Today is World Egg Day.

I’m a big fan of eggs—my favorite being ones perfectly poached in an Endurance Stainless Steel Pan. However, the eggs that come from my daughters’ hens vary in size far more per container than store-bought, graded ones. I work around this by adding or subtracting time based on my experience. I really should weigh the eggs and design an experiment to optimize the time.

Coincidentally, I just received the new issue of Chance, published by the American Statistical Association. An article titled “A Physicist and a Statistician Walk into a Bar” caught my eye because one of my Stat-Ease consulting colleagues is a physicist and another is a statistician. I was hoping for a good joke at both of their expense. However, the authors (John Durso and Howard Wainer) go in a completely different direction with an amusing, but educational, story about a hypothetical optimization of soft-boiled eggs.

The problem is that recipes suffer from the “flaw of averages” —smaller ones get undercooked and bigger ones end up overcooked unless the time gets adjusted (as I well know!).

While the physicist sits over a pint of beer and pad of paper scratching out possible solutions based on on partial differential equations related to spheroidal geometry, the statistician assesses data collected on weights versus cooking time. Things get a bit mathematical at this point* (this is an ASA publication, after all) but in the end the statistician determines that weight versus cooking time can be approximated by a quadratic model, which makes sense to the physicist based on the geometry and makeup of an egg.

I took some liberties with the data to simplify things by reducing the number of experimental runs from 41 to 8. Also, based on my experience cooking eggs of varying weights, I increased the variation to a more realistic level. See my hypothetical quadratic fit below in a confidence-banded graph produced by Stat-Ease software.

Perhaps someday I may build up enough steam to weigh every egg, time the poaching and measure the runniness of the resulting yolks. However, for now I just eat them as they are after being cooked by my assessment of the individual egg-size relative to others in the carton. With some pepper and salt and a piece of toast to soak up any leftover yolk, my poached eggs always hit the spot.

*For example, they apply Tukey’s ladder of variable transformations – a method that works well on single-factor fits and can be related to the shape of the curve being concave or convex, going up or down the powers, respectively. It relates closely to the more versatile Box-Cox plot provided by Stat-Ease software. Using the same data as Durso and Wainer presented, I found that the Box-Cox plot recommended the same transformation as Tukey’s ladder.