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Bushman Hottentot and South African Negro crania studied by distance and discrimination.

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Bushman, Hottentot and South African Negro Crania
Studied by Distance and Discrimination
G . P. RIGHTMIRE
Department of Anthropology, State University of New York,
Binghamton, N e w York 13901
ABSTRACT
Anthropometric, serological and previous skeletal studies bearing on
the question of Bushman-Hottentot similarities and the relationships of these populations to South African Negroes are summarized briefly. Measurements of well documented crania representative of these three groups are then examined using the
multivariate statistical techniques of generalized distance and discriminant function
analysis, and the following points emerge:
( 1) The Bushman-Hottentot generalized distance as computed on Mahalanobis’ DZ
for six characters, and again on DZ and Penrose’s CZH using 12 measurements, appears
small (and non-significant) relative to the Bushman-Negro and Hottentot-Negro separations, which achieve statistical significance a t the 5% level; in general the analysis
suggests Bushmen and Hottentots to be fully as similar in cranial form as i n blood
group and serum protein distributions. That these peoples should be “lumped” in a
Negro category appears doubtful on the evidence available.
(2) Simple two-group discriminant functions, computed o n subsets of variables selected from the 35 original measurements, correctly assign “race” in 89% of cases
when Bushman and Hottentot males are compared, and in 98-100% of cases when
Bushman skulls are paired with those of Zulus. The latter discriminants also perform
well when confronted with “new” (Sotho) skulls of both sexes. By showing which
measurements or aspects of morphology are important to group separation, discriminant analysis provides a n interpretation of differences between these series, and the
functions themselves should prove efficient aids for classifying material of unknown
or questionable origin, assuming that such skulls in fact belong in one of the parent
groups included i n the analysis.
( 3 ) A multiple discriminant approach, whereby seven groups of Bushman, Hottentot and Negro crania are located in a multidimensional space or statistical framework
defined by six 29-variable functions as axes, permits simultaneous discrimination by
both sex and race and allows correct assignments to be made for nearly 80% of all
(179) individuals tested. Examination of the scaled vector versions of the functions
suggests that measurements of over-all vault size are generally important in distinguishing between the sexes, while various aspects of skull form are the more efficient
race discriminators. It seems likely that other shape-directed measurements, more sensitive to racial variation in cranial morphology than many currently employed, could
and should be devised in order to exploit fully the capabilities of discriminants as
tools not only for assigning individual specimens to a population but also for classifying the populations themselves in objective terms.
The Khoisan peoples alive today, comprising both the Bushmen dwelling in semiisolated regions in or adjacent to the Kalahari desert and an undetermined number
of increasingly hybridized individuals of
Hottentot ancestry, constitute the scattered
remnants of populations which once
ranged over much of southern Africa. The
surviving Bushmen, estimated by Tobias
(’57) to number over 50,000, have been
the subject of assorted research projects.
Various tribes have been measured and
photographed, and diverse anatomical peculiarities have been duly recorded; in
other instances, determinations of skin reAM. J. Pwus. ANTHROP.,33: 169-196.
flectance, metabolic response to desert temperature extremes and nutritional status
have been of primary concern. Studies of
blood groups and hemoglobins, serum proteins and enzymes, are proceeding apace,
and members of several groups have been
tested for color blindness, cholesterols, and
estrogens. Many useful data have emerged
from such work, and more is certain to
follow. However, despite this trend, there
is yet scant agreement as to the range and
importance of morphological variation
among Bushmen and Hottentots, and little
information concerning the origins of these
peoples has come to light. We should like
169
170
G. P. RIGHTMIRE
to know more, not only about the interrelationships of Bushmen and Hottentots
and thc ties of each to other modern populations (e.g., the Bantu-speaking peoples),
but also about the wealth of ancient skeletal material from southern Africa, which
must hold the key to our understanding of
human evolution as it has occurred in this
area since the Late Pleistocene.
The present study is biometric in approach and comparative in nature, the
material to be compared consisting of
Bushman, Hottentot and South African
Negro crania. As such, it is neither novel
in concept, measurements having been
used by Linnaeus and Blumenbach to separate races in the eighteenth century, nor
especially broad in scope, but differs from
previous work carried out on the same or
similar material in the mode of analysis
employed. Emphasis is here placed on the
application of multivariate statistical techniques which, unlike more traditional univariate approaches, allow comparisons of
several groups or populations to be based
on many variables - all treated simultaneously and with due regard for the effects
of intercorrelation.
General aims and objectives of this work
may be set out briefly as follows.
( 1 ) Determination of generalized distances, based on measurements of skulls,
between Bushman, Hottentot and South
African Negro populations, and comparison of results yielded by different distance
techniques (e.g., Mahalanobis’ D2and Penrose’s CZn).
(2) Calculation of simple, two-group
discriminant functions useful for distinguishing members of these populations,
and also computation of multiple discriminants which, as axes, together define a
multidimensional space within which the
groups may severally be located by both
race and sex; such functions serve a purely practical purpose, as aids in the classification of individuals, on the one hand,
but also provide indications as to which
measurements or skeletal features are important to the differentiation of particular
groups.
The topics to be dealt with are thus rather specialized, both within the broad confines of human biology and, to a degree, in
the statistical concepts necessarily intro-
duced and utilized. This does not of cousse
detract from their general importance. Despite an unfortunate tendency on the part
of some more genetically-minded anthropologists to downgrade craniometry as old
fashioned, there is certainly no sound basis
for assuming, because development in such
systems is complex and not under simple
genetic control, that skulls or other skeletal
components are not a potential source of
valid taxonomic information. However, the
findings of craniometry do in fact encompass only a small part of measureable human variation and are perhaps best viewed
in the light of anthropometric, anthroposcopic and serological investigations of the
living peoples. The essential results of such
investigations, as well as a review of previous skeletal studies carried out on the
South African populations, are presented
below. Treatment here is in part historical,
but selective, and is not meant to be a fullscale history of all work done to date.
Mophology of living Bush,men and Hottentots. The numerous reports left us by
European travelers who had reached South
Africa in the seventeenth and eighteenth
centuries contain many references to indigenous populations encountered. Much
of this early material is illustrated, and a
woodcut apparently depicting Hottentots
(Ottentoo, Hottentoo, etc. : the origin of
the term is uncertain) was published as
early as 1508 (Singer and Jopp, ’67); in
some instances these sources provide valuable ethnographic data and physical descriptions of native South Africans. Impressions as usually recorded indicate the
pastoral Hottentots to be culturally and
physically distinct from the Bushman
hunter-gatherers. Cultural differences have
been confirmed by subsequent work,
though the question of morphology remains a tender one.
Anthropometric surveys of the living
shed some light on this and related problems, though studies in this field have
yielded some rather remarkable and largely unacceptable conclusions. Dart’s (’37)
much cited paper on the /?Auni-ZKhomani people of the southern Kalahari is a
case in point. After much careful observation and measurement of some 77 Bushmen, Dart affirms that in this group he
can detect evidence of segregation into
BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA
two separate “types” and that these types
are “sex-linked.” The first, prevalent
among females, is labeled “Bush’ and the
second, to which a majority of males is
allocated, is termed the “Boskop.” These
stocks, isolated primarily on the basis of
head form but later characterized as to
hair and eye color and even the nature of
the external genitalia, are thought to represent pure races which in the past had
hybridized to form present day Bushmen
and Hottentots. In addition, varying
amounts of “alien admixture” with the
“Brown race,” the “Armenoid” and the
“Mongolian” races can be recognized. This
sort of approach, while not out of place
30 years ago, is somewhat less palatable
today.
Strong typological seasoning also flavors
much of the work done since, though this
has not impeded a modest flow of useful
anthropometric data. The Kalahari group
studied by Dart has subsequently been
found to resemble most closely a sample
of 20 Bushmen from the Lake Chrissie
area of the eastern Transvaal, although
the latter are “smaller in stature, length
of head, minimum frontal width, bizygomatic width, . . . cranial width . . . and
arm length” (Toerien, ’58). These findings
render the /?Auni-#Khomani and Lake
Chrissie peoples generally shorter than central Kalahari (Naron) and Northern Bushmen (Kung, Auen, Heikum), but Wells
(’52, ’60) doubts that these differences are
“significant.” Dart’s Bushmen appear to
have wider (and shorter?) faces and broader noses than do the Kung, though possible
differences in measurement technique
make comparison awkward at best.
Perhaps the most complete single summary of Bushman and Hottentot measurements is that of Tobias (’55-’56). In this
comparative study of some 49 Auen and
Naron Bushmen (spread from Gobabis in
South West Africa to Ghanzi in Botswana),
the author finds both groups to be of relatively large stature (male means of about
158 cm) and thus concurs with previous
opinions concerning a north-south stature
gradient. Still, the tallest Northern Bushmen apparently fall slightly short of the
Nama Hottentot male mean of 163 cm recorded by Schultze (’28) and that for Kor-
171
ana (Hottentot) males given as 160 cm
by Grobbelaar (’56).
Thus, beyond the fact that Hottentots
seem to be generally taller than Bushmen,
and that some Bushmen differ from some
Hottentots in a few other miscellaneous
features, not much can be concluded from
the anthropomctric treatment so far accorded the living peoples. Perhaps a more
significant contribution of this type of research lies in the elucidation of that complex of anatomical characters common to
many Bushmen and Hottentots but distinguishing them from other African populations. Certain peculiarly Khoisan traits
have received considerable attention over
the years and are now mentioned in any
elementary text on race. The most striking
of these is of course steatopygia, referring
to a localized accumulation of fatty tissue
on the buttocks and thighs of the individual affected. This condition is largely restricted to females, though the associated
lumbar lordosis is present in both sexes.
The popular suggestion that it is analogous
to the camel’s hump (or tail of the fattailed sheep) and hence acts as a reserve
supply of fat useful in times of food shortage seems to be unsubstantiated, though a
similar function of nutriment for mother
and fetus during pregnancy bears looking
into (Tobias, ’57; Coon, ’65). In an analysis of subcutaneous adipose tissue taken
from the Hottentot buttocks, Krut and
Singer (’63) find a significant sex difference in fatty acid composition, but this
difference is paralleled in other white and
Bantu populations examined. Comparability in the composition of adipose tissue between groups leads the authors to stress
the role of fibrous (non-adipose) tissue in
the steatopygeous protrusion; it is hoped
that this new emphasis may yield more
concrete results concerning causal relationships involved.
Other morphological distinctions include
the well-known “pepper-corn” or tufted
type of scalp hair, short stature and small
faces, presence of eye-folds, macronympha
(protrusion of the large labia minora)
among females, a horizontal or semi-erect
placement of the penis in males, and a
light yellow-brown skin coloration. African
variation in the last feature has recently
been investigated with the aid of sophisti-
172
G.
