Intimidation And Violence By Males In High School Athletics

Adolescence, Fall, 1999 by Edgar W. Shields, Jr.

The four-component solution, with two variables loading on each component, accounted for 74.4% of the variability in the observed eight antecedent variables. The breakdown was Component 1 (contextual setting), 31.1%; Component 2 (attitude), 17.3%; Component 3 (pressure), 14.8%; and Component 4 (coaching), 11.2%. Although the four-component solution explained only 11.2% more variability than the three-component solution, the purposes of this study were better served by retaining the fourth component.

A critical decision is selecting how many factors or components to retain, a decision influenced by the number of substantial loadings per component. If the primary purpose of the PCA is to summarize the data set, a minimum of two substantial loadings per component is sufficient (Zwick & Velicer, 1986). The four-component model, following a varimax orthogonal transformation, is presented in Table 4. As can be seen, component loadings were substantial. Measures of orthogonal variable complexity ranged from 1.063 to 1.204, with a mean of 1.118, indicating the approximation of a reasonably ideal simple structure in which each variable is accounted for by no more than one component.

It is noteworthy that both orthogonal and oblique rotations yielded similar transformed results, but the orthogonal rotation was selected as best for the final solution after examination of component plots for both rotations. Also, in orthogonal rotation, the components are not correlated, thereby facilitating the description and interpretation of results. Not only did the selection criteria suggest a four-component solution, but these four seemed conceptually logical. Each component accounted for approximately one-quarter of the orthogonal solution's common variance. Component 1 accounted for 25.4% of the variability, independent of the other components. Components 2, 3, and 4 accounted for 26.9%, 21.2%, and 26.4%, respectively. Each variable loaded high on only one component, regardless of extractional or rotational technique. This suggests that they were relatively pure variables. These "marker variables" clearly defined the nature of the components.

Multiple regression analysis was used to investigate possible relationships between the antecedent components, identified by PCA, and verbal intimidation, physical intimidation, and physical violence. Following the orthogonal transformation, a component-score coefficient matrix was generated to estimate scores on components from observed antecedent variable scores for each athletic director. Component scores were thus estimates of the scores all 148 respondents would have had on each of the components had they been measured directly. In PCA, multicollinearity is not a problem, a characteristic that makes component scores attractive for use in other analyses (Tabachnick & Fidell, 1989).

Table 5 presents the multiple regression results. Overall, the relationships between the antecedent components and VI, PI, and PV were significant (VI, p [less than] .0096; PI, p [less than] .0055; PV, p [less than] .0352). Component 4 was a significant predictor for all three (VI, p [less than] .0012; PI, p [less than] .0002; PV, p [less than] .0313). Component 1 was found to be an additional predictor of PV (p [less than] .0199).