Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-08T09:10:41.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Bug Distribution and Statistical Pattern Classification

Published online by Cambridge University Press:  01 January 2025

Kikumi K. Tatsuoka  and
Maurice M. Tatsuoka
Kikumi K. Tatsuoka*
Affiliation:
University of Illinois at Urbana-Champaign Computer-Based Education Research Laboratory
Maurice M. Tatsuoka
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Kikumi Tatsuoka, Computer-based Education Research Laboratory, 252 Engineering Research Laboratory, 103 S. Mathews Avenue, Urbana, IL 61801.
Get access Rights & Permissions [Opens in a new window]

Abstract

A model (called the rule space model) which permits measuring cognitive skill acquisition, diagnosing cognitive errors, detecting the weaknesses and strengths of knowledge possessed by individuals was introduced earlier. This study further discusses the theoretical foundation of the model by introducing “bug distribution” and hypothesis testing (Bayes' decision rules for minimum errors) for classifying subjects into their most plausible latent state of knowledge. The model is illustrated with the domain of fraction arithmetic and compared with the results obtained from a conventional artificial intelligence approach.

Keywords

rule space modelcognitive error diagnosistask analysiserror analysisbug distributionBayes' decision rulespattern classificationitem response theorystochastic model
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 2 , March 1987 , pp. 193 - 206
Copyright
Copyright © 1987 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The authors would like to acknowledge Mr. Robert Baillie for developing several computer programs used for this research.

This research was sponsored by the Personnel and Training Research Program, Psychological Sciences Division, Office of Naval Research.

Some of the analyses presented in this report were performed on the PLATO® system. The PLATO® system is a development of the University of Illinois and PLATO® is a service mark of the Control Data Corporation.

References

Alvord, G., Macready, G. B. (1985). Comparing fit of nonsubsuming probability models. Applied Psychological Measurement, 9(3), 233–240.CrossRefGoogle Scholar
Birenbaum, M., Tatsuoka, K. K. (1986). On the stability of students' rules of operation for solving arithmetic problems, Urbana, IL: University of Illinois, Computer-based Education Research Laboratory.Google Scholar
Brown, J. S., VanLehn, K. (1980). Repair Theory: A generative theory of bugs in procedural skills. Cognitive Science, 4(4), 379–426.CrossRefGoogle Scholar
Fukunaga, K. (1972). Introduction to statistical pattern recognition, NY: Academic Press.Google Scholar
Goodman, L. A. (1975). A new model for scaling response patterns: An application of the quasi-independence concept. Journal of the American Statistical Association, 70, 755–768.CrossRefGoogle Scholar
Klein, M., Birenbaum, M., Standiford, S., Tatsuoka, K. K. (1981). Logical error analysis and construction of tests to diagnose student “bugs” with addition and subtraction of fractions, Urbana, IL: University of Illinois, Computer-based Education Research Laboratory.Google Scholar
Lee, T. T. (1983). An algebraic theory of relational databases. The Bell System Technical Journal, 62(10), 3161–3128.CrossRefGoogle Scholar
Paulson, J. A. (1985). Latent class representation of systematic patterns in test responses, Portland: Portland State University.Google Scholar
Reingold, E. M., Nievergelt, J., Deo, N. (1979). Combinatorial algorithms, theory and practice, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Tatsuoka, K. K. (1983). Rule space: An approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20(4), 345–354.CrossRefGoogle Scholar
Tatsuoka, K. K. (1984). Analysis of errors in fraction addition and subtraction problems, Urbana, IL: University of Illinois, Computer-based Education Research Laboratory.Google Scholar
Tatsuoka, K. K. (1984). Caution indices based on item response theory. Psychometrika, 9, 95–110.CrossRefGoogle Scholar
Tatsuoka, K. K. (1985). A probabilistic model for diagnosing misconceptions by the pattern classification approach. Journal of Educational Statistics, 10(1), 55–73.CrossRefGoogle Scholar
Tatsuoka, M. M. (1971). Multivariate analysis: Techniques for educational and psychological research, NY: John Wiley & Sons.Google Scholar
Tatsuoka, K. K., Baillie, R. (1982). Rule space, the product space of two score components in signed-number subtraction: An approach to dealing with inconsistent use of erroneous rules, Urbana, IL: University of Illinois, Computer-based Education Research Laboratory.Google Scholar
Tatsuoka, K. K., Linn, R. L. (1983). Indices for detecting unusual response patterns: Links between two general approaches and potential applications. Applied Psychological Measurement, 7(1), 81–96.CrossRefGoogle Scholar
Tatsuoka, K. K., Tatsuoka, M. M. (1982). Detection of aberrant response patterns. Journal of Educational Statistics, 7(3), 215–231.CrossRefGoogle Scholar
Tatsuoka, K. K., Tatsuoka, M. M. (1983). Spotting erroneous rules of operation by the individual consistency index. Journal of Educational Measurement, 20(3), 221–230.CrossRefGoogle Scholar
Tatsuoka, M. M., Tatsuoka, K. K. (1986). Rule space. In Kotz, , Johnson, (Eds.), Encyclopedia of Statistical Science, New York: Wiley.Google Scholar
VanLehn, K. (1983). Felicity conditions for human skill acquisition: Validating an AI-based theory, Palo Alto: Xerox Palto Alto Research Centers.Google Scholar