P. RIGHTMIRE
cated spectrophotometric equipment, and
this technique provides clear separation
of Khoisan from Bantu peoples (Weiner,
Harrison, Singer, Harris and Jop, ’64). Naron Bushmen and Richtersveld Hottentot
males give percent reflectance figures of 40
to 45 at 685 mp, whereas Okavango Bantu
register in the low ’20’s. Although results
vary somewhat with the wavelength used,
Bushmen and Hottentots are thus appreciably ‘lighter” than the Negroes studied.
That these small light (“yellow”) skinned
peoples have been deemed similar in many
respects to Mongoloids is perhaps not surprising; however, despite claims to the
contrary (see Dart, ’52, ’54), it is difficult
to envision any substantial flow of Asiatic
genes into southern Africa, a conclusion
strengthened by the absence of the Diego
blood type in African populations (next
section). The cause of these resemblances
must therefore be sought elsewhere. Tobias
(’55-’56, ’ 5 7 ) , while not rejecting Dart’s’
theories out of hand, opines that both
groups have been subject to “infantilizing
tendencies” over long periods and have
thus come to resemble one another largely
via mutual retardation of developmental
processes underlying differentiation of bodily structures. So-called “pedomorphic” features have long been recognized in supposed early “Bush crania and are coilsidered quite prominent in extant groups,
though just why this tendency, accompanied by short stature, has prevailed remains a mystery. Part of the answer may
lie in adaptation to a dry desert environment, but Tobias (‘64) argues convincingly
that this cannot be a factor, desert conditions having been forced upon the Bushmen only in recent, historic times. Also, a
hormonal basis cannot be discounted; preliminary studies with South West African
Bushmen show these individuals to have
surprisingly high levels of total urinary estrogens, levels differentiating them from
Bantu and European subjects tested (Tobias, ’66).
Whatever the reasons, the fact that the
South African Bushmen share with Hottentots a rather distinctive set of morphological traits is certain and well documented;
however, whether these findings should be
viewed as conclusive evidence for separation of the Khoisan peoples from other,
Negro Africans is questionable. Blood group
investigations allow of no such simple dismissal of the problem and instead underline its complexity.
Serological considerations. Peoples of
Africa south of the Sahara, including Bushmen and Hottentots, were by no means exempted from the attentions of early investigators eager to apply the then relatively
new techniques of blood typing to as many
of the worlds populations as possible. The
various tentative and often conflicting conclusions arising out of this work (ABO
system only) have been summarized by
Dart (’50) and need not be considered further. Suffice to say that, with the recognition of new alleles and loci (including
some confined almost exclusively to persons of African origin) and continuing
perfection of methodology, a rather more
reliable serological picture of affinities
among these groups is becoming available.
Studies of more than 400 northern Bushmen from South West Africa carried out
by Zoutendyk, Kopec and Mourant ( ’ 5 3 )
not only suggest ABO similarity with other
(Heikum) people from the same area (Pijper, ’ 3 2 ) but also provide evidence for essential continuity of pattern (MNSs, Henshaw, Duffy) with African Negroes. Other
Bushman groups, resident in the central
Kalahari near Ghanzi, have been subjected
to extensive testing by Weiner and Zoutendyk (’59 ) , and the results do much to confirm previous conclusions. Thus, in their
high frequency of cDe (one of the highest
yet recorded for the continent), the ratio
of A, to A1, and most notably in the occurrence of V and Js, the Bushman closely
resemble their African neighbors. That
some differences do exist however is apparent in the Bushman Combination of
high A and low B frequency coupled with
a virtually complete absence of Rh-negative individuals.
Information relating to Hottentot blood
groups is also available for a variety of
tribes and localities across southern Africa,
though exact identification of individuals
tested has not always been reported. ABO
frequencies appear to be similar for “South
West African Hottentots” sampled by Pijper (’35), two groups of Korana centered
near Upington, Cape and from Kimberly
eastward into the Orange Free State (Grob-
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
belaar, ’55), and for more than 200 individuals living on reserves in South West
Africa (Zoutendyk, Kopec and Mourant,
’55). More recent findings also demonstrate
marked parallels among the Nama Hottentots and the Eondelswarts (Singer, Weiner
and Zoutendyk, ’61; Singer and Weiner,
’63).
To a large extent these Hottentots reflect that series of serological traits peculiar
to African Negroes and Bushmen; V and
Js are both present, A1 is more frequent
than A, and cDe and Henshaw occur in
relatively high proportions (the cDe figure
is not extreme as in the Bushmen, but the
Henshaw frequency is one of the highest
known). The total lack of Diego antigen
apparent in the Nama and the Bondelswarts agrees with the Bushman result and
may hold for (most) other African populations as well. Nevertheless the Hottentots, while Bushman-like in the absence of
Rh-negatives, are somewhat distinctive in
possessing a B frequency high by South
African standards.
Published data on the distribution in
Africa of abnormal haemoglobins, haptoglobins, transferrins, enzymes and their
deficiencies, etc., are still rather scarce (see
Tobias, ’66, for a review), but several relevant population differences have been
noted. The sickle-cell trait, present in varying amounts among Bantu-speaking Negroes, has yet to be identified in the Bushmen and Hottentots studied, this despite
the fact that Bushmen sampled at the Etosha Pan and along the Okavango River are
regularly infected with malaria parasites
during the annual rainy period (Singer,
’60). The Bushmen are also set apart from
other African peoples in their incidence of
the Hp’ (haptoglobin) allele: these Kalahari people geld a frequency of 29%,
whereas the figures for the rest of the continent rarely drop below the 51% recorded
for Nama Hottentots (Barnicot, Garlick,
Singer and Weiner, ’59; Singer, ’61). That
this should be the case is rendered (even
more) remarkable upon recalling the opposite Bushman extreme in frequency for
“typically African” cDe.
Still, while no adequate explanation in
terms of selective agents or migrations can
be advanced to account for the observed
patterns in gene frequencies, one may rea-
173
sonably conclude that both Bushmen and
Hottentots are generally African and Negroid serologically. This concordance has
led Singer and Weiner (’63) to suggest altering the definition of “Negro” to include
both groups, though obvious differences
prompt reservations to the effect that each
has undergone extensive local differentiation in the southern part of Africa. One
point is definite : blood group evidence
militates against any appreciable contribution by Mongoloids or Caucasoids to these
gene pools. “Europoid or Hamitic influence, “Australoid brow ridges, and Mongoloid eye-folds notwithstanding, the Bushman, Hottentot and Bantu Negro skeletal
material at hand must be analyzed with
strictly African evolution, perhaps from a
common stock, in mind.
Previous skeletal studies. Probably the
major portion of all anthropological and
anatomical investigation of the Bushman
and Hottentot peoples has been centered
on their skeletal remains. The volume of
literature dealing with this subject is
considerable, and, not surprisingly, a number of different points of view have been
put forward. However, in all this three
main classes or schools of interpretation
seem apparent, the central themes of
which may be set out as follows.
(1) Bushmen and Hottentots, thought
to be indistinguishable morphologically,
are considered as representatives of a single homogeneous “ B u s h or Khoisan race
(Shrubsall, ’1 1; Schapera, ’30; Galloway,
’33, ’37; Dart, ’37).
(2) A second view, adumbrated in
Dart’s (’37) work on living Bushmen,
holds that present day Bushmen and Hottentots are physically diverse, hybrid populations. Differences both within and between these groups are postulated and attributed to the unequal contribution of
some five or six (pure) strains or physical
types (e.g., Bush, Boskop, Kakamas,
Gerontomorph or Australoid, Europoid or
Europide, etc.) to the make-up of the
various regionally distinct modern peoples (Wells, ’49, ’51; Tobias, ’55, ’57; see
also the discussion of morphology of the
living.)
(3) Inherent in other studies is the assumption that, although most living
Khoisan peoples are heavily hybridized,
174
G . P. RIGHTMIRE
“true” Bushman and Hottentot physical
types may be discerned in certain of the
skeletal remains exhumed from old burials, middens, and the like; there is disagreement as to just which material best
exemplifies either type. This view difIers
from both ( 1 ) and ( 2 ) above in that by
and large the traditional Bush-Hottentot
dichotomy is retained as physically significant (Shrubsall, ’07, ’22; Slome, 29;
Broom, ’23, ’41; Drennan, ’38; Dreyer and
Meiring, ’37, ’52; Keen, ’47, ’52).
The evident confusion surrounding the
question of Bushman-Hottentot similarities
or differences is not traceable to any one
simple cause, but must stem in part from
the nature of the skeletal material available. That forming the subject of most
studies has been obtained through excavation or chance finds and is often of entirely unknown provenience; reliably documented specimens, skeletons secured
from individuals known as Bushman or
Hottentot during life, for example, are at
a high premium indeed, and though the
value of such remains has been pointed
out by Wells (’51) there has been little
attempt to build up a collection of this
sort for systematic study.
Further, heavy reliance on a typological
approach (wherein some individuals are
recognized as “typical” or “pure” on the
basis of preconceived ideas as to what a
Bushman or Hottentot skull should look
like while others are diagnosed as hybrids
on similar morphological grounds) has
tended to obscure results even in cases
where the material itself is reasonably
adequate. Shrubsall’s final ( ’ 2 2 ) assertion
that “the Hottentot skull is longer, narrower and higher and more prognathous
than that of the Bushman” seems to be
fairly soundly based, at least some of his
material being assignable to “known native tribes,” but Slome’s (’29) descriptions
of skulls of “relatively pure Bushman type”
and Keen’s more recent (’47, ’52) comparisons of “typical Bushman” “typical Hottentot” and “Bush-Hottentot hybrid’ crania
(not separated by sex) are of little value,
the “sampling” procedures employed taking no account of the range of variation
to be expected in any natural populations.
A rather more significant contribution
to the craniology of these peoples has been
made in a preliminary report by Stern and
Singer (‘67), who have in fact heeded Well’s
(’51) suggestion in the selection of their
specimens. Using only authenticated material (eight skulls identified as Bushman
male, six as Bushman female and four as
Hottentot), these authors are able to demonstrate via a series of univariate (t-test)
comparisons that, while Bushman males
are significantly larger than females, “racial‘‘ differences are slight and confined
mainly to general size; overlap in the
ranges of most metrical features between
the two categories is quite extensive. However, as Stern and Singer are quick to emphasize, the sizes of the samples employed
are dangerously small, and the conclusions
reached are subject to revision.
