On a theory of relativity

Research results are mostly relative.  Einstein gets credit for a Theory of Relativity, and he was a pretty clever guy, but just about every notion we consider is somehow compared with or relative to something else.  Indeed I often point out that you don’t know beautiful until you’ve seen ugly.  A concept of cold is needed to appreciate bitter cold.

So in my line of work I often visit with farmers who want to discuss the performance of their soybean crop.  “Last year my beans made 50 bushels”.  On its face this is too little – for if this farmer is used to raising 70 bushels it represents an extreme disappointment.  And for a farmer used to 35 bushel yields this is a great windfall.  Which is it?

Results from a yield trial – a test of more than one variety of a crop – are reported in various ways, but in simple conversation one might explain that variety A yielded 104% of the trial mean.  So once all the yields are measured one simply computes the arithmetic mean of all varieties and then calculates what variety A’s yield was as a percentage of the overall trial average.  In this case 104% is probably a good result (until it is held up against variety G which yielded 107% of the mean…  such is life).

Not all variety trials are created equal, and in order to evaluate the relative merits of one trial vs. another we can apply statistics.  And if we leave Mark Twain’s thoughts about statistics on the table for a moment, we can begin to make inferences about the relative strengths (or weaknesses) of two varieties when we compare them over more than one trial.  Comparing varieties to each other, and across trials (e.g., locations, years, other treatments) is an important undertaking – relatively speaking.