase “I don’t know.” I do not even know of a good reference – but if I did know of such a source, I would likely not have to say, “I don’t know.”
Personally, I believe PP is more of a generalization than an absolute. It recognizes the highly disproportional quantities that nature often provides. In this context, we often observe the effect of the “vital few” versus the “trivial many.” To this point, it should be noted that some would advocate PP to be 85/15, not 80/20. Along these lines, I am far more than prone to employ the ratio of 85/15 than that of 80/20.
As you may know, 86.64 percent of the area under the normal curve lies between the 1.5 sigma limits. Obviously, this percentage is closer to 85 percent than it is to 80 percent. In support of the 85/15 ratio, it should also be recognized that each of the 1.5 sigma limits (associated with the standard normal curve) uniquely represent a “point of diminishing return” with respect to its cumulative probability curve. Is this a valid justification for using 85/15 in lieu of 80/20? Again, we have the dreaded phrase “I don’t know.” However, I can say “It makes good sense to me.”
As yet another point on the PP issue – be wary of plotting confounded data. The tallest bar may not represent the greatest risk factor. The reason for this is a concept called “complexity”. For example, consider the various systems of an automobile – electrical, engine, transmission, etc. For one particular automobile manufacturer, the “transmission” would always be the “tall bar” on the defects-per-unit (DPU) chart. Owing to this, the transmission executives were constantly “under the gun” during quality meetings.
Then one fine sunny day a certain consultant come along and normalized the chart to defects-per-opportunity (DPO) and then prepared a new Pareto chart. As one might surmise, the new chart of DPO indicated that “transmissions” had the best quality, not the worst (probably because they had been hammered for so many years about their DPU level). Only by normalizing to the “opportunity level” was it possible to really see the “meritorious few” versus the “harmful many.” Thus, we judiciously conclude that the quality picture (per se) can look very different when our line-of-sight is moved from the “unit level” to the “opportunity level”.