Clearly then, there is yet room for, even
need for, some added clarification of Bushman and Hottentot origins and interrelationships. Modern multivariate statistical methods have been little used in such
studies and would seem to constitute valuable tools with which to get at the question of what, if any, morphological significance can be attributed to the terms
“Bushman” and “Hottentot” and further
to obtain estimates of biological distance
separating these groups from South African Negroes.
MATERIALS
Of utmost importance here is the selection of samples of crania which are reliably documented as Bushmen, Hottentot
and South African Negro. Although a
number of “Bushman” and “Hottentot”
skeletal remains can be found in South
African museum and medical school collections, inspection of the (often very limited) catalogue entries associated with this
material reveals that in many instances
identification has been based on morphological criteria alone. In the present study,
such specimens of obviously dubious origin
have been excluded from consideration,
and instead, an attempt has been made to
utilize only those skulls for which racial
diagnosis is supported by some evidence
(records giving some particulars, such as
tribal affiliation, indicating that the individual was known in life, for example)
other than that of skeletal anatomy. As
already noted, Bushman and Hottentot
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
material meeting this requirement is h a d
to come by, so that sample sizes are not as
large as might be hoped; well documented
South African Negro skulls are fortunately
more plentiful, and adequate numbers of
these could be obtained in the Raymond A.
Dart collections of the University of the
Witwatersrand, Johannesburg.
The material finally selected for use has
been described in greater detail in another
paper (Rightmire, ’70) and is here listed
only in brief:
Bushmen. Twenty males and 16 females, examined at the University of the
Witwatersrand Medical School, Johannesburg; the McGregor Museum, Kimberley;
the South African Museum and the University of Cape Town Medical School, Cape
Town.
Hottentots. Sixteen males and three
females, from the institutions cited above.
South African Negroes. Sixty-two Zulu
(30 males and 32 females), 65 Sotho ( 3 5
males and 30 females), and 24 Xosa
males, all from the University of the Witwatersrand Medical School.
Sex as listed in institution records was
usually accepted, though wherever possible
these designations were checked by inspection of diagnostic postcranial remains;
in seven instances (all Bushmen), sex
was necessarily assigned on the basis of
cranial appearance alone. All specimens
included in the samples were clearly adult.
175
complete at the time of actual card punching.
GENERALIZED DISTANCE
The concept of intergroup distance,
measured in terms of gene frequencies or
miles, biometric or (as possible for man)
linguistic criteria, is basic to the assessment of affinity, whether between closely
related populations within a species or
between such diverse organisms as rattlesnakes and tuna fish.’ Recent advances
made possible through the availability of
modern computing equipment have been
concerned mainly with the estimation of
divergence at the molecular level, or at the
level of gene frequencies, and several measures of so-called genetic distance (based
mainly on blood traits) now seem promising for the study of man. However, the
trend in anthropology has been toward
development of generalized distance statistics designed for use with morphological
(e.g., anthropometric) characters. The history of Pearson’s “Coefficient of Racial
Likeness” is well known, and while no
longer in use in its original form, the
C.R.L. has given rise, directly or indirectly, to the family of distance techniques employed today.
Mahalanobis’ D2
One such technique, which has perhaps
acquired an undue reputation for difficulty
of computation, is the Dz statistical apMEASUREMENTS
proach suggested by Mahalanobis as early
A complete listing and description of as 1925 and later elaborated by the same
the 35 cranial measurements employed, author (’30, ’36) and by Rao (’48, ’ 5 2 ) .D’
together with a discussion of the criteria has been applied fairly frequently to probunderlying this selection, may be found lems involving morphological divergence
in human populations (Trevor, ’47; Maelsewhere (Rightmire, ’70).
Data collected “in the field were re- halanobis, Majumdar and Rao, ’49; Mukcorded on mimeographed blanks prepared herjee, Rao and Trevor, ’55; Hiernaux, ’56;
so as to permit easy transfer to standard Talbot and Mulhall, ’62) and seems to be
80-column computer punch cards. In those rather widely accepted as the best method
few cases where localized damage to a allowing mutual comparison of three or
skull had resulted in missing observations more groups (Campbell, ’63; Marshall and
(not tolerated by the several computer Giles, unpublished). Although there is
programs used), preliminary means were some doubt as to whether the conditions
calculated for the variables and groups in (normal distributions, homogeneous variquestion, and these sample means were ances and correlations) underlying the use
then inserted into individual data records
1 See Fitch and Margoliash (’67)for an example of
comparisons (via “mntation distance”) on
so as to make all specimens (excepting intergroup
a grand scale. Howells (’66a) has reviewed the question
of
correlation
between various distance estimates
Hottentot females, numbering three, for
(biological, geographical, linguistic) in a specifically
which no corrections were introduced) anthropological
context.
176
G. P. RIGHTMIRE
of this statistic are met by most anthropological data (Penrose, '54), the extensive
testing undertaken in several studies has
yielded encouraging results (see especially
Talbot and Mulhall, '62) ; likewise the
close agreement between D2 and other
simpIer distance techniques obtained in
some limited comparisons (Huizinga, '62;
Hiernaux, '64) does not in any way detract
from the status of D2 as that method most
soundly based in theory. The advantages
apparent in treatment of intragroup correlations and insensitivity to variations in
sample size should easily compensate for
any "extra" time spent in applying this
slightly more complex statistic.
The actual determination of Dz has been
considered extensively by Rao ('52), and
his method of transforming ("decorrelating") the original measurements, summarized in Rightmire ('69), is followed
here. Since the computation of distance
becomes laborious if more than 10 to 12
variables are included, the usual procedure is to effect a choice of measurements
to be used in the analysis. A general rule
of thumb is that highly correlated characters should be avoided, and that those
selected should have means which vary appreciably between groups; a better method
of selection exists, as will be demonstrated later on, but traditional approaches
are here followed throughout. Pooled coefficients of correlation for 12 measurements (basibregmatic height, maximum
frontal breadth, biauricular breadth, prosthion subtense, maximum malar length,
occipital sagittal chord, total sagittal arc,
orbit height, inter-orbital breadth, nasal
breadth, palate breadth and mastoid
length) meeting these criteria are given in
table 1.
Raw (uncorrected) D2 values for the
Bushman, Hottentot and Negro male
groups (lack of Hottentot and Xosa specimens precluded similar treatment for females), computed for only the first six
variables and again using the entire subset, are presented in tables 2 and 3 respectively. These raw distances may be
tested for significance quite simply, as the
quantity (nml / ni -k n,) Da, is distributed
as chi-square with p degrees of freedom
(ni = sample size of group i; nj = sample
size of group j; Deil = square of the gen-
m
I6
ii
i
M
m
0
IT
0
oi
N
cd
N
%
E
d
N
Y
Y
c
3o.i
s
0 0 0 0
BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA
177
Interpretation of results. Firstly it
eralized distance between groups i and j ;
and p = number of characters employed). should be pointed out that the set of disThe magnitude of this quantity is com- tances computed using only six characpared with the value of chi-square for ters provides essentially the same picture
the desired probability level in order to of group interrelationships as that obassess significance of any given I)” (Talbot tained after application of the entire 12
and Mulhall, ’62).
measurement battery. All individual D2
Since the samples are small and differ estimates, and especially those for Hottensomewhat in size, a correction should be tot-Negro pairings, increase to a limited
applied to all raw D2 found to be signifi- extent as more variables are included in
cant. The amount p (ni nj / ninj) is the analysis, but there is no change in
subtracted from DZijso as to insure that the distribution of values found to be sigthis value is an unbiased estimate of the
actual population distance. If ni and nj nificant at the 5% level. Here one might
were large, then this correction would be logically assume that the analysis has
trivial and need not be carried out. Table been carried far enough and that succes4 contains corrected values of (signifi- sive distance determinations based on even
cant) Dz calculated for 12 measurements. greater numbers of measurements (all at
least moderately correlated with those entered previously) would not yield “new”
TABLE 2
information
in a quantity sufficient to
Uncorrected values of DZ f o r male groups based
justify the additional effort expended. That
on six characters, and chi-square figures
f o r significance
this should be the case has been suggested
on
theoretical grounds, though empirical
Bush.
Hott.
Zulu
Sotho
Xosa
proof is so far lacking (Talbot and MulBush.
1.011 4.217’ 3.124’ 3.4801 hall, ’62).
Hott.
8.895
1.847 1.814 1.7031
Granting then that the 12-character Dz
Zulu
50.604 19.271
0.577 0.325
Sotho 39.759 19.917 9.320
0.174
values adequately reflect the actual interXosa
37.963 16.348 4.333 2.477
group distances, there remains the quesDistances are i n upper portion of the table, chition of attaching some biological interpresquares are below.
tation to the results. Of the ten distances
1 Significant ( p < 0.05).
listed in table 3, those separating the
TABLE 3
several Negro samples from each other
are the lowest recorded and are statistiUncorrected values of D 2 for male groups based
on 12 characters, and chi-square figures
cally non-significant; i.e., the null hypothef o r significance
sis that there is no difference between
these group means is not rejected at the
Bush.
Hott.
Zulu
Sotho
Xosa
5% level arbitrarily selected. This would
Bush.
1.506 4.561 3.416’ 4.0601
Hott.
13.385
3.132 2.700 2.961 1 seem not unreasonable in view of de
Villiers’ (’68) conclusion, based on examiZulu
54.732 32.679
1.255
1.203
Sotho 43.475 29.646 20.272
0.490
nation of some hundreds of crania, that
Xosa
44.290 28.425 16.039 6.976
the four tribal series (Cape Nguni, Natal
Distances are in upper portion of the table, chiNguni, Sotho and Shangana-Tonga) studsquares are helow.
ied by her “may be considered as samples
1 Significant ( p < 0.05).
of a single South African Negro population.” However, the simple fact of staTABLE 4
tistical significance, or lack thereof, is not
Corrected values of D2 f o r male groups
based on 12 characters
to be overemphasized, especially when
sample sizes are of the order dealt with
Bush.
Hott.
Zulu
Sotho
Xosa
here; non-significance of a D2 value does
Bush.
n.s.
3.562 2.474 2.960
not in itself prove that two samples are
Hott.
1.982 1.608
1.711
drawn from the same population but does
Zulu
- n.s.
n.s. 1
Sotho
- n.s. 1 indicate that differences in the characters
Xosa
used are too small for detection in groups
of the size available.
no
correction
introduced.
1 n.s , not significant;
+
178
G.
