There is an interesting section on ‘Bias and Consistency’, somewhat
complementary to what is being discussed, in the 1960 book by Simpson,
Roe and Lewontin, Quantitative Zoology, pp 27 – 30.
Antonio G Valdecasas
Fred Bookstein <[email protected]> escribió:
Seattle, November 19, 2022
Hello, morphometricians,
Let me put in my oar on this interesting discussion about
"bias" between observers. The topic is actually older than
my entire discipline of statistics -- the discussion began
199 years ago, in 1823, when Friedrich Wilhelm Bessel
(1784-1846), the great German astronomer, published some observations
about differences between two observers noting the time
of a certain event (ref. _Astronomische Beobachtungen auf der
Koniglichen Universitaets-Sternwarte in Koenigsberg von
F. W. Bessel, 8. Abtheilung vom 1. Januar bis 31. December 1822_,
1823, iii-viii [this citation is from Hoffmann, see below].)
The relevant term from history of
science is "personal equation," so named in English by the
British astronomer John Pond in 1833, when he introduced some early
least-squares approaches for their resolution.
It was first in astronomy that it was realized this would not be a proper
use of the word "bias," as when data-gathering is modulated by
human cognitions there is no such concept as "the true value."
Here's Wikipedia on the topic, from the article "Personal
equation" retrieved 11/19/22:
"Astronomy.
"The term originated in astronomy, when it was discovered that
numerous observers making simultaneous observations would record
slightly different values (for example, in recording the exact
time at which a star crossed the wires of a reticule in a
telescope), some of which were of a significant enough difference
to afford for problems in larger calculations. The existence
of the effect was first discovered when, in 1796, the Astronomer
Royal Neville Maskelyne dismissed his assistant Kinnebrooke
because he could not better the error of his observations
relative to Maskelyne's own values. The problem was forgotten
and only analysed two decades later by Friedrich Wilhelm Bessel
at Koenigsberg Observatory in Prussia. Setting up an experiment
to compare the values, Bessel and an assistant measured the
times at which several stars crossed the wires of a reticule
in different nights. Compared to his assistant, Bessel found
himself to be ahead by more than a second.
"In response to this realization, astronomers became increasingly
suspicious of the results of other astronomers and their own
assistants and began systematic programs to attempt to
find ways to remove or lessen the effects. These included
attempts at the automation of observations (appealing to the
presumed objectivity of machines), training observers to try
to avoid certain known errors (such as those caused by lack
of sleep), developing machines that could allow multiple
observers to make observations at the same time, the taking
of redundant data and using techniques such as the method of
least squares to derive possible values from them, and trying
to quantify the biases of individual workers so that they could
be subtracted from the data. It became a major topic in
experimental psychology as well, and was a major motivation
for developing methods to deal with error in astronomy."
A good recent reference on all this, including its role
in the history of sciences beyond astronomy (particularly
experimental psychology), is Christoph
Hoffmann, "Constant differences: Friedrich Wilhelm Bessel,
the concept of the observer in early nineteenth-century
practical astronomy and the history of the personal equation,"
_British Journal for the History of Science_ 40(3):333-365, 2007.
We morphometricians should feel free to try borrowing any
or all of the approaches Wikipedia listed. The first step is to
stop using the word "bias" in any discussion of these matters,
as Rohlf just suggested a couple of emails ago. The phrase
"personal equation" is clumsy, of course. Bessel himself referred
to it as a "constant difference between observers."
For GMM, the equivalent question might be along the lines
of "where, exactly, is this landmark?" to which the proper
response would be an authoritative "Wait, what?! The question is a
category error -- landmarks don't HAVE an 'exact' location --
their location differs from person to person, from image to image
of the same specimen, and from algorithm to algorithm of any
image analysis." (Especially in exceptional cases -- asking,
e.g., about the location of Menton in a Treacher-Collins
patient, or the exterior Lambda in a male gorilla skull.)
Indeed we can only fantasize that these differences turn
out to be "constant" between observers across data sets. I would
doubt that to be the case for most landmark configurations
as they arise in comparative anatomy and in paleontology.
In my opinion, the better way to proceed is not to classify
interpersonal differences as an aspect of "error," one
component of variance and covariance among several,
but instead to turn to modes of biometric explanation on which
different investigators can agree, for instance, the varimax
factor analyses of landmark configurations that I recommended
in my AJPA article of 2017 ("A method of factor analysis for
shape coordinates," AJPA 164(2):221-245, 2017). Different
investigators, with different "personal equations," should
nevertheless arrive at the same explanatory patterns for
the same sample of specimens. But usually different samples
of convenience lead to different pattern findings -- this is one of
the important ways in which biometrics differs from astrometrics.
Fred Bookstein
[email protected]
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