Relational complexity (RC) theory conceptualizes an individual’s processing capacity and a task’s complexity along a common ordinal metric. The authors describe the development of the Latin Square Task (LST) that assesses the influence of RC on reasoning. The LST minimizes the role of knowledge and storage capacity and thus refines the identification of a processing-capacity-related complexity effect in task performance. The LST is novel with one explicit rule that is easily understood by adults and children. In two studies, a test of 18 items encompassing three RC levels was administered to university (N = 73; 16-33 years) and school (N = 204; 8-19 years) students. Rasch analyses indicate that the LST scores were psychometrically stable across age groups and provides important diagnostic clues for task development. Consistent with RC theory, the LST is sensitive to parallel and serial (via segmentation) processing demands. The LST provides a strong basis for research on working memory and related constructs (fluid intelligence).
Andrews, G., & Halford, G. S. (1998). Children’s ability to make transitive inferences: The importance of premise integration and structural complexity. Cognitive Development, 13, 470-513.
2.
Andrews, G., & Halford, G. S. (2002). A cognitive complexity metric applied to cognitive development. Cognitive Psychology, 45, 153-219.
3.
Andrews, G., Halford, G. S., Bunch, K. M., Bowden, D., & Jones, T. (2003). Theory of mind and relational complexity. Child Development, 74, 1476-1500.
4.
Andrich, D. (1988). Rasch models for measurement. Newbury Park, CA: Sage.
5.
Andrich, D., Lyne, A., Sheridan, B., & Luo, G. (1998). RUMM: Rasch unidimensional measurement models. Perth, Australia: RUMM Laboratory.
6.
Birney, D. P. (2002). The measurement of task complexity and cognitive ability: Relational complexity in adult reasoning. Unpublished doctoral dissertation, University of Queensland, St Lucia, Brisbane, Australia.
7.
Birney, D. P., & Halford, G. S. (2002). Cognitive complexity of suppositional reasoning: An application of the relational complexity metric to the knight-knave task. Thinking and Reasoning, 8, 109-134.
8.
Boag, C. C., Härtel, C. E. J., & Halford, G. S. (in press). An integrated model of situation awareness and decision making in air traffic control to explain performance errors. In Proceedings of the European Association for Aviation Psychology Conference, Scotland.
9.
Cohen, J., & Cohen, P. (1975). Applied multiple regression/correlation analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum.
10.
Embretson, S. E. (1993). Psychometric models for learning and cognitive processes. In N. Frederiksen, R. J. Mislevy, & I. I. Bejar (Eds.), Test theory for a new generation of tests (pp. 125-150). Hillsdale, NJ: Lawrence Erlbaum.
11.
Embretson, S. E. (1996). Multicomponent response models. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 305-321). New York: Springer.
12.
Embretson, S. E. (1998). A cognitive design system approach to generating valid tests: Application to abstract reasoning. Psychological Methods, 3, 380-396.
13.
Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum.
14.
English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. Mahwah, NJ: Lawrence Erlbaum.
15.
Fisher, R. A. (1925). Statistical methods for research workers. London: Oliver & Boyd.
16.
Foley, E. J., & Berch, D. B. (1997). Capacity limitations of a classical M-Power measure: A modified dual-task approach. Journal of Experimental Child Psychology, 66, 129-143.
17.
Green, K. E., & Kluever, R. C. (1992). Components of item difficulty of Raven’s Matrices. Journal of General Psychology, 119, 189-199.
18.
Green, K. E., & Smith, R. M. (1987). A comparison of two methods of decomposing item difficulties. Journal of Educational Statistics, 12, 369-381.
19.
Halford, G. S. (1993). Children’s understanding: The development of mental models. Hillsdale, NJ: Lawrence Erlbaum.
20.
Halford, G. S., Andrews, G., Dalton, C., Boag, C. C., & Zielinski, T. (2002). Young children’s performance on the balance scale: The influence of relational complexity. Journal of Experimental Child Psychology, 81, 383-416.
21.
Halford, G. S., Baker, R., McCredden, J. E., & Bain, J. D. (2005). How many variables can humans process?Psychological Science, 16, 70-76.
22.
Halford, G. S., Wilson, W. H., & Phillips, S. (1998a). Processing capacity defined by relational complexity: Implications for comparative, developmental, and cognitive psychology. Behavioral and Brain Sciences, 21, 803-831.
23.
Halford, G. S., Wilson, W. H., & Phillips, S. (1998b). Relational complexity metric is effective when assessments are based on actual processes. Behavioral and Brain Science, 21, 848-864.
24.
Hambleton, R. K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Norwell, MA: Kluwer-Nijhoff.
25.
Linacre, J., & Wright, B. (1994). Chi-square fit statistics. Rasch Measurement Transactions, 8(2), 361.
26.
Marshalek, B., Lohman, D. F., & Snow, R. E. (1983). The complexity continuum in the radex and hierarchical models of intelligence. Intelligence, 7, 107-127.
27.
Masters, G. N., & Wright, B. D. (1996). The partial credit model. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory. New York: Springer-Verlag.
28.
Maybery, M. T., Bain, J. D., & Halford, G. S. (1986). Information-processing demands of transitive inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12, 600-613.
29.
Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63, 81-97.
30.
Nunnally, J. C. (1978). Psychometric theory. New York: McGraw-Hill.
31.
Pedhazuer, E. J., & Schmelkin, L. P. (1991). Measurement, design, and analysis: An integrated approach. Mahwah, NJ: Lawrence Erlbaum.
32.
Perline, R., Wright, B., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3, 237-255.
33.
Sheehan, K. M. (1997). A tree-based approach to proficiency scaling and diagnostic assessment. Journal of Educational Measurement, 34, 333-352.
34.
Spilsbury, G., Stankov, L., & Roberts, R. (1990). The effect of a test’s difficulty on its correlation with intelligence. Personality and Individual Differences, 11, 1069-1077.
35.
Stankov, L. (2000). Complexity, metacognition and fluid intelligence. Intelligence, 28, 121-143.
36.
Sweller, J. (1998). Can we measure working memory without contamination from knowledge held in long-term memory?Behavioral and Brain Science, 24, 845-846.
37.
Tabachnick, B. G., & Fidell, L. S. (1989). Using multivariate statistics (2nded.). New York: Harper Collins.
38.
Thomson, G. H. (1941). The use of the Latin square in designing educational experiments. British Journal of Educational Psychology, 11, 135-137.
39.
Waltz, J. A., Knowlton, B. J., Holyoak, K. J., Boone, K. B., Mishkin, F. S., de Menezes Santos, M., et al. (1999). A system for relational reasoning in human prefrontal cortex. Psychological Science, 10, 119-125.
40.
Wright, B. D. (1999). Fundamental measurement for psychology. In S. E. Embretson & S. L. Hershberger (Eds.), The new rules of measurement: What every psychologist and educator should know (pp. 65-104). Mahwah, NJ: Lawrence Erlbaum.
41.
Wright, B. D., Linacre, J., Gustafson, J.-E., & Martin-Lof, P. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8(3), 370.