P. RIGHTMIRE
With these reservations in mind, it is
clearly rather premature to suggest that
Bushmen and Hottentots, whose Dz estimate of 1.506 quite definitely fails to attain significance on chi-square, differ no
more than would be expected of local
breeding isolates; still it is evident that
those two groups are closely associated,
more so than either is with any Bantu
tribe. In other words, the Bushman-Hottentot generalized distance is “small”
within the framework of the present study,
but it would be informative to have a
somewhat less restricted scale against
which to assess the degree of afinity implied by a distance of this magnitude.
One would like, for example, to know
just how “large” a DZ (preferably based
on cranial measurements) might be obtained in an analysis involving widely
divergent human populations. Unfortunately a comparison of the D2 results given
here with those published by previous
investigators is complicated both by variations in the number and type of measurements employed-most prior studies are
based on anthropometric, not craniometric, data-and
by minor differences in
actual computation of the generalized distance.
In an attempt to clarify further these
limited conclusions arrived at using Mahalanobis’ D’, an additional generalized
(i.e., multivariate) distance technique has
been applied to the Khoisan and Bantu
Negro data. Values of Penrose’s mean
square distance ’ calculated for each group
pair on the same subset of 12 variables
utilized for D2 are given in table 5, and
much the same set of relationships is apparent; in fact, CZHand D2are here highly
correlated, with r = 0.959. Bushmen and
Hottentots are again closely allied while
both, but Bushmen especially, are somewhat removed from the Bantu cluster.
However, coincidence of the two sets of
distances is by no means exact, and the
simpler Penrose estimates appear to overemphasize the basic Khoisan-Bantu dichotomy; on D2 Bushmen are roughly three
times as distant from Zulus as from Hottentots, while CZHyields a figure of over
6 : 1 for the same distance ratio. Other discrepancies exist, and in fact one must be
wary of attaching any quantitative sig-
TABLE 5
Values of Penrose’s mean square distance (C%)
partitioned into size and shape components. Distances apply to males only, and are computed on
the same subset of 12 measurements used for D’
-~
-
Bush.
Bush.
Hott.
Zulu
Sotho
Xosa-
0.180 1.159 1.010 1.250
0.109
Hctt.
Zulu
Sotho
Xosa
0.579 0.504
0.071
1.028
0.642
0.467
0.056 0.059
0.131 0.112
0.926 0.399 0.002
0.064
1.179
0.105
0.570
0.054
0.005
0.046
0.015
0.070 0.072 0.054 0.031
Values of .mean square distance are in the upper
part of the table; size and shape components are given
as thc upper and lower figures, respectively, in each
cell in the lower part of the table.
nificance to relations between the mean
square distances computed for different
pairs of groups (see Cain and Harrison,
’58, for a pertinent discussion); in this
respect, D2is far preferable, as betweengroup separations may be visualized as
“real” distances in Euclidean space (Kendall, ’57).
Despite these shortcomings, Penrose’s
method is informative in that the total
distance (CZH)may be broken down into
“size” (the square of the mean of all
character differences) and “shape” (the
variance of the character differences)
components, which appear to be independent or uncorrelated with each other.
If this is done, the Bushman-Hottentot
distance is seen to be heavily size dependent, in the sense that the dispersion
of group mean differences is relatively
slight. The size component again outweighs the contribution of shape in the
several Bushman-Bantu and HottentotBantu distances listed in table 5, but shape
seems to become important in distinguishing between the closely related Zulu,
Sotho and Xosa tribes. However, a cautionary note : the terms “size” and “shape”
as used here refer to statistical approximations and are only very loosely related
to biological reality; the suggestion that
an over-all difference expressed in the
form of C2,, is based predominately on
zThe mean square distance, C%, is computed bj
summing the squares of differences between (stan
dardized) mean values in any two populations and
dividing the result by the number of characters used
This statistic incorporates n o correction for measure
ment intercorrelations. See Penrose (’54).
BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA
size (or shape) differences in actual morphology may therefore be quite misleading (Huizinga, ’65). Further evidence
bearing on this point, available from discriminant analysis, will be presented later
on.
DISCRIMINANT ANALYSIS
That human skeletal morphology provides many indications of racial affinity
(as well as sex) is well known, and it is
generally agreed that the skull, more than
any other portion of the skeleton, is of
value in studies of this nature. However,
accurate appraisal of “race” from osseous
remains is an exacting task usually reserved for the trained anatomist or physical anthropologist, and even those most
skilled in these fields make no claim to
100% success in all trials. A discriminant
function approach to the problem has the
advantage of simplicity (one need be
familiar only with common cranial landmarks in order to apply a function) while
yielding good results, judging from the
limited number of reports so far available
(see Giles and Eliott, ’62; Howells, ’66b).
Also, inquiry as to the way in which discrimination is actually accomplished in
specific cases may provide substantial insight into which aspects of cranial morphology are important in distinguishing
between groups or populations; information of this sort is generally not obtainable from a D’ analysis, though Penrose’s
partitioning of mean square distance into
size and shape components is a step in
this direction.
In the discussion following, cranial
measurements have been utilized to compute a series of simple two-way discriminant functions serving to distinguish between Bushmen, Hottentots and South
African Negroes when sex is held constant; i.e., the sexes are treated separately
throughout. Various Limitations, both of
machine time and in the material itself,
dictate that the number of comparisons
be kept to three:
(1) Bushman males vs. Hottentot
males.
( 2 ) Bushman males vs. Zulu males.
( 3 ) Bushman females vs. Zulu females.
Dz results and the work of de Villiers
(’68) suggest that the several groups of
179
Bantu Negroes are much the same in their
morphology, so use of Zulus only in computing the discriminants should cause
little loss of generality; this can be
checked, employing Sotho males and females as test series where appropriate.
The several discriminant analyses were
carried out at the University of Wisconsin
Computer Center using a slightly modified
version of program EIDISC, written by D.
Morrison and C. Art and distributed by
the Vogelback Computing Center, Northwestern University, Evanston, Illinois.
Selection of variables. Before a discriminant function can be computed, one
must first make a decision as to which, if
not all, of the available measurements are
to be included in the analysis. A total of
35 cranial dimensions could be used here
(the computer will accept 5 or 55 with
equal grace), but application of the resulting discriminant would be quite laborious if more than a handful1 of skulls are
to be tested. Also, a shorter function computed on a subset of variables might be
nearly as effective in terms of the level of
discrimination achieved. Selection of such
a subset has previously been discussed
with reference to D2,though the method
employed is f a r from soundly based; variables were chosen by virtue of their low
interdependence as determined by simple
inspection of correlation coefficients. The
12 measurements selected then had to be
transformed before being utilized in distance determinations.
ClearIy a better procedure, as pointed
out by Howells (’66b), is to remove correlation before, rather than after, inclusion
of a measurement in a subset, as the
“best” variables for discrimination should
be those which contribute most to group
separation after having been adjusted for
correlation with others already selected.
That is, after a first character has been
specified, and its correlation partialed out
for all those remaining, the second entered should be that which now provides
the best discrimination between groups; a
third may be chosen after the effects of
these two have been partialed out, and
so on until all the variables have been
ranked in an order reflecting their efficiency, when taken together, in distinguishing the particular groups under scru-
180
G. P. RIGHTMIRE
tiny. The discriminant function may then
be constructed using some number ( a
subset) of the characters which are ranked
most highly. The decision as to just how
many variables are to be used is still fairly
arbitrary, as there is no way to predict
beforehand how effective a given function
will be; however, any set of characters
selected in this fashion should in all likelihood perform better than one composed
of the same number of variables chosen
without regard for the effects of intercorrelation.
Thus, as a preliminary to computation
of discriminants for the South African
material, 33 measurements ( 2 were omitted for technical reasons) were first run
on a program (BMD07M, distributed by
the Health Sciences Computing Facility,
U.C.L.A.) capable of ranking them by a
procedure similar to that briefly outlined
above. This program computes pooled
within-groups and total sample crossproduct matrices using all the data and
selects the character giving the highest
F-ratio as the first and “best” measurement; other characters are then added in
stepwise fashion. At each step the variables are divided into two disjoint sets
(“included and “remaining”), and the
two cross-product matrices are partioned
to permit independent analysis of the dispersion of those remaining. The variable
entered is that which gives the highest
F-value computed after removal of the
effects of those already selected. The results of this serial ordering procedure
were then used as a guide in selecting the
measurements to be employed in each of
the three discriminant trials carried out.
Bushmen ‘us. Hottentots. Sequencing
of all measurements, when the groups considered are male Bushmen and Hottentots,
indicates that 19 characters are best combined to form a discriminant, as shown in
table 6.
Group differences in most of these characters are quite small (see table 7), and
only two of the univariate F-ratios, given
to illustrate the discriminatory power of
each measurement when considered alone,
are significant ( p < .05 for palate length;
p < .001 for basibregmatic height). The
immediate expectation, that discrimination achieved with these variables will be
poor, is not entirely fulfilled, however, as
is evident from figure 1; this plot shows
the distributions of scores in both groups.
The mean discriminant score for 20 Bushman males is - 60.18 with a variance of
11.12 and a standard deviation of 3.33;
that for 16 Hottentot males is - 68.29
with a variance of 8.93 and a standard
deviation of 2.98.
Graphed results indicate three Bushmen
and one Hottentot to be incorrectly as-
TABLE 6
The 19 characters best combined to form a discriminant function between male
Bushmen and male Hottentots
Variables
Y=
1. Cranial length
Alveolare-basion
Basibregmatic height
Maximum frontal breadth
Bizygomatic breadth
Bimaxillary breadth
Prosthion subtense
Subspinal subtense
Maximum malar length
Malar subtense
Malar height
Frontal sag. chord
Frontal angle
Occipital subtense
Orbit breadth
Orbit height
Nasal breadth
30. Nasal height
33. Palate length
4.
5.
9.
10.
12.
13.
14.
15.
16.
17.
18.
20.
22.
26.
27.
29.
Scaled
vector
Weights
0.214
-0.556
-0.933
- 0.823
0.657
0.664
0.506
-0.705
- 0.655
0.800
0.764
0.169
0.793
0.727
0.331
- 0.802
- 0.451
0.500
0.509
-
Univ ariate
f-ratio
- 23.404
-20.296
15.992
19.546
7.116
- 12.221
- 10.127
2.06
0.61
17.00
0.66
0.00
0.36
2.73
3.72
0.58
4.550
0.12
8.293
4.002
14.799
12.734
3.980
- 9.236
- 5.680
7.486
8.421
0.67
0.68
1.44
0.78
0.75
0.54
0.01
2.45
4.71
6.059
- 16.873
-
-
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
SECT. PT.
