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Incorrect size correction.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 66191-92 (1985)
Incorrect Size Correction
ROBERT S. CORRUCCINI
Anthropology Department, Southern Illinois University, Carbondale,
l l h o i s -62901
KEY WORDS Size, Correction, Adjustment, Regression, Allometry,
Morphometrics
ABSTRACT
ln critiquing some size-removal algorithms for morphometric
data, Hartman professes to find error in Corruccini’s approaches. Actually the
error is Hartman’s: he assumed identity of different algebra symbol systems,
in fact ultimately using the inverse of the proper coefficient of adjustment.
a. Otherwise, as I point out (Corruccini,
1978:224), k‘lr = rla (where r is the correlation coefficient with size). Hartman (1983:
Fig. 2) finds “undesirable” results and that
“the modifications augment rather than diminish allometric influence” (Hartman,
1983:307) because he reverses independent
and dependent variables from my algebra
into his convention.
Y = bX”
Again, in Corruccini (1978:224, Equation
6) I follow an earlier source in using X to
between a given variable, Y , and overall size, represent what Hartman is calling Y (and
X . He then attributes to me (Hartman, 1983: my p<x) stands for the size variable, his X).
Equations 4 and 5) the procedure of correct- In simplified form, and translated to Hartman’s symbol system, I (1978:224) recoming to a form of:
mend a form of the correction
In reviewing size adjustments in morphometric analysis, Hartman (1983)asserts that
Corruccini (1972, 1978) “went astray,” that
my algorithms are “not to be recommended,”
and that a variety of my published results
“should be considered in that light.”
Using Hartman’s (1983:307) own symbolism, he finds regression of form:
Yadj =
Ya/x
Yadj = [ Y l ’ a ] / x
(where Yadj is the adjusted shape variable),
and points out that this is illogical. Indeed it
is, but Hartman’s symbol usage conflicts with
mine and his comments result from mistranslation of one system of presentation to
another.
My actual procedure (using the same X and
Y )was to perform regression of form:
X
= b‘yk’
(see Corruccini, 1972:379, second equation).
Then I (1972:380, Equation 1)recommended
y adJ. = y k ’
My k’ will be inversely proportional to Hartman’s a.
Provided either that major axis (Type ID
regression is used, or that correlation is
nearly unity between X and Y, then k’ = 11
0 1985 ALAN R. LISS, INC.
and this obviously will be directly proportional to the
that Hartman (1983:307) concedes “does give
the desired result.”
A possible cause of confusion is the earlier
(1972) uae of &-mode correlation coefficients
(similarity coefficients) to assess morphometric affinities in the adjusted data. Q-mode
correlations are dimensionless and putatively automatically remove the effect of size.
Like other workers, I have subsequently
(1978 and others) used distance coefficients
(dissimilarity coefficients), and their use necessitates dividing by X following exponentiation of Y to remove the gross size effect as
Received January 16, 1984;accepted August 22, 1984
92
R.S. CORRUCCINI
well as the allometric residual. The Q-mode
correlation coefficient behaves eccentrically
and I have not employed it for 13 years nor
do I recommend that others do so.
Obviously, this “spilling of ink” in our journal
be reduced by correspondence between authors of strong personal attacks and
the objects thereof prior to publication.
LITERATURE CITED
Corruccini, RS (1972) Allometry correction in taximetrics. Syst. Zool. 21t375-383.
Corruccini, RS (1978) Relative growth and shape analysis. Homo 28:222-226.
Hartman, SE (1983)A critique of some regression adjustments used in allometric size “correction” in numerical taxonomy. Am. J. Phys. Anthropol. 62r305-309.
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