It is not plausible that statistics has made no meaningful advance over the past one-half century. After just several years, the difference between researchers using modern statistics and those using older methods will become substantial. Most importantly, statistical advantages become embodied in germplasm advantages reflecting a history of superior selections. Eventually, a slowly advancing breeding population falls so far behind another more rapidly advancing population that the future offers virtually no prospect of ever catching up again. Whether or not we are approaching a leveling off of the yield curve for a given crop, efficient research is critical in a manner that compounds from year to year.
Efficient research makes a modest difference the next year, but a huge difference the next decade.
It will not be possible for farmers to increase crop yields commensurate with expected world population increases, nor will it be possible for seed producers to maintain competitive advantages or increase market shares, if agricultural researchers conduct inefficient experiments. Bad design or bad analysis is equivalent to paying for yield data, and then throwing away half or three-quarters of the data. An inefficient experiment has excessive costs relative to the benefits it delivers. This documentation merely sketches the relevant theory, leaving a fuller account to these three publications. By definition, the expected or average value of the largest draw is the first order statistic.