20 BUSHMAN
I
-52
I
-54
I
-56
I
-58
I
-60
HOTTENTOT
16
181
d
d
I
-62
I
-64
I
-66
I
-68
I
-70
1
-72
I
-74
I
-76
Fig. 1 Djstribution of individual scores on the Bushman-Hottentot (male) discriminant. Relative to the sectianing point (-64.24),
three Bushmen and one Hottentot are misassigned by the
function.
signed by the function when a sectioning
point (here - 64.24, the average of the
group mean scores) is used as the basis
for decision on group membership; correct
assignments then total 32 or roughly 88%.
The erring Hottentot and one Bushman
are also misclassifwd (i.e., excluded from
their own group) relative to the 5% limits
of their respective distributions, the direction of deviation being in each case toward
the mean of the inappropriate group; these
individuals are thus rather emphatically
rejected as belonging in the populations
to which they were originally a l l ~ c a t e d , ~
Applying a one-sided test for exclusion
yields the limits and results listed below:
( 1 ) At a 99% probability, 13 Bushmen
with scores of - 61.35 or higher (less
negative) are excluded from being Hottentot; eight Hottentot skulls, falling at
- 67.93 or below (Le., with more negative
scores), are excluded from the Bushman
distribution.
(2) At a 95% probability, 15 Bushmen
scored at - 63.38 or above are excluded
as Hottentots; 13 Hottentot skulls, with
scores of -- 65.67 or lower, are excluded
from being Bushman.
On the second, less stringent, test, over
77% of all crania are excluded from the
“wrong” group, or to the correct one, and
the function is performing about as well
as could be hoped for, considering the
obvious similarities (and low Dz) between the two populations. This close
agreement in cranial morphology is underlined by the fact that, despite the larger
number of characters (19) included in
the function, the level of discrimination
observed is noticeably lower than that for
any of the other discriminant trials reported.
Careful reading of the Bushman-Hottentot scaled vector (the vector of weights
re-scaled to correct for differences in measurement size and dimensionality) suggests that the group differences upon
which discrimination depends can be summarized approximately as follows.
The Hottentot skull is higher (basion
to bregma) with greater breadth across
the frontal bone as measured at the coronal suture; these characteristics, both
quite heavily weighted on the function,
seem of prime importance to group separation. Also, the subnasal portion of the
face is generally more projecting, a condition implied by the moderate negative
scaling for alveolare-basion length and
subspinale subtense (and confirmed by a
review of the means for both measurements given in table 7). Greater height
of the Hottentot orbit plays a somewhat
smaller role.
The Bushman cranium is lower, both
absolutely and as measured by a height/
length index, but is “fuller” in the frontal region; i.e., the bone is expanded in
an antero-superior direction rather than
postero-laterally as in Hottentots. The
forehead is thus more nearly vertical in
appearance. Greater breadth across the
middle face and orbits seems a prominent
Bushman feature (bimaxillary breadth is
3 Nevertheless, the Hottentot is reliably documented
as such in the records of the South African Museum,
Cape Town; the Bushman’s credentials are less satisfactory, as identification is based mainly on the locality (Pearston, S.E. Cape) in which the skeleton was
found.
G . P. RIGHTMIRE
182
TABLE
7
Male and female arouz)means for 86 cranial measurements
Measurement
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
Cranial In.
Glabella prot.
Nasion-basion
Alveolare-basion
Basibreg. ht.
Upper face ht.
Cranial br.
Least front. br.
Max. front. br.
Bizygomatic br.
Biauricular br.
Bimaxillary br.
Prosthion subt.
Subspinale subt.
Max. malar In.
Malar subt.
Malar ht.
Front. sag. chord
Front. subt.
Front. angle
Occ. sag. chord
Occ. subt.
Occ. angle
Tot. sag. arc
Horiz. circ.
Orbit br.
Orbit ht.
Inter-orhital
Nasal br.
Nasal ht.
Nasion subt.
Nasion angle
Palate In.
Palate br.
Mastoid In.
Bush.
Male
180.60
4.80
94.20
92.95
123.30
62.05
134.80
94.40
110.35
124.40
111.80
90.45
30.60
19.95
51.20
11.30
19.43
111.00
29.50
31.10
88.45
28.45
33.65
360.20
502.05
39-60
31.20
21.95
25.80
44.15
16.40
18.20
43.25
36.95
24.55
Bush.
Female
Zulu
Male
Female
Zulu
Sotho
Male
Sotho
Female
Xosa
186.33
5.10
102.00
101.oo
134.43
68.56
135.20
9S.13
115.80
129.80
113.13
95.23
35.23
23.93
55.73
180.44
4.50
96.81
96.18
129.72
65.62
133.34
95.31
114.37
123.50
109.97
90.81
33.93
21.43
51.68
187.17
5.11
101.34
101.77
131.91
68.42
133.82
98.14
115.85
130.28
114.73
93.88
35.37
23.54
55.22
179.56
4.13
96.76
98.00
126.33
66.40
188.08
5.08
100.87
11.86
12.12
11.88
11.46
11.66
Hott.
Male
170.68 182.94
3.50
5.37
90.37
96.93
88.43 94.31
119.25 129.25
59.43
62.87
130.25 135.81
9o.m 92.43
106.12 111.50
117.25 124.43
105.00 112.00
86.43
89.44
29.87
31.94
20.00
21.87
46.31
51.87
10.87
11.43
17.00
18.94
105.00 112.12
29.25
28.31
29.81
33.18
87.00 92.31
26.56 27.56
31.68 32.25
345.75 368.37
478.06 505.37
39.00
37.62
31.50 31.68
22.81
22.18
25.87
24.62
45.50
42.62
15.62
15.50
17.37
18.18
45.31
41.12
35.81
38.25
20.12 24.50
Male
101.24
132.04
67.37
130.03 135.70
98.45
9zao
110.30 116.12
121.03 130.50
108.50 113.70
90.53
93.54
36.03
35.16
23.13
24.08
51.37
55.08
20.23
18.56
20.51
19.10
18.83
112.63 110.56 113.25 109.30 113.04
27.77 28.34
28.63 28.23 27.79
30.20
30.87
30.28 31.43
29.50
95.80 96.91
94.91 93.03
96.45
26.76 26.56
27.05 26.83 28.50
30.66
28.46 29.74
30.30 31.50
368.30 365.56 371.65 359.73 375.83
513.96 503.93 514.85 496.76 518.66
38.86 39.03
39.34
38.13
39.50
33.46
33.53
33.51 33.16 33.66
24.47 23.15 22.91
22.03
24.00
27.66
27.65
27.60
26.73
28.33
49.57
46.81
50.00
46.03 49.45
17.86
15.68
16.71 15.77 17.37
19.17
17.53 18.08 ia.13
18.58
48.63
46.21
49.02
47.60
46.91
39.40
38.71
39.45 37.73
40.33
28.53
24.53
28.28 23.73
28.66
Values are given in mm or, where appropriate, dezrees.
weighted positively), as does strong development of the cheek bones; bizygomatic
breadth, absolutely about the same in both
groups, is relatively greater in these skulls.
The malar itself is longer in Hottentots
but more robust, deeper in a vertical dimension, in the Bushmen. Differences in
other characters, of skull length and nose
form for example, are de-emphasized on
the scaled vector and are of lesser significance to discrimination.
Discriminant analysis thus suggests
that, while Bushman crania are generally
a little smaller than those of Hottentots,
gross size is only one of several factors
permitting (limited) success in separation
of these groups; predominance of the
“size” component in CgH, the interpopulation distance calculated by Penrose’s
method, is somewhat misleading. Aspects
of form in the frontal region, of facial
projection, and of malar development are
also important, though to repeat, “important” does not here imply statistical
significance of mean measurement differences. The relative inefficiency of the computed function complements the distance
results in showing considerable homogeneity among the Khoisan peoples.
Bushman males vs. Zulu males. Preliminary checking of Bushman and Zulu
measurements with program BMD07M
suggests that the discriminant function
for males be composed of 15 variables,
given in table 8. Quite a few of these
measurements, now showing generally
high F-ratios, appear in the preceding
Bushman-Hottentot comparison; but the
weighting is here rather different, and
the function evidently does not operate
183
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
TABLE 8
The 1 5 characters best combined to t o m a discriminant functw?ebetweea
male Bushmen and male Zulus
Variables
Y = 1.
2.
3.
4.
5.
6.
7.
10.
12.
13.
20.
21.
22.
23.
30.
_____
Cranial length
Glabella protrusion
Nasion-hasion length
Alveolare-basion
Basibregmatic height
Upper face height
Maximum cranial breadth
Bizygomatic breadth
Bimaxillary breadth
Prosthion subtense
Frontal angle
Occipital sag. chord
Occipital subtense
Occipital angle
Nasal height
SECT.
PT.
Weights
0.242
0.212
- 0.421
0.391
0.444
-0.399
- 0.368
0.420
-0.452
0.482
0.484
0.574
- 0.348
0.336
0.517
Scaled
Univariate
f-ratio
vector
7.236
1.822
- 14.715
12.058
16.368
- 10.249
'- 12.526
13.161
- 15.457
7.895
10.683
20.670
- 7,981
9.957
9.882
-
65
21.19
0.70
28.70
39.17
52.44
37.16
0.08
17.11
11.26
46.11
0.96
24.01
3.10
5.84
46.19
NEGRO^
SOTHO
20 B U S H M A N d
I
135
I
I40
I
145
BZULU
1
I50
I
155
1
I60
a
I
165
Fig. 2 Distribution of individual scores on the Bushman-Negro (male) discriminant. Relative
to the sectioning point (143.93), one Zulu and four Sotho test crania are misassigned as Bushman
by the function.
in the same way. Discussion of the scaled
vector is better left until the corresponding
female function can be considered at the
same time.
The mean discriminant score for 20
Bushman males is 137.92 with a variance
of 4.69 and a standard deviation of 2.16;
that for 30 Zulu males is 149.93 with a
variance of 9.74 and a standard deviation
of 3.12. Not surprisingly, segregation of
Bushmen and Zulus is better than that
obtained for Bushmen and Hottentots;
with respect to the midpoint (143.93), all
of the Bushman crania and 29 of 30 Zulu
skulls are assigned correctly, for a total
of 98%. Assignment becomes perfect, all
individuals are properly allocated, if the
sectioning point is shifted by 1.5 units to
142.43. (That the function really serves
to distinguish Bushmen from Bantu Negroes generally is demonstrated by the
following: of 35 Sotho male skulls run as
a test series, only four are incorrectly assigned as Bushmen when the original sectioning point is used, bringing the total
number of correct assignments to 80,/85
or 94% (see fig. 2). (Only two Sothos are
misassigned if the lower point is substituted.)
