| 1. |
Data transformation: Data from a large data set was transformed to 3-point scale (Agree with expert, Neutral, Disagree with expert). |
| 2. |
Factor analysis: To find statistically valid categories of student thinking, a factor analysis was run in PASW (SPSS, Chicago, IL) with the following parameters: Correlation matrix: Pearson; Extraction Method: Principal Component Analysis; Rotation Method: Direct Oblimin; Cross-loading: Allowed. |
| 3. |
Category analysis and revision: For each potential component (hereto referred to as category), the effects of individual statements on the category were analyzed, such that if category statistics became stronger by either removing a statement or adding a potentially related statement, the category composition was changed to reflect the strongest statistics. The statistics used to make these judgments were the strength and similarity of factor loadings (contribution of each statement to that category), strength and similarity of statement correlations, and the linearity of the scree plot (an indication of whether a single component accounted for the variability in the statement group). |
| 4. |
Robustness indicators: An RI based on the aforementioned statistics was calculated for each potential category. Robustness indicators range from 0–10 and scores higher than 5 represent both high factor loading and high statement correlations, and thus a meaningful grouping of student thinking
where cc = average absolute value of the correlation coefficients between statements; fl = average absolute value of factor loadings; ΔE = shape of scree plot; N = number of statements in category; R2 = Pearson product moment correlation (the linearity of a scree plot). |
| 5. |
Category names: Final categories were named according to expert opinion of the commonalities among the composition of statements within each category. |
