Facet Theory: Mapping and Regionalization

1. Facet Theory Basic ConceptsErik H. CohenBar Ilan UniversityRome July 2005 3rd International Lab Meeting – Summer session 2005 11th Edition of the International Summer School of the European Ph.D.

2. Submit a small matrix to convert in hand SSA, according to two rules: inverse and direct • Submit a small number of profiles to be transformed by hand in POSAC

3. Table of Contents The Who Population The What Population The Concept of Mapping Sentence What is a Facet? The Range Definition of theory by Guttman The various components of the research process according to Facet Theory Regionality hypothesis Theoretical Regionalization (I) What is the meaning of each geometrical figure? What is good manager? Our findings Interpretation

4. Extension of the research A new mapping sentence Hypothesis The Findings relating to the second facet Interpretation Conclusion Theoretical Regionalization (II) The axial model The modular model The polar model What is the meaning of each of these three geometrical figures? The axial model The modular model The polar model

5. An Exploratory Mapping Sentence for Assessing Jewish Education Factorial design (R.A. Fisher) Cumulative Knowledge Another example Israel Experience Programs mapping sentence The Monotonicity The research process The Smallest Space Analysis (I, II, III) Bibliography

6. Facet Theory Basic ConceptsThe Who populationWe know how to cover a population in such a way that the surveyed sample represents the referenced population.p represents P

7. For this purpose, one may use many methods of sampling : - Quota method - Random - Snowball technique - etc.

8. According to certain rules, we may be even capable of estimating the degree of error in the sampling. For example : + or – 2,5% is a quite good such estimate for surveys in elections.

9. The population may be everything in the world: people of a certain country, trees of a forest, articles published in international conferences, stamps of a certain year / country / language, etc.

10. The What population But there is another kind of population, which is generally less systematically analyzed: the population / universe of contents. How can we know - as we can do it in the Who population - that the survey will represent the What population? What kind of tool could help us in this aim?

11. The bibliography literature survey is obviously the first thing to do.A state of the art survey is surely helpful. It may even lead to discover uncovered issues in the research.

12. The Concept of Mapping Sentence As Louis Guttman claims : “the problem of proposing fruitful facets to the design of the content for a system of variables has generally been found to be a far more difficult one than for that of proposing background variables or experimental conditions for populations”(Guttman, 1992 in Levy 1994).

13. In order to allow a systematic design of a field under investigation, Guttman introduced the concept of a mapping sentence. A mapping sentence, which is a basic device of facet theory, contains a variety of facets. Each facet is one way of classifying the research content. (Guttman 1982)

14. What is a Facet? A facet is one way of classifying the research content. Each facet contains elements. It is a set with a rule in such a way that its elements are both exclusive and exhaustive

15. The Range When we survey a field, any field, we apply some range in our observation. In esthetic judgment, we refer to the extent of beauty in some object. What may define an item as value, is its range from “important” to “not important”. (See Levy 1985 in Canter)

16. The most basic abstract symbolic mapping sentence has the following format: see Levy 1976 P {A}  R Population Content facet  Range

17. Though the mapping sentence introduces formality, it is a flexible device as it can easily, but systematically, be enlarged or condensed by adding or reducing facets or elements within the facets.

18. Definition of theory by Guttman As some basic concepts are now understood, we may approach the definition of Theory. This definition will transform these concepts into an operational and integrative process of research.

19. A theory is an hypothesis of a correspondence " between a definitional system for a universe of observations and an aspect of the empirical structure of those observations, together with a rationale for such an hypotheses" (Guttman 1973, 1982; in Levy 1994)

20. The various components of the research process according to Facet Theory (I) Definitional system for an Universe of observations Regionalization Rationale An aspect of the empirical structure

21. The various components of the research process according to Facet Theory (II) Definitional system for an Universe of observations = mapping sentence Regionalization Rationale = facet role An aspect of the empirical structure = intercorrelations

22. Regionality hypothesisAccording to the regionality hypothesis, to each element of the facet considered, there will be a specific and continuous region in a geometric representation of the various items analyzed. There will be a distinction among the various items according to the facet definition of each item.

