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J . M. LAMBERT AND M. B. DALE
from attempts to describe vegetation as it occurs in the field rather than
to subject it to efficient and searching analysis. With objective analytical
techniques, the question of “forcing” units into one type of grouping
or another does not in fact arise: the data are made to reveal their own
internal relationships, and the classification eventually constructed
depends on the requirements of the user rather than on any preconception as to “true” relationships.
Much of the controversy concerning the appropriateness or otherwise
of hierarchical classification in fact seems to be due t o a confusion of
concepts : “multidimensional” is frequently regarded as synonymous
with “reticulate”, and either or both terms are often used as the direct
antithesis of “hierarchical”. We shall attempt to clarify the situation
here by defining the terms as we understand them in a statistical context. The term “hierarchical” normally applies to methods of obtaining
groups at several levels which can be ranked in importance, in which a
unique relationship is specified between any group and the entire
population at any given level ; the hierarchy need not be dichotomous,
but the route by which the groups arise, as distinct from intergroup
relationships, can be simply displayed in not more than two dimensions.
The term “reticulate” concerns intergroup distances irrespective of the
method by which the groups are extracted, and methods of “reticulate
classification” could in fact be regarded as hierarchical methods with
a single polychotomous division. The term “multidimensional” concerns attempts to display intergroup relationships ; it can be applied
equally as well to a reticulum provided by intergroup distances defined
at any level in an hierarchy as to the groups derived directly from a
reticulate classification.
In hierarchical classification, therefore, the emphasis is on the extraction of groups at successive levels of relationship, while reticulate
methods are concerned with a single level only: as soon as any reticulately-formed groups are combined into “supergroups” or split into
subgroups’’, the classification immediately becomes hierarchical. Since
both methods of analysis are aimed at simplifying the data to a greater
or lesser degree, some information must be disregarded in either form
of classification; and the more powerful the method used for either
type, the more the final results of the one are likely to diverge from those
of the other. The decision between the use of the one or the other
method must therefore again rest on both the ease of computation and
the general convenience of the user. There have so far been very few
statistical attempts to proceed directly to a reticulate system, and the
fact that in practice most classificatory systems in other fields are
essentially hierarchical in nature is itself a pointer to their generally
greater usefulness and efficiency. We shall accordingly follow the
r (
J . M. LAMBERT AND M. B. DALE
from attempts to describe vegetation as it occurs in the field rather than
to subject it to efficient and searching analysis. With objective analytical
techniques, the question of “forcing” units into one type of grouping
or another does not in fact arise: the data are made to reveal their own
internal relationships, and the classification eventually constructed
depends on the requirements of the user rather than on any preconception as to “true” relationships.
Much of the controversy concerning the appropriateness or otherwise
of hierarchical classification in fact seems to be due t o a confusion of
concepts : “multidimensional” is frequently regarded as synonymous
with “reticulate”, and either or both terms are often used as the direct
antithesis of “hierarchical”. We shall attempt to clarify the situation
here by defining the terms as we understand them in a statistical context. The term “hierarchical” normally applies to methods of obtaining
groups at several levels which can be ranked in importance, in which a
unique relationship is specified between any group and the entire
population at any given level ; the hierarchy need not be dichotomous,
but the route by which the groups arise, as distinct from intergroup
relationships, can be simply displayed in not more than two dimensions.
The term “reticulate” concerns intergroup distances irrespective of the
method by which the groups are extracted, and methods of “reticulate
classification” could in fact be regarded as hierarchical methods with
a single polychotomous division. The term “multidimensional” concerns attempts to display intergroup relationships ; it can be applied
equally as well to a reticulum provided by intergroup distances defined
at any level in an hierarchy as to the groups derived directly from a
reticulate classification.
In hierarchical classification, therefore, the emphasis is on the extraction of groups at successive levels of relationship, while reticulate
methods are concerned with a single level only: as soon as any reticulately-formed groups are combined into “supergroups” or split into
subgroups’’, the classification immediately becomes hierarchical. Since
both methods of analysis are aimed at simplifying the data to a greater
or lesser degree, some information must be disregarded in either form
of classification; and the more powerful the method used for either
type, the more the final results of the one are likely to diverge from those
of the other. The decision between the use of the one or the other
method must therefore again rest on both the ease of computation and
the general convenience of the user. There have so far been very few
statistical attempts to proceed directly to a reticulate system, and the
fact that in practice most classificatory systems in other fields are
essentially hierarchical in nature is itself a pointer to their generally
greater usefulness and efficiency. We shall accordingly follow the
r (