Making the most from measuring counts

In a previous Statistician's Corner (Volume 38, Issue 1), my colleague Shari Kraber detailed ways for "Improving Your DOE" via "Analysis with Response Transformations."She highlighted the most commonly used transformation-the log.As a follow up to this article, let's delve into another transformation-the square root, which, as Shari noted, deals nicely with count data such as imperfections in flexible packaging.Counts follow the Poisson distribution, where the standard deviation is a function of the mean.This is not normal, which can invalidate ordinary-least-square (OLS) regression analysis.An alternative modeling tool, called Poisson regression (PR) provides a more precise way to deal with count data.However, to keep it simple statistically (KISS), I prefer the betterknown methods of OLS with application of the square root transformation as a workaround.When Stat-Ease software first introduced PR, I gave it a go via a design of experiment (DOE) on making microwave popcorn.In prior DOEs on this tasty treat I worked at reducing the weight of unpleasant unpopped kernels (UPKs).However, I became a victim of my own success by reducing UPKs to a point where my kitchen scale could not provide adequate precision.With the tools of PR in hand, I shifted my focus to a count of the UPKs to test out a new cell-phone app called Popcorn Expert.It listens to the "pops" and via the "latest machine learning achievements" signals users to turn off their microwave at the ideal moment that maximizes yield before they burn their snack.I set up a DOE to compare this app against two optional popcorn settings on my General Electric Spacemaker microwave ovenstandard ("GE") and extended ("GE++").As an additional factor, I looked at preheating the microwave with a glass of water for 1 minute-widely publicized on the internet to be the secret to success.Table 1 lays out my results from a replicated full factorial of the six combinations done in random order (shown in parentheses).Due to a few mistakes following the software's