Planting Container Trees

I recently planted two pecan trees in my backyard (Carya illinoinensis ‘Caddo’ and ‘Kanza’). Both trees came in plastic containers, unlike how I ordinarily get my trees (usually I buy them B&B or “balled and burlapped”). My one previous experience with a container tree, a magnolia that I ironically paid to have professionally planted, died within two years. When I went to dig it out, the entire rootball came up. Basically, the tree had been completely root bound, and the encircling roots never spread into the surrounding area. After that costly experience, I have planted my trees myself.

So how to properly plant a container tree? Apparently, traditionally, one makes some vertical cuts with a utility knife in an attempt to prevent encircling roots. But most interestingly, recent research done at the University of Minnesota suggests a more dramatic solution. You “box” the tree. You cut off the sides of the root ball to form a box shape. On the one hand, it seems insane.. On the other hand, it makes perfect sense: if you cut all the encircling roots, the new roots will spread out. (See their instructional video here.)

So after taking a deep breath, I turned on my reciprocating saw and chopped off the sides of the root balls of my two new pecan trees. We’ll see what happens!

Balanced Incomplete Block Designs for FairScore

The FairScore score normalization program tries to address the problem of judge variability in competition scoring.  Some judges may grade harshly, whereas others may grade generously.  Without normalization, participants can unfairly face an especially harsh or generous group of graders as a matter of chance.

FairScore works best when there is a significant amount of "mixing" between judges and participants.  In other words, we want Judge A to judge a different group of participants from Judges B, C, and D.  Obviously there will be some overlap (and in fact the overlap is critical to the normalization), but we want different kinds of overlap.  We don't want Judges A and B to judge participants 1, 2 and 3, and Judges C and D to judge participants 4, 5 and 6.

Sometimes, some of the overlap is structural.  In a moot court competition, judges sit in panels, and participants present to the panels in teams.  Those judges will necessarily all judge those teams.  In other contexts, however, we may have complete control over the matching of judges with participants.  In these more flexible cases, what's the optimal way to match judges with participants?  Well, it turns out that is solved through something called Balanced Incomplete Block Design (BIBD)

A BIBD is defined by five parameters.  The standard description is that there are "v treatments repeated r times in b blocks of k observations."  (Lambda, the fifth parameter, is the number of blocks where a pair of treatments appear.  So BIBD is also known as a vrbk-lambda problem.) Translated into our scoring context: v is the number of participants or entries to be judged;  b is the number of judges, who judge k participants each, resulting in each participant being judged r times.  Note that there isn't always a clean solution for any given v, r, b and k.  Just as you can't divide 8 evenly by 3, sometimes there will be extras left over.

There's some beautiful mathematics behind the scenes, but for our purposes, all that we need to know is that procedures exist for generating these BIBDs.  So you can maximize the power of FairScore at really minimal hassle.  See for example, https://www.r-bloggers.com/generating-balanced-incomplete-block-designs-bibd/.