Assumptions are everywhere, and as technical leaders, we get paid to have “judgment” and assumptions. But as someone once said:
In God we trust–all others, bring data.
Knowing how to check our assumptions is vital. Pictures help, as you will see below.
(The following is an excerpt from Where Do We Go From Here.)
As a common example of this process [checking our assumptions] in action, consider the illustration known as the fat pencil test. In many statistical techniques, we rely on an assumption of normality. In ANOVA (analysis of variance), we assume that the residuals are distributed normally. We plot these residuals on a normal probability plot [see below] and imagine that a fat pencil is placed over the points and the straight line representing the normal distribution. If the imaginary pencil covers the points, then we smugly accept what we had already assumed. If however, one or two points stray from beneath our nominal fat pencil, we imagine a slightly fatter one. If these points are now hidden, we continue with our analysis, satisfied that our assumption is true.
(Plot credit: Jay Kadane, Intro to Prob & Stats Using R)
When still more points remain uncovered by our slightly fatter pencil, we begin to listen to the argument this chart is making, begin to consider the alternative that our assumption is wrong. We force the evidence to disprove our assumption.
How do we find our way then, when we are exploring the unknown, blazing a trail into uncharted territory? How do we apply elementary statistical principles to transform uncertainty into decisive action? What is to prevent us from making a preposterous application of ATOMs when we deal with very complex situations, those in which our intuition fails?
These questions are not much different from those faced by Chuck Yeager before he ever broke the sound barrier or Neil Armstrong as he took that first step on the moon. Neither of these men, nor anyone around them–with hundreds or thousands of highly educated, very scientific people on these teams–knew what to expect. Or did they…?
ATOMs is a monthly column that introduces analytical tools of mathematics and statistics and illustrates their application. To read more about ATOMs, you can read Where Do We Go From Here, or view the online workbook here.