23. Regionality hypothesis (2) A facet with n elements A map with n regions With a rationale

24. Regionality Theoretical Regionalization (I) Let first consider the smallest facet existing, i.e. a facet with only 2 ordered elements. This facet may be represented in two and only two different geometric ways, according to the regionality hypothesis.

25. First theoretical regionalization of a Facet with two elements All the items of element a All the items of element b

26. Second theoretical regionalization of a Facet with two elements All the items of element a All the items of element b

27. In the first one, the two elements have an equal role / status In the second one, the two elements have a different role / status. What is the meaning of each geometrical figure?

28. What is good manager? A very simple example of mapping sentence.and structural verification through SSA and regionality hypothesis assessment

29. In their work, “The ‘good manager’: masculine or androgynous” (1979), Powell and Butterfield were the first researchers to specifically apply the concept of androgyny to the work setting. Based on findings in non-organizational settings, they hypothesized that the “good manager” would be perceived as androgynous in sex-role identification.

30. This hypothesis was not supported; both male and female business students described a good manager most of all in masculine terms and least of all in feminine terms. A study, twenty years later (Cohen & Bloom 2000), re-explores the same research questions.

31. 79 Israeli students completed the Bem Sex Role Inventory (BSRI) (Bem, 1974), a standard tool for measuring femininity, masculinity, and androgyny, both for him/herself and for a good manager.

32. A first very simple mapping sentence has the following format:

33. Israeli students consider the characteristics of management as

34. In the facet content, “masculine” and “feminine” are called facet elements

35. Our findings

36. Interpretation The previous geometric representation of the intercorrelations between the 80 various items shows clearly (there is only one “error”) that the respondents distinguish between male and female characteristics of the good manager. The regions corresponding to the two elements of the Facet are specific and contiguous, without a “mixed” region.

37. Extension of the research As we already said, the mapping sentence is a formal but flexible way to formulate the content of a domain. Now that we have established a first Facet, we may be conducted to enlarge the mapping sentence by a new Facet. As the respondents were asked to designate the characteristics of a good manager in general, but also if they consider themselves as fitting these characteristics, we can add a new Facet, which formulates the person targeted by the definition.

38. A New Mapping Sentence Israeli students consider the characteristics of management regarding

39. Hypothesis As the first Facet, the new Facet includes only 2 elements. We may expect a modular geometric representation, with the himself/herself items in the center.

40. Findings re to the second facet

41. Interpretation The previous geometric representation of the intercorrelations between the various items shows that the respondents DO NOT distinguish between himself/herself characteristics and the characteristics of a good manager in general. There are not regions corresponding to the two elements of the Facet! The various items belonging to the two elements of the new Facet are “mixed”.

42. Conclusion The interviewees do clearly distinguish gender characteristics. The interviewees do not clearly distinguish between themselves and the good manager.

43. Theoretical Regionalization (II) Let now consider a more complex facet, i.e. a facet with 3 elements. This facet may be represented in three and only three different geometric ways, according to the regionality hypothesis.

44. The axial model First theoretical regionalization of a Facet with three elements All the items of element a All the items of element b All the items of element c

45. The modular model Second theoretical regionalization of a Facet with three elements All the items of element a All the items of element b All the items of element c

46. The polar model Third theoretical regionalization of a Facet with three elements All the items of element a All the items of element b All the items of element c

47. What is the meaning of each of these three geometrical figures?

48. The axial model The three elements are ranged. For instance, from simple to complex (for instance the Bloom taxonomy is expected this model: Cohen, Clifton & Roberts 2001) All the items of element a All the items of element b All the items of element c

49. The modular model The three elements have a different role / status, from a core to the periphery. For instance the intelligence tests analysis shows such a structure, with from the core to the periphery: inference, application, learning Guttman Levy 1991 All the items of element a All the items of element b All the items of element c

50. The polar model The three elements have a partially range format. The life areas appear in such a way (Levy Guttman 1975 Cohen 2000). All the items of element a All the items of element b All the items of element c