I have been thinking a lot lately about the idea that statistical questions are often seemingly simple questions, that contain complex answers, or answers that have complex operationalizations.
Without getting into a lot of detail in this blog post, it is also an issue that comes up a lot in teaching. I’ve written up some more detailed examples of this kind of issue here and here.
One thing that I often say in teaching is that because so many of the outcomes we study are so important–and are often unequally allocated–we want to make sure our answers are as precise, and as close to correct, as we can make them. It turns out that failing to understand some of the hidden complexities of statistical thinking may lead to providing very wrong answers to important questions.
Two images that help me convey this idea are the Nautilus Shell, and the Mandelbrot Set.
mandelbrot by Moore & dos Reis (2017)Each of these structures is based upon simple rules that produce a complex set of outcomes. A nautilus shell is a logistic spiral, a structure that depends upon maintaining a constant angle with the center as the structure expands (Livio, 2002). The Mandelbrot set is a complex pattern that emerges from some simple rules about iterating the values of a complex function (Moore & dos Reis, 2017).