Although it is computationally intensive, it is desirable to apply the ID3 algorithm directly to the original total database. We can use as the goal attributes the complete range of responses for each dimension scale and not simply "universalistic" or "particularistic." For example, when examining the information content of the database with respect to "individualism-collectivism," we note the five contributing questions on our scale means there are 32 (=25) possible states for the goal attribute. This was effected using the well-established computational method of list processing which has the further advantage of being applicable to string data. For this reason it was not necessary to recede the original database with pseudonumeric codes to represent each categorical item. Furthermore, this type of analysis does not lend itself to SPSS recode like procedures readily.
Because the ID3 algorithm is concerned with the frequency of occurrence of each combination of attributes and not the value of the attributes, it is not necessary to re-scale attributes. Thus age is processed as a category, not a scaled variable. The ID3 algorithm automatically takes care of different types of variable for each attribute and enables us to explore our full database directly.
A recursive procedure, "CATEGORIZE," was constructed to process each iteration. After one iteration on our example set, this produces:
(country (USA CATEGORIZE (((universalist USA senior male) (universalist USA senior female) (universalist USA junior male)))))
(VEN CATEGORIZE (((particularist VEN senior female) (particularist VEN senior male) (particularist VEN senior male)))))
(UK CATEGORIZE (((universalist UK junior male) (particularist UK senior female) (particularist UK senior male) (universalist UK junior female)))))
The above list of lists was split by CATEGORIZE at "country" because application of the ID3 algorithm revealed that "country" had the lowest entropy.
The final list returned by CATEGORIZE is:
(country(USA(status(universalist)))
(VEN(status(particularist)))
(UK(function(senior(status(particularist)))
(junior(status(universalist)))))
In some situations there may be cases where the same attribute values produce different goals. These are known as data conflicts. Thus not every American (male) senior manager may have responded as a universalist. These are accommodated simply by weighting these cases and the basic ID3 algorithm is applied accordingly.
To explain the total variety, it would be necessary to use the same variety as there are cases. This is the same as saying that the 65,000 respondents are all individuals and we could require 65,000 attributes to describe them. Alternatively, we could use one attribute with 65,000 values (such as their name) to uniquely identify them. In the above parlance, their "name" has the highest information content and lowest entropy. However this is not our aim. We refer to earlier discussion repeated throughout this book, namely that we are seeking to develop a model based on a number of dimensions (attributes) that help structure managers' experiences. The analysis we are attempting here is intended to support this aim by exploring the relative importance of different attributes rather than containing the total variety within the data set as a ideological statistician may prefer.
The outcomes of this analysis applied to the whole database reveals the following: It is to be noted that "country" has the lowest entropy for each dimension which is very good evidence to support the main thesis of Tromepanaars' work.
Entropy
unpa
indcol
neaf
spdi
achasc
intex
time
lowest
country
country
country
country
country
country
country
industry
religion
industry
industry
industry
industry
industry
religion
industry
job
religion
religion
job
religion
job
education
religion
age
job
religion
education
age
age
corporate
gender
age
gender
job
corporate
gender
age
education
education
age
age
education
job
gender
job
corporate
education
gender
highest
gender
corporate
education
corporate
gender
corporate
corporate
Whilst this discussion might be viewed as an exercise in statisticulation, it is consistent with the face validity of the dimensions and Ashby's law of Requisite Variety - too few dimensions would not account for the richness of cultural diversity we see in the world.
If we apply other methods such as factor analysis, image factoring, and Kohenen neural networks then the conclusions are identical.
LIMITATIONS OF THE CURRENT DATABASE
It is a difficult - if not an impossible - task to present in a few pages a fully-fledged, validated theory dealing with such complex issues as socially constructed systems of human relationships and systems of shared meaning. We have, however, attempted to develop sufficient conceptual and empirical evidence of the close relationship between culture and the way it affects the meaning of organization.
These analyses, however, need not be limited to between-cultural comparisons. For the attainment of supplementary information, within-cultural analyses are suggested to be added to the set of investigations. Through this procedure, however, we depart from the ecological type of comparison to an individual type of comparison. By doing so a large pool of new variety is tapped, which significantly increases the number of samples.
Consequently, the number of possible statistical procedures and levels of significance increases. Results which are derived from these operations, however, need to be interpreted as personality factors rather than as cultural factors.
FUTURE WORK AND EXTENDING THE ANALYSIS
Clearly we would wish to do more work in this whole area, to collect more data, to increase the validity of the generalizations, and extend the findings.
We are currently building a neural network that is expected to give further insights into the data.
For bona fide researchers and other interested parties, further access to our methods, tools, and data analysis is available. In particular we welcome applications from students intending to research for a PhD to extend our work.
A last comment is saved for those who have found parts of the presented discussion simplistic, and for those who have found parts rather complex. For those of the former category, we admit that parts of the analysis were relatively simplistic. It was, however, never our aim to disguise complicated realities by an apparent simplicity. The simplicity, for those of the latter category, we again have to admit that certain of our (re)presentations were indeed rather complex. The complexity of parts of our analysis, however, are the result of the fact that quite often social reality doesn't seem to care about difficulties of (re)presentation. Nature, argues Fresnel, "doesn't care about mathematical difficulties." The social reality we have analyzed sometimes just seemed to prefer complexity.
In summary, we have shown that the present research has reconciled simplicity with complexity. A reconciliation allowing the reader to follow the main arguments concerning the relationship between the meaning of organization and the organization of meaning, and at the same time stimulate the reader to do the necessary further research in this area.
Bibliography
Alker, H. R. (1966) "A Typlogy of Ecological Fallacies," in Merrit, R. and Rokkan, S. (eds), Comparing Nations, Yale University Press.