Conflicts based on correlations

Description
The first approach to mathematically derive a conflict measure based on grid data was presented by Slade & Sheehan (1979). They based their operationalization on an approach by Lauterbach (1975) who applied Heider’s (1958) balance theory for a quantitative assessment of psychological conflict. The measure uses inter-construct correlation as a basis. It assess via the sign of the correlations of a triad of constructs if the constructs triad is balanced or imbalanced. A triad is imbalanced if one or three of the correlations are negative, i. e. when they leading to contrary implications (Slade & Sheehan, 1979). The function indexConflict1 in OpenRepGrid calculates the proportion of conflictive triads in the grid as devised by Slade and Sheehan (1979).

Slade and Sheehan’s approach has several drawbacks, as it does not take into account the magnitude of the inter-construct correlations. As a consequence significant and insignificant correlations are not differentiated. Also, correlations of small magnitude, i.e. near zero, which may have a positive or negative signe due to chance alone distort the measure (Winter, 1982, Bassler et al., 1992). An improved version of the index that overcomes these shortcomings was proposed by Bassler et al. (1992) and incorporated into the program CT (correlation test). The index enhances the identification of imbalanced triads by using a criterion that incorporates the magnitudes of correlations. From a psychological viewpoint, it remains unclear though what is measured. Connections to the concept of cognitive differentiation have been presumed (Krauthauser et al. 1994). The function indexConflict2 in OpenRepGrid calculates the proportion of conflictive triads in the grid as devised by Bassler et al. (1992).

Slade and Sheehan approach
Multiply all correlations from a triad (formed by the constructs A, B and C) $$r_{AB} r_{AC} r_{BC}$$. If the sign of the result is negative, the triad is imbalanced.

The table below shows when a triad made up of the constructs A, B, and C is balanced and imbalanced.

Bassler's et al. approach

 * 1) Order correlations of the triad by absolute magnitude, so that $$r_{max} > r_{mdn} > r_{min}$$.
 * 2) Apply Fisher's Z-transformation and devision by 3 to yield values between 1 and -1
 * 3) Check whether the triad is balanced by assessing if the following relation holds:
 * If $$Z_{max} Z_{mdn} > 0$$, the triad is balanced if $$Z_{max} Z_{mdn} - Z_{min} <= crit$$
 * If $$Z_{max} Z_{mdn} < 0$$, the triad is balanced if $$Z_{min} - Z_{max} Z_{mdn} <= crit$$

R-Code
To use the Slade and Sheehan approach use: indexConflict1(boeker)

For the Bassler et al. approach use: indexConflict2(boeker) indexConflict2(boeker, crit =.05)  # change critical value

Literature

 * Bassler, M., Krauthauser, H., & Hoffmann, S. O. (1992). A new approach to the identification of cognitive conflicts in the repertory grid: An illustrative case study. Journal of Constructivist Psychology, 5(1), 95-111.


 * Heider, F. (1958). The Psychology of Interpersonal Relation. John Wiley & Sons.


 * Krauthauser, H., Bassler, M., & Potratz, B. (1994). A New Approach to the Identification of Cognitive Conflicts in the Repertory Grid: A Nomothetic Study. Journal of Constructivist Psychology, 7(4), 283-299.


 * Lauterbach, W. (1975). Assessing psychological conflict. The British Journal of Social and Clinical Psychology, 14(1), 43-47.


 * Slade, P. D., & Sheehan, M. J. (1979). The measurement of 'conflict' in repertory grids. The British Journal of Psychology, 70(4), 519-524.


 * Winter, D. A. (1982). Construct relationships, psychological disorder and therapeutic change. The British Journal of Medical Psychology, 55 (Pt 3), 257-269.