Mathematical Social Sciences 38 1999 275–293
A Boolean approach to the measurement of group processes and attitudes
The concept of integration as an example
Rudi Janssens
Centrum voor Vrouwenstudies , Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium
Abstract
Most social research involves comparison of some sort. Numerous tests are developed to examine if a person A is, for example, more intelligent or more creative or more stressed than a
person B. Nevertheless, researchers not only compare cases but also want to make some statements on the group level. This article focuses on this type of problem. As an example, the
process of cultural integration is discussed. My aim is to compare the evolution of the integration process between different Islamic minorities confronted with a Western value system. Starting
from a set of individual response patterns, indicating the presence or absence of a set of attitudes referring to this aspect, a Boolean approach to analyse and compare group behaviour is developed.
First, a formal approach of the process of integration is presented. Afterwards, the methodological tool is described. Finally, an example illustrates some possibilities of the Boolean approach.
1999 Elsevier Science B.V. All rights reserved.
Keywords : Cultural integration; Boolean approach; Attitudes; Group processes
1. Integration: a formal approach
One of the most important research topics in contemporary sociology is the adaptation of specific cultural minorities to the norms and values of the modern urban industrialized
society. Whether this process is defined as a shift between cultures or as a shift from tradition to modernity, most theories emphasize the variability of the individual attitudes
in reaction to the confrontation with a different value system. A person does not become integrated by switching immediately from a traditional to an integrated attitude. This
process contains at least several stages of integration, depending on the creativity and
Tel. fax: 132-26-292-582 E-mail address
: rdjanssevub.ac.be R. Janssens 0165-4896 99 – see front matter
1999 Elsevier Science B.V. All rights reserved.
P I I : S 0 1 6 5 - 4 8 9 6 9 9 0 0 0 2 1 - 9
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. Janssens Mathematical Social Sciences 38 1999 275 –293
flexibility of the individual. Not only the personal characteristics but also the nature of the minority group itself plays an important part in this process of change. The influence
of the group one belongs to determines the range of possible changes. One may assume that a group with a similar cultural background shows similar attitudes. A core set of
dominant attitudes within a group is called the group norm. This norm may allow for deviations or not: within a coherent group, the possibilities of change will be restricted;
where as in a loose group, increasing complexity in a greater variability of possible attitudes. In light of the above considerations, integration can be defined as ‘a one-way
learning process
, whereby somebody gradually closes the gap between the native culture of the land of origin and the culture of the society he or she lives in
, depending on the
1
adaptability of the individual and the group he belongs to’. The attitude of a particular person is measured by a set of items covering different
aspects of integration. As a result, each person is characterized by a pattern of co-occurring features, referring to the presence or absence of these aspects. This binary
pattern, written as a vector with a fixed order of the items, is called a response pattern. More formally:
let I 5 hi , i , . . . , i j be the set of n indicators of integration,
1 2
n
and H 5 hh , h , . . . , h j be the set of m respondents
1 2
m
then, every respondent h can be characterized by his response pattern i , i
, . . . , i
1,h 2,h
n,h
where i [
h0, 1j, for all j51,2, . . . , n such that if a respondent h agrees with the
j,h
attitude reflected in i , then i 5 1 and if a respondent h does not agree with the attitude
j j,h
reflected in i , then i 5 0.
j j,h
Since the relation between the indicators is unknown, one may assume that if the response pattern of respondent h contains more positive responses than the response
1
pattern of respondent h , then h is considered to show a ‘more integrated attitude’ than
2 1
person h . So, the arithmetic sum s 5 o
i is defined as the degree of integration.
2 h
1j n j,h
Before groups can be compared, a standard or ‘group norm’, derived from the various attitudes of the individual group members, must be constructed. Two possible
subsets of members can easily be identified: those with a response pattern containing all 0s reflecting a traditional position, and those characterized by a response pattern
containing all 1s referring to an integrated position. The main problem lies in representing the evolution between both positions, an evolution typical for the group
under study. Working with real life data, most respondents are characterized by a response pattern showing a mixture of 1s and 0s. The only information that one can
derive from such a pattern is the degree of integration as a vague indicator of its position in relation to the concept of integration. What one actually wants to know is its position
in relation to the other response patterns. In other words, one wants to know how the integration process between the traditional and integrated positions is structured.
The definition of integration provides the materials for a formal approach to the integration process. A first important element is the fact that integration is defined as a
1
For an extensive description of the theoretical background behind this definition, see Janssens 1995.
R . Janssens Mathematical Social Sciences 38 1999 275 –293
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one-way process. This assumption is based on previous research findings among similar and even relatively more closed minority groups stressing the adaptation of the group to
the peremptory demands of the cultural majority see e.g., Mugny, 1982; Levine and Moreland, 1985; Bar-Tal, 1990; Lesthaeghe, 1997. This does not exclude an individual
regressive transition. However, such regression seems to be an exception to the rule that a cultural minority almost inevitably evolves into the direction of a more integrated
position. Another essential element is the gradual evolution of the process. This implies that the degree of integration is supposed to increase only one unit at a time. The fact
that the degree of integration increases or not depends on both the individual and the group he belongs to. This means that some aspects are more prone to change than others.
An example illustrates the mechanism behind the way the process of integration is structured. Suppose a set of indicators I 5
hi , i , i , i j and a set of respondents H 5 hh ,
1 2
3 4
1
h j, and
2
respondent h is characterized by the response pattern 1000,
1
respondent h is characterized by the response pattern 1110.
2
If we are interested in the evolution of the attitude of person h , two possibilities may
1
occur: 1. h does not change his attitudes since he only agrees with the common indicators
1
2. h does change his attitude influenced by the attitude of h .
1 2
According to the definition of integration, h does not change his attitude.
2
If h changes his attitude, he will first evolve towards a position characterized by the
1
response patterns 1100 or 1010, before he can reach the position on which h is
2
situated. Fig. 1 illustrates the possible evolution of h .
1
If within our group of respondents H, only two possible response patterns are found, namely 1000 and 1110, Fig. 2 presents the structure of the integration process of that
group. Fig. 2 demonstrates that there are two possible ways to move from a traditional to an
integrated position: from 0000 over 1000, 1100 and 1110 towards 1111; or from 0000 over 1000, 1010 and 1110 towards 1111. In accordance with graph
theory, these ways are defined as the paths of the integration process. Although within the dataset only two response patterns are found, the corresponding structure is
composed of six different patterns. The response patterns characterizing the respondents
Fig. 1. Possible evolution of the attitude of person h .
1
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. Janssens Mathematical Social Sciences 38 1999 275 –293
Fig. 2. Digraph representing the integration process of group H.
are called actual patterns. The other component patterns are called possible patterns. Both the traditional 0000 and integrated position 1111 are included by definition.
The previous example presents the possible attitude changes in the case only two response patterns are observed. Usually, more patterns will be found. In this article, a
method based on the Boolean analysis of questionnaires Flament, 1976 is introduced which enables one to structure the integration process based on a large set of response
patterns.
2. Boolean analysis: the method
