Running Head: Supplement on Fuzzy Sorting
A supplementary note to Questionnaire Sorting and Fuzzy Sorting
Research note
Joachim Harloff
Soft Use, Munich, Germany
Rudolf-Wilke-Weg 10
D 81477 München
Deutschland
Phone 0049 89 74493795
Fax 0049 89 74493794
e-mail harloff@softuse.com
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Abstract
This note supplements the article “An exploration of Questionnaire Sorting and Fuzzy
Sorting” (this volume). It relates to recent methodological improvements by Capra
(2005), who introduced a factor analysis solution to cover set cluster analysis.
Keywords
sorting, cognitive structure, knowledge elicitation, semantic structure, cover set, cover
set cluster analysis, fuzzy sorting, information architecture, web-site structure
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Recent improvements to cover set cluster analysis
One of the final statements of the article “An exploration of Questionnaire sorting and
Fuzzy Sorting” (this volume) was the desire for a future method to retrieve easily
interpretable cover sets from fuzzy sorting results. Recently, however, Capra (2005)
successfully used factor analysis of a covariance matrix of fuzzy sorting data to
unravel cover sets. Therefore, factor analysis was employed here using data from the
second case study (fuzzy sorting of web-site content items from checkbox paper
questionnaires).
Methods
Considering the questionnaires described, they can be viewed as visual
representations of cluster x item tables with selected radio buttons or check boxes
representing “1” and unselected buttons/ boxes representing “0”. (Such tables are
commonly produced as an intermediate step in correspondence analysis.)
Transposed tables of this kind were produced for each participant, and combined
writing them below each other (with items as columns and clusters by participant as
rows). Then, Factor Analysis was applied to this combined table using the ‘factanal’
object of R (R Development Core Team, 2004). Factor loadings were obtained for 9
factors (the lowest number of factors leading to a p level of ‘factanal’ above 0.05) and
3 factors (already known to show the dominant item structure).
Subsequently, the loadings of each item were multiplied by the items total frequency
(column sum) and divided by the number of participants, this way producing ratings.
Such ratings facilitate interpretation for cover sets since items placed in several
clusters necessarily show only low loadings with individual factors.
Subsequently, items were “securely” assigned to the factor with the highest rating, if
that rating was 0.4 or higher. Additionally, they were “optionally” assigned to any
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further factor with ratings above 0.4, thus producing cover sets. Finally, items not yet
assigned to any factor were “optionally” placed in the factor of their highest rating.
Results and Discussion
Fig. 1 shows the result of factor analysis for 9 factors (dashed lines), and 3 factors
(solid lines). Two items were “optionally” assigned only for the 3 factor solution.
Considering optional multiple placement (or linkage) of items is a reasonable basis
for website design decisions, which must take other arguments into account as well
(layout, workflow, marketing).
Results from figure 1 are considered readily interpretable here. This further supports
the importance of factor analysis as a means to unravel cover sets (Capra, 2005).
INSERT FIGURE 1 ABOUT HERE
References
Harloff, J. An exploration of questionnaire sorting and fuzzy Sorting. Quality &
Quantity (this volume).
Capra, M. (2005). Factor analysis of card sort data: An alternative to hierarchical
cluster analysis. Proceedings of the Human Factors and Ergonomics Society
49th Annual Meeting, 691-695. Santa Monica: HFES. Retrieved October 21,
2006 from http://www.hfes.org/Publications/.
R Development Core Team (2004). R: A language and environment for statistical
computing. R Foundation for Statistical Computing, Vienna, Austria. Retrieved
from http://www.R-project.org.
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Figure captions
Figure 1. Cluster assignment of 25 web site items according to factor analysis using 9
(dashed lines) and 3 factors (solid lines).