Misclassifications at 95% are about as
expected; one Bushman and two Zulus deviate beyond the limits of their distributions, calculated as 133.67 - 142.16 and
143.81 - 156.04 respectively. None of the
three individuals is similarly misclassified
at a 99% probability.
As for exclusion, results are perfect (all
Bushmen are excluded as Zulus and vice
184
G . P. RIGHTMIRE
versa) if a 5% probability of error is
accepted, i.e., using a limit of 5% for
each appropriate tail. Thirty-four of the
35 Sotho skulls, with scores of 141.48 or
higher, are also excluded as Bushmen by
the same test.
Bushman females vs. Zulu females.
When the samples compared are Bushman
and Bantu females, rather than males, the
14-variable discriminant shown in table 9
applies. This choice of measurements
shows some agreement with that used for
male discrimination, but correspondence
of the two functions is hardly exact. Discrepancies may be traced, at least in part,
to the role of basibregmatic height in the
two comparisons. For males, this variable
has the highest univariate F-ratio and is
therefore the first entered by the selection
program: for females, however, skull
height falls second to palate length in
F-value, thereby just missing a prominent
position in the subset. At subsequent steps
the measurement is again rejected and
does not appear in the function at all.
Since the order of variables obtained is
in fact heavily dependent on the first character selected, differences in this female
subset, "based on palate length, are not
surprising.
The mean discriminant score for 16
Bushman females is 91.25 with a variance
of 3.08 and a standard deviation of 1.75;
that for 32 Zulu females is 104.23 with
a variance of 9.54 and a standard deviation of 3.08. Relative to the midpoint
(97.74), assignment is correct for all
cases, so that the function does a perfect
job when tested on the same data from
which it was computed. When confronted
with new material in the form of 30 Sotho
female crania, the discriminant performs
less well, misassigning eight of these individuals as Bushmen (fig. 3). Note, however, that if the sectioning point is lowered
by 1.5 units to 96.24, only five Sotho skulls
are so misplaced, while 100% of Bushmen
and Zulus are still assigned correctly;
cases of mistaken identity then number
5/78 or 6.4% of the total sample tested.
If the actual group distributions are considered, individuals are seen to be misclassified, or excluded from their own
groups, as follows:
Two Bushmen at 95% probability, 1
at 9 9 % ; three Zulus at 9 5 % , none at
99%.
Absolutely correct classifications as assessed on a one-sided hypothesis, using a
probability of 99%, are made for:
All (16) Bushman skulls, which are
excluded as Zulus; all (32) Zulu skulls,
excluded from the Bushman distribution;
25 Sotho test crania, also excluded as
Bushmen .
The efficiency of discrimination obtained for these female skull series is thus
about the same as that observed for males
and is generally quite high, indicating a
definite divergence in morphology between
Bushmen and Bantu Negroes. Population
differences, as read from the scaled versions of the functions, seem especially apparent in the occiput, which is strongly
TABLE 9
The 14 characters best combined to form a discriminant function between
female Bushmen and female Zulus
Variables
Y = 1. Cranial length
2.
3.
9.
12.
is.
16.
17.
20.
21.
22.
28.
29.
33.
Glabella protrusion
Nasion-basion length
Maximum frontal breadth
BimaxiUary breadth
Maximum malar length
Malar subtense
Malar height
Frontal angle
Occipital sag. chord
Occipital subtense
Inter-orbital breadth
Nasal breadth
Palate length
Scaled
vector
F-ratio
9.645
2.666
-11.824
16.362
- 3.585
5.954
- 2.309
4.940
9.692
9.771
11.389
- 1.842
6.555
7.785
32.13
6.63
22.73
33.55
8.35
19.35
8.59
7.99
8.05
41.84
Weights
0.253
-0.310
-0,395
0.519
-0.107
0.220
-0.244
0.404
0.537
0.288
- 0.490
-0.106
0.406
0.554
-
-
-
0.00
1.53
17.27
64.55
185
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
62 NEGRO$!
PT.
SECT.
I
SOTHO
n
16 B U S H M A N
1
1
1
I
1
I
88
90
92
94
96
98
I
100
I
I02
QZULU
I
104
I
106
$!
I
I
I
108
110
il2
Fig. 3 Distribution of individual scores on the Bushman-Negro (female) discriminant. Relative to the sectioning point (97.74), eight Sotho test crania are misassigned as Bushman by the
function.
curved in Bushmen, flatter in the Negroes men must be determined separately; only
( a point verified by Tobias, ’59). Breadth two groups or populations may be conacross the maxilla is again a Bushman sidered in any single trial. However, this
feature in combination, while a high simple one-dimensional approach can be
cranial vault is more characteristic o i generalized without much difficulty to a
Bantu, at least for males; basibregmatic situation in which there are more than
height does not figure in the female com- two groups of objects, and discrimination
parison. Facial projection, bizygomatic is accomplished in several dimensions, or
breadth (males), and width of the frontal along several functions, simultaneously.
(females) all contribute moderately to dis- In other words, it is possible to construct
crimination, though it is of interest that a “test” space in which an individual, or
aspects of malar form and forehead full- sets of individuals distributed as natural
ness, important to the Bushman-Hottentot populations, can be located by means of
distinction, here play lesser roles.
scores obtained on some number of axes
In conclusion, then, these two-way dis- or multiple discriminant functions; fossils
criminants perform sufficiently well to be or other material to be classified can then
of practical use in distinguishing between be plotted in this space and a decision
crania of several South African popula- made as to probable group membership.
tions; they should prove efficient tools for
Such an analysis has been carried out
classifying material of unknown or ques- for seven groups of Bushman, Hottentot
tionable origin, providcd of course that and Negro crania, comprising 179 specisuch material can legitimately be con- mens in all. In order to insure the greatest
tained in one or another of the groups possible efficiency of discrimination, there
being tested. The technique supplies a has been no systematic attempt to select
decision between two specific alternatives, a subset or otherwise cut down on the
and no more; that is, judgment will not number of variables used, though six of
usually be withheld, even if neither is the 35 available measurements, missing
biologically “correct.” This limitation, un- for certain likely test specimens (Hottentot
avoidable in simple discriminant analysis, females, for example), have been omitted.
becomes less troublesome as more popula- Computation yields six functions, listed in
tions (and functions) are introduced.
table 10 with the percentage each contributes to total discrimination.
Multiple discriminants
The first discriminant is the most imThe discriminant functions presented in portant, others making successively less
the preceding sections have the advantage contribution, and it may be questioned
of being easy to apply, but their use is whether all six are indeed statistically
restricted in that sex and race of a speci- significant, i.e., whether there is “real”
186
G. P. RIGHTMIRE
TABLE 10
Multiple discriminant functions for differentiating Bushman, Hottentot, and South African
Negro crania, w i t h the percentage each contributes to total discrimination
Variables
Roofs,
per cent of trace:
1. Cranial In.
2. Glabella prot.
3. Nasion-basion
5. Basibreg. ht.
8. Least front. br.
9. Max. front. br.
10. Bizgyomatic br.
11. Biauricular br.
12. Bimaxillary br.
13. Prosthion subt.
14. Subspinale subt.
15. Max. malar In.
16. Malar subt.
17. Malar ht.
18. Front. sag. chd.
19. Front. subt.
20. Front. angle
21. Occ. sag. chd.
22. Occ. subt.
23. Occ. angle
24. Tot. sag. arc
26. Orbit br.
27. Orbit ht.
28. Inter-orbital
29. Nasal br.
30. Nasal ht.
31. Nasion subt.
32. Nasion angle
35. Mastoid In.
Weights
I
11
54.11
24.13
0.244
0.098
0.277
-0.101
0.025
0.099
-0.157
0.268
0.019
0.004
-0,147
0.214
0.038
0.125
0.166
- 0.137
0.089
0.179
-0.011
0.166
-0.077
-0.106
- 0.020
-0.148
0.166
0.016
-0.125
0.067
-0.084
-0.254
-0.039
-0.233
0.151
-0.061
-0.142
- 0.055
-0.113
-0.191
0.073
- 0.077
0.376
-0.279
-0.291
0.200
-0.042
-0.058
0.107
-0.394
-0.208
-0.157’
0.080
0.184
-0.185
0.077
0.155
0.058
-0.050
0.377
I11
8.40
-0.106
-0.018
0.372
-0.427
0.219
-0.210
-0.060
0.197
-0.a~
0.519
- 0.069
-0.018
-0.152
0.216
0.126
-0.012
-0.071
-0.313
0.158
-0.174
0.335
-0.051
0.113
-0.266
0.100
-0.174
-0.129
0.037
-0.190
VI
V
3.91
IV
6.29
0.090
0.147
0.111
0.172
- 0.247
-0.198
-0.070
-0.201
0.127
0.185
-0.059
-0.144
0.069
0.079
0.090
-0.480
-0.199
0.281
-0.179
0.069
0.037
-0.137
0.107
-0.246
0.111
-0.112
-a.i30
0.373
0.336
-0.043
0.178
0.055
-0.012
-0.016
-0.061
-0.1%
0.120
- o.oa0
- 0.034
0.329
- 0.018
0.006
- 0.096
-0.190
-0.150
0.209
-0.185
-0.171
0.268
0.185
-0.135
-0.0991
0.246
- 0.235
0.094
0.062
-0.124
- 0.132
3.15
- 0.253
- 0.009
0.243
-0.283
0.143
-0.174
0.535
- 0.208
-0.328
- 01.155
0.252
- 0.410
0.088
0.027
- 0.231
0.110
0.023
0.045
- 0.013
- 8.337
0.389
-0.191
-0.183
-0.052
-0.089
0.439
-0.090
0.122
-0.088
-
TABLE 11
The distribution of group mean scores for Bushman, Hottentot, and South African Negro crania
~~~
Discriminant functions
Variables
I
Bushman males
Bushman females
Hottentot males
Zulu males
Zulu females
Sotho males
Sotho females
70.22
65.64
71.45
77.92
72.70
77.01
71.79
separation of the group means in all six
dimensions specified. This can be tested
with the aid of Bartlett’s chi-square approximation for the latent roots associated
with each function (see Rao, ’52, pp. 371373). Using this approximation, residual
variation (distributed as chi-square) left
over after removal of the first (1, 2, 3, . . .
etc.) roots can be tested for significance;
if this residual chi-square is attributable
to chance, there is then no evidence for
variation in other dimensions, and the
remaining roots (and functions) can be
11
- 37.51
-39.64
-40.21
-42.42
-43.97
-41.24
-43.16
111
IV
71.68
67.57
71.36
69.49
69.75
72.93
71.95
64.53
63.24
69.08
65.29
67.92
67.18
64.95
discarded. Test results indicate only the
f i s t four roots (together accounting for
about 93% of the total variance) to be
significant, and the corresponding functions thus essentially exhaust the discriminatory power of the battery. Only these
four functions need be considered further.
