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566 Raymond Boudon
The best account of the measurement models proposed by psychologists and
sociologists is Torgerson’s and the most recent Coombs’.34 But there is also a
whole collection of model-less measurement methods, i.e. methods which,
without propounding any hypotheses about the subjacent properties of the
observed data, simply seek to work to purely formal criteria: for example,
minimizing the differences between individuals belonging to the same class,
and maximizing the differences between individuals in different classes. The
origin of this research tradition should undoubtedly be credited to Fisher’s
work on discriminant functions. Other methods of the same type have since
been propounded by the biologists, and borrowed by the social science re-
searchers.3 5
If one wanted to trace the history of psychosociological measurement theory
in the fewest possible words, one might say that it was very much in fashion
and in vigorous growth firstly between 1920 and 1930 and secondly between
1940 and 1950. Thereafter hardly any major progress is observable. Most of the
work published since the second of the two decades is confined to fuller explora-
tion of the formal problems posed by the models conceived in the previous
period, or to resolving the problems left open. Today, the proliferation of
measurement and classification models is characterized by a degree of rela-
tivism: no one believes any more, as was possible in Spearman’s time, that such
models can yield measurements just as well defined as those of physics. We know,
for instance, that when individuals are asked a series of questions aimed at
classifying them in terms of a particular attitude (for example, anti-Semitism),
and a measurement model is used on this information, the classification ob-
tained is quite likely to be better than what would have been obtained by
empirical means (for example, by finding the total of the number of ‘anti-
Semitic’ replies). But we also know that this classification cannot be considered
valid in any absolute sense, as a different model - which one would have no
reason to reject - would certainly give different results.
Lastly, the category of descriptive models includes a class of tools which are
not strictly speaking either measurement or classification models. These are the
dimensional analysis models, also fathered by Thurstone. Dimensional analysis
is a response to snags discovered in applying Spearman’s model, when it became
apparent that some psychometrical results could not be explained by a model of
the form zlj = ajFl + elj, in which, be it remembered, zlj is a measurement of
the success of individual i at test j, Fl the ‘intelligence’ of i, and ell a success
factor specific to the test j. The basic equation of the model suggests the generalization:
zlj = aIjFIl + + ... + anjF.t + ell.
In other words the success of the subject i at test j is considered to be a function
not of a single aptitude, but of several distinct aptitudes: F,, Fz ... F,,. If
the ‘factors’ F,, Fz ... F. are assumed to be independent they can be represented
by a system of n orthogonal axes, each subject then being represented by a point
in this space. This sort of analysis makes it possible, for example, to identify the
aptitudes brought into play by a battery of psychometric tests, or the ‘attitudes’
which explain the replies to a psychosociological inquiry.