> I welcome input on what normalcy tests between honey yield and population
would be more statistically relevant or what the article above gets wrong-
this is definitely above my pay grade.

It is not above ANYONE's pay grade. There is a barrier of jargon and
mystique around statistics, and most people hate math simply because they
had horrible math teachers who neither loved nor understood math themselves.
Science (in general) is the process of describing how certain/uncertain we
are about something, and statistics help with that, but some jerks walk
around trying to pretend that science is the art of proving one's own
infallibility, and use statistics the way a drunk uses a lamppost - not for
better illumination, but to try to support a shaky stance.

Here is a very detailed discussion of the subject, aimed at
"Non-Statisticians", and it even gives an example using Shapiro-Wilk, but
note that they list 9 different tests, so a wise man might use more than one
of them to see if one's data is truly normal.  (The "SPSS" package mentioned
costs money, there are over a dozen equally capable and free stats packages
out there that will run fine on even an outdated laptop.)

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3693611/

Better yet, here is a very accessible book that covers broad swaths of
statistics, and is illustrated well:
https://archive.org/details/TheCartoonGuideToStatistics

The importance of the issue of "normality" of a dataset cannot be
over-stressed.  Quoting the first paper - "Normality and other assumptions
should be taken seriously, for when these assumptions do not hold, it is
impossible to draw accurate and reliable conclusions about reality."

Yep, reality itself!  In simplest terms, nearly everything one can measure
will, given enough measurements, plot out in a bell curve. This is true for
simple "binomial" tests like coin flips, and for more complex scenarios,
where the outcomes are influenced by multiple unrelated and seemingly random
effects (each of them a binomial when viewed as an individual element).  So
nearly everything that is correctly measured will tend to plot out into a
bell-shaped curve.  If you don't have a bell-shaped curve, it reveals that
the data set is deeply flawed due to some flaw in the measurement/sampling
and the dataset DOES NOT DESCRIBE REALITY.

So, if claiming a "correlation", one had better first show that the two
datasets are "normal".  There are several ways to do this, and some involve
the dreaded calculus beastie, but suffice to say that when I see two
incomplete and very old sets of data,  I have higher expectations about
verification of their normalcy.   (That said, there was a project where a
large number of people transcribed handwritten ships logs from whaling
vessels to extract weather data readings from voyages in the Southern Ocean,
and the data that emerged was very nice, as things like thermometers were
treated as delicate scientific equipment by the men who relied on
chromometers, sextants, and not much else.)

Not having a firm grasp of basic statistical analysis and commenting on a
paper that uses statistics is much like a deaf man being an opera critic.
He can only comment upon what he can see, and there is no such thing as
"silent opera".





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