Group mean scores on each of the significant discriminants are presented in
table 11.
As coordinates, these figures specify the
mean vectors or “centroids” (analogous to
distribution means in the univariate case)
187
BUSHMAN, HOTTENTOT A N D AFRICAN NEGRO CRANIA
of each group in the discriminant space.
Individual skulls, also located by their
scores on the four functions, are distributed as swarms of points surrounding the
centroids, these distributions (simple ellipses in 2 dimensions) here taking the
form of hyperellipsoids oriented differently
for each group. Graphic portrayal of the
mean vectors, some shown with expected
distribution limits (90% contours, or ellipses drawn so as to contain 90% of individuals belong to the populations indicated), is attempted in figures 4, 5 and 6.
Each plot utilizes only two functions, so
that the figures really represent slices or
planes taken through the test space of
four (actually 6 ) dimensions. This is a
convenient way of visualizing the relative
proximity of one group to another and
also the placement of individuals with respect to their own and other group centroids; however, it is not especially accurate and can give false impressions
concerning inter- and intragroup relation-
ships, which are better interpreted by
reference to classification data computed
by the program.
The problem of inferring an individual's group membership from his several
discriminant scores is rather complex, as
the sectioning point and standard deviation approach, familiar from the two-way
analyses, is no longer applicable. Instead, chi-square is used to provide an index of the extent to which a skull resembles a particular group, or one centroid
resembles another; these classification
chi-squares are computed by pre- and
postmultiplying the inverse of a group's
dispersion (variance-covariance) matrix
by a vector of the individual's deviation
scores (Cooley and Lohnes, '62, chapter
7). The seven figures resulting for each
skull are used as the basis for assignment
(e.g., to that group with which the specimen has the lowest chi-square and hence
the greatest similarity) and also classification. For example: since for six degrees
-50r
I
+ZULU
A
I-
60
MALE SKULLS
HOTTENTOT F E M A L E
SKULLS
I
I
I
1
I
65
70
75
80
85
Fig. 4 Bushman, Hottentot and Negro group centroids on multiple discriminants I and 11;
90% contours are shown for Bushman and Zulu groups. Zulu male and Hottentot female crania are
plotted individually.
188
G. P. RIGHTMIRE
Hottentot males (26). Correctly assigned in 14 cases; two misassigned as
Sotho female. No misclassifications at
95%.
Zulu males (30). Five skulls misassigned, four as Sotho male, one as Sotho
female. Two misclassified at 95%, none
at a 99% probability. (Of the Zulu males
plotted in fig. 4, 3 are shown lying outside
of the 90% probability ellipse; computed
chi-squares indicate that in fact 4 individ75
80
85
uals are misclassified at this level.)
Fig. 5 Group centroids on multiple discrimiZulu females (32). Seven cases misnants I and 111.
assigned, two as Sotho male, five as Sotho
female. Only one skull is misclassified at
a 95% probability.
Sotho mazes ( 3 5 ) . 12 individuals misI
Hd
assigned, two as Hottentot, the rest as Zulu
male or Sotho female. Two misclassified
Ozp
.sd
at 95%, none at a 99% probability.
Sotho females ( 3 0 ) . Nine skulls misassigned, three as Bushman or Hottentot,
five as Zulu, and one as Sotho male.
Again, two are misclassified at 9 5 % ,
none at a 99% probability.
Correct assignments, using multiple
tH I L25
discriminants, are thus made for 141
70
75
80
05
Fig. 6 Group centroids on multiple discrimi- cases totaling approximately 79% of the
nants I and IV.
entire series tested. Although lower than
that obtained on the several separate twoof freedom the probability of obtaining way functions (which are not directly
chi-square larger than 12.6 is 0.05, an in- comparable), this level of efficiency seems
dividual would be excluded at 95% prob- quite satisfactory, considering the numability from any group for which his ber of groups involved. It is worth pointcomputed value is 12.6 or higher but ing out that ( a ) fewer than 10% of Bushwould be correctly classified at the same man and Hottentots are misassigned, and
probability if chi-square for his own group (b) Bantu individuals are misassigned
were below this level. Thus the distances mainly by sex or tribe (or both), but not
of a particular skull from each of the pop- as members of some Khoisan population.
ulation centroids may be tested for sig- Considerable blurring of the Zulu-Sotho
nificance and an appropriate assignment distinction, rather than sharp discriminamade, or, if the skull is sufficiently dis- tion, is only to be expected.
Absolute classification at a 95% probsimilar to all populations included in the
analysis, it may be excluded from mem- ability, meaning exclusion at this level of
a n individual from all groups other than
bership in any group.
Assignments and classifications as read his own, is made for only 23% of cases,
directly from the program output are as the figures ranging from a high of 69%
(11/16 Bushman females) to 6% ( 2 / 3 2
follows :
Bushman males ( 2 0 ) . Correctly as- Zulu females). Things are somewhat betsigned in 18 cases; one misassigned as ter if only two categories, Khoisan and
Hottentot, another as Sotho female. No Bantu, are employed, in which case 50%
(26/52) Bushmen and Hottentots) and
misclassifications at a 95% probability.
Bushman females (16). 15 skulls as- 57% (72/127) Zulu and Sotho) of skulls,
signed correctly, one incorrectly as Sotho respectively, are excluded from membership in the inappropriate group constellafemale. No misclassifications at 95%.
.
I
I
J
189
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
tion. Three additional Negro specimens,
correctly excluded from being Bushman
or Hottentot, also deviate beyond the expected 5% limits of all Bantu distributions.
When the functions are tested against
new material of known Bantu origin (24
Xosa male skulls), results are again encouraging. In all, 19 of the test crania, or
nearly 80% of the series, are excluded by
chi-square from the several Khoisan distributions, and the five remaining specimens are at least outside the Bushman
5% limits (though just within the corresponding Hottentot distribution). None
of the Xosa skulls are assigned (‘%best
fit”) as Bushman or Hottentot.
Three Hottentot female crania, useless
as a sample, have also been treated as test
material and are plotted in figure 4. Their
positions in the discriminant space are
about as expected, and no further comment seems required.
Interpretation of the functions. The
several discriminants, together demon-
strated to be reasonably efficient in assigning both sex and race of South African
crania, may now be examined on an individual basis; each is contributing rather
differently to over-all group separation,
and from one function to another, corresponding measurements do not everywhere have equal roles. Scaled vectors
and univariate F-ratios, again useful as
interpretory aids, are listed in table 12.
Function I, which accounts for 54.1%
of total discrimination, appears to separate the groups by sex primarily; the listing of mean scores and figure 4 show a
segregation of males from females within
both Bantu and Bushman categories
(along axis I in the figure). Also, if function I is considered for the moment as
an independent sexing formula and applied
in separate trials within populations, results are reasonably good; using appropriate sectioning points (again the average
of mean scores for the two groups, males
and females, tested in a given trial), totals
of 89% of Bushman. 85% of Zulu and
TABLE 12
Scaled vectors and iinivariate F-ratios for differentiating Bushman,
Hottentot, and South African Negro crania
~
~~~~
1.
2.
3.
5.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
26.
27.
28.
29.
30.
31.
32.
35.
Cranial In.
Glabella prot.
Nasion-basion
Basibreg. ht.
Least front. br.
Max. front. br.
Bizygomatic br.
Biauricular br.
Bimaxillary br.
Prosthion subt.
Subspinale subt.
Max. malar In.
Malar subt.
Malar ht.
Front. sag. cha.
Front. subt.
Front angle
Occ. sag. chd.
Occ. subt.
Occ. angle
Tot. sag. arc
Orbit br.
Orbit ht.
Inter-orbital
Nasal br.
Nasal ht.
Nasion subt.
Nasion angle
Mastoid In.
~
Scaled vectors
Variables
I
17.726
0.063
- 8.771
14.879
2.433
7.654
9.668
- 7.491
5.503
6.691
0.402
7.720
- 1.453
- 2.801
- 1.256
- 5.235
6.019
1.115
- 5.390
3.550
- 14.302
- 6.051
- 1.060
- 8.145
4.779
6.673
1.913
- 1.574
12.843
-
I1
7.134
4.717
- 6.036
1.762
6.265
- 9.661
15.629
1.037
3.792
- 5.295
- 2.054
- 5.259
- 3.580
1.942
4.932
13.280
- 10.091
- 20.658
8.628
- 2.245
- 9.835
2.549
- 10.651
- 7.278
- 4.960
3.447
6.055
- 5.m
2.609
-
-
I11
- 7.681
- 0.300
22.202
-29.692
13.833
- 12.856
- 3.484
10.752
- 5.124
19.368
- 2.549
- 0.842
-
2.847
5.710
8.017
0.412
2.566
-22.195
6.829
9.193
57.144
- 1.208
3.054
9.315
3.166
- 7.485
4.237
1.157
6.475
-
-
IV
- 14.613
-~
~
2.158
11.009
- 4.117
- 9.095
4.255
4.616
4.896
- 29.652
- 7.417
10.443
- 8.287
1.302
0.972
- 8.739
3.777
- 8.923
7.838
- 4.831
- 6.868
63.534
8.001
- 1.173
6.214
1.744
- 0.531
- 0.531
- 1.925
- 6.253
F-ratio
20.88
5.15
17.61
21.10
9.31
13.12
26.91
13.96
8.72
16.54
7.80
17.12
1.98
7.51
6.69
1.13
3.06
10.35
0.90
4.34
9.04
3.07
5.90
6.91
5.07
16.17
3.12
1.52
28.84
190
G . P. RIGHTMIRE
89% of Sotho skulls are correctly assigned
by sex. Distinctions by race are not as
clear on this discriminant, despite, for
example, the extreme divergence of Bushman females from Zulu and Sotho males.
Further examination of the scaled vector indicates that the variables contributing most to separation of the sexes are
mainly gross measurements of the skull
vault: maximum length, height taken
from basion to bregma, total sagittal arc,
and various breadths, that taken across
the zygomatic arches outweighing the
biauricular dimension in relative importance. Maximum frontal breadth fares
well, though the closely correlated minimum breadth (perhaps not properly a vault
dimension at all) does not seem particularly useful.
Further generalization is difficult, though
evidently mastoid length, height of the
nasal aperture and maximum malar
length provide additional independent information while other measures of malar development and angularity do not.
Breadth taken between the orbits achieves
at least a moderate loading on all sexing
functions and surpasses both orbit breadth
and height in this respect; this is unexpected as the inter-orbital distance has the
lowest F-ratio of the three.
