Statistics Tip of the Week: For Nuisance Factors in Designed Experiments, Block what you can and Randomize what you can't.
In our Statistics Tip of the Week for April 6, 2017, we described the difference between Common Cause Variation in a process and Special Cause Variation. Common Cause Variation is like random noise in a process that is under control. Special Cause Variation comes from external factors outside the process, like the effect that the ambient temperature in a factory rising through most of the workday has on a chemical reaction. This type of factor is sometimes called a "Nuisance Factor" in the discipline of Design of Experiments.
And, we said that any Special Cause Variation must be eliminated before one can attempt to narrow the range of Common Cause Variation. Narrowing the range of Common Cause Variation is a major objective of process improvement disciplines like Six Sigma.
Factors -- the inputs -- are denoted by x's, and y is the output -- also known as the Response. Briefly, statistical software for Design of Experiments can provide us the number of trials ("Runs") to do and the levels of x for each trial. We might get test results that look like the following. (There is a lot to explain here, more than we can cover in this blog post).
Our Tip for April 12, 2018 said that Designed Experiments, together with Regression Analysis, can provide strong evidence of Causation. When we're doing these experiments, we are often not able to easily get rid of the Special Cause (Nuisance Factor) Variation, but we can try to reduce or eliminate its effect on the experiment.
A known Nuisance Factor can often be Blocked. To “Block” in this context means to group into a Block. By so doing, we try to remove the effect of Variation of the Nuisance Factor. In this example, we Block the effect of the daily rise in ambient temperature by performing all our experimental Runs within a narrow Block of time. And, if it takes several days to complete all the Runs, we do them all at a similar time of day in order to have the same ambient temperature. We thus minimize the the Variation in y caused by the Nuisance Factor.
There can also be Factors affecting y which we don’t know about. Obviously, we can’t Block what we don’t know. But we can often avoid the influence of Unknown Factors (also known as “Lurking” Variables) by Randomizing the order in which the experimental combinations are tested.
For example – unbeknownst to us – the worker performing the steps in a process may get tired over time, or, conversely, they might “get in a groove” and perform better over time. So, we need to Randomize the order in which we test the combinations of Factors. Statistical software can provide us with the random sequences to use in the experiment.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.