It is proposed that the multivariate, multidimensional discovery approach to the correspondence analysis technique has significant potential for data analysis in the social sciences. The goal of correspondence analysis is to find a low-dimensional representation of the dependency between predetermined categories in a two-way contingency table (Hair, Anderson, Tatham, and Black, 1995; van der Heijden and de Leeuw, 1985). Examples of the use of correspondence analysis can be found in medical research (Greenacre, 1992), students' and teachers' cognitions about good teachers (Beishuizen, Hof, Putten, Bouwmeester and Asscher, 2001), intercultural attachment patterns (van IJzendoorn and Kroonenberg, 1988 ), image of higher education institutions (Ivy, 2001), personalities (Nishisato, 1994) and marketing research (Bendixen, 1996).
The correspondence analysis program then produces a graphical representation of the distance coordinates (major column coordinates) in low-dimensional space. Correspondence analysis using the main normalization rows does the same as just described, but for the contingency table rows. A major assumption or limitation of correspondence analysis is that all relevant variables are included in the analysis (Hair et al., 1995).
Although most literature on correspondence analysis deals with two or three dimensions, there are some exceptions, such as Nishisato's (1994) interpretation of seven dimensions of personality. To explain each dimension, the authors met several times to review the correspondence analysis solution and identify potential latent concepts underlying the combination of variables contributing to each dimension. Our discussions were extensive, comparing each dimensional combination of variables with our knowledge of the literature and contemporary teaching and learning environments.
A peer review or debriefing is a review of the data and research process by someone who is familiar with the research or phenomenon being explored. A peer reviewer provides support, plays devil's advocate, challenges researcher assumptions, pushes researchers to the next step methodologically, and asks tough questions about methods and interpretations (Lincoln & Guba, 1985). It can be seen that one variable, personal development, seems to be off the chart.
Therefore, when interpreting each dimension, it is necessary to consider the contribution of variables to that dimension. For example, in Figure 3, the variable community of students appears to the right of dimension 1, and a superficial analysis might suggest that it is part of an interpretation of dimension 1. It is also necessary to consider the contribution of each dimension to an explanation of the variance in each participant's profile.
Some participants' profiles do not fit well in certain levels (both dimensions each contribute less than a nominal cutoff of 10 percent to the variance in the participant's score). However, 45 percent of the variance in her profile is accounted for by Dimension 5, and a further 15 percent is accounted for by Dimension 6 (from Table 6; Columns P to V).
In summary, the left pole of Dimension 1 appears to have an intrinsic flavor, addressing issues related to the learner's role in focusing on cognitive engagement and management of learning. The right pole of Dimension 1 appears to contain variables relating to learning as an externally facilitated, sometimes very task-oriented activity, and to knowledge as something transferred from external sources. Dimension 1 can thus be interpreted as a dimension of Learning Focus, with a continuum running from a focus on the intention to construct knowledge at the left pole to a focus on learning as work to be done at the right pole.
At the bottom pole of dimension 2 are variables related to the teacher's role in organizing learning, including the logistics (0.067) of organizing people and equipment, facilitating (0.044), which refers to things that teachers and other people do, such as providing support and encouragement, passing on/collecting information (0.068) and assessment (0.057). Together, the variables at the bottom pole of Dimension 2 appear to relate to the teacher's role in organizing effective learning, and so it is possible to assign the label external to this pole. In summary, Dimension 2 can be interpreted as Motivation, consisting of a continuum of intrinsic motivations at the upper pole, and external enablers and motivators at the lower pole.
However, while transmission/gathering lies at the outer poles of both dimensions 1 and 2, evaluation/feedback lies at the inner end of Dimension 1 and the outer end of Dimension 2, indicating a transaction between the inner nature and external teaching and learning, and teacher and student. Three of the medical student scores (Roxy, Troy, Anne) are not well fitted on this plane of Dimension 1 and 2. The remaining medical student scores cluster to the left of Dimension 1, closer to the goal of constructing the pole of knowledge, while none of the results of childcare students or teachers are near this pole.
