Statistical Analyses Trapped in Time – And It Could Really Cost You

- Dieter Mulitze

Years ago, when I was conducting yield trials as a plant breeder, drought seemed imminent a few months after planting. Rather than lose the entire trial, I requested sprinkler irrigation at the research station. Unfortunately, water pressure to the far end of the station wasn’t ideal, and there wasn’t a perfect fit for one of the pipe connections. I could see the tragedy unfolding: uneven irrigation perpendicular to the blocks in the randomized complete block design (RCBD) and thus a high covariance (CV).

During the season, anyone could see an obvious gradient along the plots. The plants on the left side of the trial were shorter, and the plants on the right were taller and greener. This was a statistician’s worst nightmare. Due to the conditions and variability, I thought the trial might still be a loss.

When I finally analyzed the trial, the CV was indeed high. However, around that time, I happened to come across a small software program that analyzed trials with a spatial algorithm to account for trends in the field. I wondered if it would work for me. Much to my surprise it estimated the trends and even the exact spot where the pipes didn’t connect and water gushed out for a few hours. The CV went way down, and heritability went way up.

But what shocked me most were the adjustments in the means for the varieties now estimated in the absence of confounding trends – in this case, from uneven irrigation. The RCBD analysis just gives the arithmetic mean of entries, whereas the spatial analysis estimates means in the absence of trends (estimated iteratively from solely plot data). Among the RCBD-ranked Top 5, three were actually low yielding. Furthermore, some of those ranking lower in the trial were actually among the top yielding when estimated by this spatial data analysis. It was a night-and-day difference.

Which analysis would I believe? What if I chose the wrong varieties because they were incorrectly ranked? This had massive implications for my breeding program. Years later, and after further research co-published in Crop Science and American Statistician, I remain firmly convinced that nearest neighbor analysis is a simple but powerful approach in spatial analysis. It is called “nearest neighbor” because the nearest plots (the ones to the left and immediate right of a central plot) are used in the algorithm in sequence.

In the years since my discovery, I’ve had the opportunity to reanalyze yield trial data for a number of seed companies, and often, the spatial analysis proved superior with greater confidence in selecting the best hybrids and varieties. In fact, one client reanalyzed 25 years of yield data, comparing it to the RCBD and incomplete block analyses, and came to different conclusions through the spatial analysis, which was decidedly superior.

This meant somewhat different decisions as to the release of final varieties, which are million-dollar decisions for seed companies. But still, all too many companies rely on the RCBD analysis developed by Sir Ronald Fisher in the 1920s, almost as if statistical time stood still.