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A Normative Three-Center Study of 407+404+406 Students

Data Material

Power analyses based on available data suggested a sample size of 400 subjects to cover 90% of the expected empirical variance (1,500 subjects for 95%). Accordingly, our study was comprised of (1) a "learning sample" of 407 college students from Pasadena (USA); (2) a second "learning sample" of 404 university students from Lausanne (French speaking part of Switzerland); and (3) a "test sample" of 406 university students from Zurich (German speaking part of Switzerland). The three study sites were chosen in such a way that socio-cultural differences of clinical relevance could be detected. All students were asked to fill out the 28-item Coping Strategies Inventory "COPE" [Carver et al. 1989; available in standardized form for 6 languages] along with the 63-item Zurich Health Questionnaire "ZHQ" which assesses the factors "regular exercises", "consumption behavior", "impaired physical health", "psychosomatic disturbances", and "impaired mental health" [Kuny & Stassen 1988; available in standardized form for 6 languages].

Methods

The intrinsic structure of the COPE instrument was determined by means of Neural Network (NN) analysis. In particular, we searched for the optimum number of dimensions that were reproducible across study sites while explaining a maximum of the observed between-subject variance. The function "crit" with free parameters "N" (number of dimensions/scales) and "Nk" (number of items that make up the k-th scale; k=1,2, N) served as criterion for the iterative optimization that simultaneously optimized within- and between-scale association (absolute values):

optimization

Upon completion of each optimization step, results derived from the learning sample were verified through the replication sample so that over-adaptation to the local properties of each single sample could be avoided. As this algorithm does not distinguish between local and global maxima, a "random-walk" strategy was applied using 10,000 random permutations as start configurations for the optimization. All scales were orthogonalized by standard Gauss transformation, normalized (zero means, standard deviations of 10), and validated by computing the correlation between the resulting scales on the one hand, and the ZHQ factors "regular exercises", "consumption behavior", "impaired physical health", "psychosomatic disturbances", and "impaired mental health", on the other. We estimated empirical variances by systematically evaluating all possible n×(n-1)/2 Euclidean distances between the "n" subjects’ 28-dimensional feature vectors.

discrimination
Fig. 8a: Scatter plots of the raw scores "activity" (x-axis) versus "defeatism" (y-axis) as derived from the COPE data of 407 college students from Pasadena. These highly stable and reproducible scales (factors) explain the observed inter-individual variation in coping behavior sufficiently well (68.6%) and reveal considerable inter-individual variation with scores covering ranges of 10-70 (activity) and 10-40 (defeatism).
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