Function I1 contributes roughly half as
much (24.1% ) to overall discrimination
and furnishes limited segregation of
groups in a new dimension, this time
mainly by race or population rather than
by sex. The Bushmen receive the highest
(least negative) scores and are removed
from Bantu of either sex; Hottentots, with
a lower mean score, make a closer approach
to the Negro groups and so occupy a more
intermediate position. Sex differences
within each population are consistent
(males have higher scores than females)
but slight, and discrimination on a sex
basis seems of only minor concern.
That this function is indeed doing
something different from discriminant I
is obvious from its scaled vector; while
bizygomatic breadth is again ranked
highly (and apparently is operating once
more as a sex indicator), many other
measurements seen to be of major importance in sexing (e.g., cranial length
and height, biauricular breadth, and mas-
toid length) here receive little emphasis
and have some of the lowest scaled
weights listed. Sagittal arc (registering
size?) and nasal height are also reduced,
though the contrast is not so striking.
Far more significant to discrimination
along axis I1 are various measurements
already demonstrated to be of use in distinguishing Bushman crania from those
of Hottentots and Negroes. As expected,
the occipital chord and subtense are reversed in sign, the result being a positive
bias for (Bushman and Hottentot) skulls
with curved occipitals; a flatter occiput,
characteristic of Negro crania, makes for
a lower, more negative, score. Dimensions
registering maximum width and, more
important, curvature or fullness of the
frontal contribute heavily to discrimination and in much the same way; the bone
is broader in Hottentots and Bantu, less
sloping in Bushman skulls. Orbit height,
greater in Negroes, also plays a role of
some note, and the two measurements
registering protrusion of the nasal root
(nasion subtense and angle) are relatively
more important here than on the f h t discriminant.
All in all then, it seems quite clear that
the dimensions stressed on function I1 relate primarily to shape or form of the face
and braincase, not to general size of the
vault. These measurements, which include
several rather unorthodox subtenses and
angles taken with a coordinate caliper, are
evidently the crucial ones for discrimination between populations, though not for
separation of the sexes. The obvious inference here, that racial differences among
the South African cranial series are a
matter of shape while sexual dimorphism
is reflected in size, must be made with
reservation, however; the distinction implied is one of degree and of course not
absolute. Neither sex nor race differences
in these skulls are wholly “shape” or “size”’
dependent, though one or the other of
these two aspects of morphology may predominate.
Functions I11 and IV together absorb
only about 14% of the total generalized
variance and so contribute little to discrimination as afforded by the entire
six-function battery. However, both are
significant on Bartlett’s chi-square approxi-
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
mation and merit at least passing mention here. Discriminant I11 serves to set
off Sotho males and females from Zulu
individuals of both sexes and hence seem
to be picking up differences confined
within a broad Bantu Negro framework;
segregation by sex is not obvious (except
perhaps “accidentally” among the Bushmen), and this function adds nothing to
the separation of Khoisan from Bantu
groups accomplished on axis 11. Measures
of skull height, facial prognatbism, the
occiput and total sagittal arc seem most
useful in discrimination, though ZuluSotho mean differences in most of these
characters are small.
Function IV is of consequence only in
so far as it is the first discriminant to
separate Hottentots from both Bushman
series; male representatives of these
groups are closely associated on the three
axes previously described. Prominence of
bimaxillary breadth in the scaled vector
is not surprising, as this middle facial
measurement is among those weighted
heavily on the separate Bushman-Hottcntot race discriminant.
TO sum up; these four functions, each
a compound of 29 cranial measurements,
make separate (and unequal) contributions to discrimination in the sense that
each is measuring some different aspect
of total variation within and between the
populations studied; to some extent at
least, differences of sex and race, and finer
distinctions within the Khoisan and Bantu
categories, are treated in statistically independent fashion, but are scaled always
in proportion to the biology involved; the
technique, no matter how sophisticated
mathematically, cannot inflate or conjure
into being a distance between groups
which does not exist in nature. The end
result, when the several functions are
viewed together as axes in a discriminant
space, is a biologically accurate (given
the limitations of the original measurements) and statistically satisfying rendering of relationships among the seven
groups included in the analysis.
DISCUSSION
Generalized distance estimates calculated with Dz and CzH already have been
treated at some length and need not be
191
reexamined in detail. The independent sets
of distances are mutually consistent in
suggesting Bushman and Hottentot males
to be quite similar cranially (in fact not
significantly different) from samples of
Zulu, Sotho and Xosa tribal populations.
Two points are of particular interest here.
Firstly, the Bushman and Hottentot series
are judged to be composed of individuals
documented more reliably than has generally been the case in previous comparative surveys, excepting that of Stern
and Singer (’67) in which multivariate
statistics have not been used. These
samples are not as large as could be hoped
but must include nearly all of the authenticated specimens to be found in
South African museum and medical school
depositories.
Secondly, the distance analysis, based
on cranial characters, implies a degree of
Bushman-Hottentot affinity at least as
great as that which has been inferred
from the study of morphological and biochemical variation in the living peoples.
However, whether the Bushman-Bantu
and Hottentot-Bantu distances should
also be interpreted as “small” (and therefore indicative of a close Khoisan-Negro
tie as is suggested by the serological evidence) is a question not easly decided.
Comparison of the present Dz values with
those published elsewhere is hampered by
differences in both computational methodology and number and type of measurements used, and there is little information as to how sensitive to such differences
the statistic may be. Thus, while these
distances appear only moderate in magnitude relative to others calculated, say, for
Nigerian tribes (Talbot and Mulhall, ’62)
or Indian caste groups (Mahalanobis, Majumdar and Rao, ’49), there is no certainty
that the latter D* values are actually being
measured on the same scale as are the
former. Because, of this, inclusion of
Bushmen and Hottentots in a Xegro category does not seem justified on the evidence available. (An additional finding,
that 98% of male and 100% of female
Bushman and Zulu crania can be differentiated in discriminant analysis, connotes
a marked degree of morphological divergence and argues against any lumping of
these groups. )
192
G. P. RIGHTMIRE
Much the same set of relationships as by virtue of their performance when conindicated by D2is also evident when the sidered alone, without appreciation of
groups are run in a multiple discriminant their intercorrelations; i.e., a high unianalysis, though here more variables are variate I?-ratio is not necessarily a reliable
utilized, and treatment has been expanded guide and, where choice of a subset of
to include samples of female crania as variables must be made, selection is better
well as males. (Distances between cen- based on some step-wise ordering procetroids in the discriminant space, while not dure such as that available in program
computed as such by the program used, BMD07M.
may be thought of as D” determinations
Bushman-Hottentot mean differences in
based on 29 measurements; the two ap- cranial characters are small in an absolute
proaches, distance and discrimination, are sense, though Hottentots seem to be a
conceptually quite similar and would be little larger, especially in height of the
expected to yield about the same result.) skull vault. Cranial length, found by Stern
Addition of the several female series is and Singer (’67) to differ significantly
seen to be a necessary adjunct to the male between these two groups, plays only a
only analysis carried out with D2,as the minor role in the computed discriminant,
female centroids are well removed from whereas certain other measures, of frontal
the corresponding male means in the expansion, facial breadth and projection,
space provided. Sexual variation is ob- malar length and height, account for the
viously important in these South African greater apart of the “racial” separation
populations - recall that the first and observed. Other “shape” differences, no“best” function of the six computed sepa- tably degree of occipital curvature as
rates the groups largely on a sex basis - registered by the occipital subtense and
and to ignore it would quite severely lessen angle, contribute to the discrimination afthe value of the (discriminant) approach forded by the Bushman-Zulu functions
as a tool for the classification of unknown and by function I1 of the multiple disor unsexed material.
criminant set, so that shape-directed
All in all, in showing the importance measurements appear to be most useful in
of specific variables to group separation, in distinguishing between these populations
treating populations as distributions of while measures of general skull size tend,
individuals and providing estimates of dis- on the whole, to be the better sex indipersion, and not least, in yielding results cators. Whether this holds for other than
in a form amenable to graphic represen- IUloisan and South African Negro series
tation in a limited number of dimensions, remains to be tested, though a somewhat
multiple discriminant analysis provides a similar conclusion, that dimensions of the
good deal more information than does DZ, face and primarily of the nasal region are
even when this is combined with canonical more efficient in race discrimination than
variates as in Mahalanobis, Majumdar those taken on the cranial vault, has been
and Rao (’49). Probably, in biometric reached by Crichton (’66) in a study of
studies of this nature, generalized dis- Egyptian and Teita Negro skulls.
tance as a separate technique could be
In any case, certain sets of characters
replaced entirely by discriminants, though which when combined in multivariate
D2 values are fairly easily obtained with analyses separate the South African crania
Rao’s transformations and their use should by sex and race have been identified, and
be retained in cases where the facilities these should serve as a convenient guide
necessary for the computation of discrimi- €or workers planning further craniometric
nant functions are not available.
research on similar material. There is of
Simple two-group discriminants also course no guarantee that the measureprove useful for separating Bushman ments cited are the best or only ones that
skulls from those of Hottentots and South could be found, and if this work were to
African Negroes, and it is of interest that be done over, some changes in original
measurements found to be quite useful dis- choice of variables and in measurement
criminators in a multivariate context are technique would be introduced. Since in
not always those which would be selected a multivariate analysis of this sort it is
BUSHMAN, HOTTENTOT AND AFRICAN NEGRO CRANIA
possible to treat a skull as a unit, rather
than as a series of single traits, and to
compare these units in population terms,
inter-related measurements likely to bring
out aspects of shape characterizing populations should be the goal in mind. Some
such characters, which do not all correspond with those traditionally employed in
univariate comparisons, have been included here, but there is much need for
continued experimentation.
ACKNOWLEDGMENTS
Professors J. T. Robinson, L. Freedman,
G . Wahba, R. Singer and R. H. Osborne
provided advice and assistance during
various stages of the planning and execution of this work, and Miss C. Hughes is
responsible for final drafting of the figures.
Access to collection of skeletal material
was kindly given by the following: Professor P.V. Tobias and Dr. H. de Villiers,
Johannesburg; Professor L. H. Wells, Dr.
T. Barry and Mr. Q. B. Hendey, Cape
Town; and Mr. A. J. B. Humphreys, Kimberley.
I am indebted to the National Institute
of Dental Research for support on a Training grant (144-8742) and to the National
Science Foundation for the award of a
Doctoral Dissertation Completion Grant
(GS-1960). Use of the University of Wisconsin Computing Center was made possible through support, in part, from the
National Science Foundation, other United
States Government agencies and the
b7isconsin Alumni Research Foundation
(WARF) through the University of Wisconsin Research Committee.
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