It seems reasonable to conclude that, even with poor scores removed from the plane of Dimension 1 and 2, participants' scores cluster into three distinct groups: medical students on the Dimension 1 construct knowledge pole; childcare students in the learning-as-work-to-do pole of Dimension 1 and the intrinsic motivation pole of Dimension 2; and teachers in the learning-to-be-doing pole of Dimension 1 and the extrinsic facilitating and motivating pole of Dimension 2. It is interesting to note that the two teachers who are with the childcare students in the learning-to-do pole of Dimension 1, are actually the childcare students' own teachers, suggesting some congruence between the teachers' and their students' perspectives.
Interestingly, all medical student scores align poorly with Dimension 2 (from Table 6), indicating that Dimension 2 contributes very little to medical student scores. The scores of one teacher (Dr. B) fit poorly into the Dimension 1 and 2 planes, while the scores of the two childcare teachers (Dany, Chloe) are in the lower right quadrant, closest to extrinsic facilitators and motivators, and learning processes. as variables that have to do work. The symmetric normalization method chosen for this correspondence analysis allows for the placement of variable and participant scores in the same graphical representation.
However, it is appropriate to consider the relative placement of participant and variable scores, and especially to consider the relative placement of participant scores to the meaningfully interpreted poles of dimensions (Gabriel, 2002; Greenacre, 1994). The relationship of the variables at the two poles of Dimension 4 indicates a continuum of Context, with authentic, situated practice describing the upper pole, and learning by studying describing the lower pole. The positioning of participants' scores in dimensions 3 and 4 tells a different story than the easily identifiable groups that emerged in dimensions 1 and 2.
From Table 6, columns R and S, it can be observed that each of Dimensions 3 and 4 accounted for less than 10 percent of the variance in half of the participants'. Two more childcare students' scores almost reach the nominal 10 percent cutoff for inclusion in this dimension, namely Jen (0.097) at the group management pool and Juli (0.091) at the individual management pool. At the other end of the Dimension 4 continuum, learning by studying, only Jen's (childcare) score is located, although the scores of Arma (childcare, 0.099) and Dany (teacher, 0.091) can be included in this dimension.
In summary, there may be some indication of group differences in Dimension 3, which captures so little variance in medical student scores but places childcare students and teachers at opposite poles. It seems reasonable to propose that Dimension 3, with issues of self-regulation and external regulation of individuals and groups, is the domain of the childcare group.
Furthermore, Dimension 6 is a good example of the value of examining higher dimensions, because the variables mastery and theory x practice only emerge in the sixth dimension, and will therefore be lost from the analysis if a lower dimensional solution is accepted become Where dimensions 3 and 4 account for little of the variance in the medical students' scores, dimensions 5 and 6 do contribute to some of the medical students' scores. Interestingly, dimension 5 is the first dimension that accounts for a significant portion of the variance in Roxy's score (45 percent).
The scores of the three medical students are on the left pole (uncertain/reflective expectation) of that dimension. Cait and Mary's scores are on the uncertain/reflective expectation pole, and Arma's, Jay's, and Dr.'s scores are. B are on the positive expectation pole. While in Dimension 5 Roxy and Troy's scores are at the same pole, in Dimension 6 Roxy and Troy's scores are at opposite poles of the Goals continuum, from achieving mastery (Roxy) to abstract and long-term goals (Troy).
B's (teacher) scores are in the upper right quadrant of the graphical representation of dimensions 5 and 6. It appears that the only clustering of participant cohorts in dimensions 5 and 6 occurs with the placement of three medical students on the insecure-reflective pole of dimension 5. Therefore, our interpretation of the dimensions has been largely dependent on the underlying statistics in table 6.
However, dimension 7 is the first dimension that makes a substantial contribution to Anne's (medical) score and is responsible for 15.3 percent of the variance in her profile. The scores of Anne (medical), Troy (medical), and Jay (childcare) are at the positive pole, and Jess's score (childcare) is at the negative pole. This accounts for more than 10% of the variance in the scores of 1 medical student, 1 childcare student, and 1 teacher.
From a methodological perspective, we would like to draw attention to the value of correspondence analysis for providing elegant graphical representations to help understand the richness of information contained in large data sets.
