Using Item Response Theory to Obtain Individual Information From Randomized Response Data: An Application Using Cheating Data

Abstract

The authors discuss a new method that combines the randomized response technique with item response theory. This method allows the researcher to obtain information at the individual person level without knowing the true responses. With this new method, it is possible to compare groups of individuals by means of analysis of variance or regression analysis. To illustrate the advantages of this new method, 349 students of a university in the Netherlands were surveyed with respect to frequency and reasons to cheat on exams, and students' attitudes toward cheating were investigated. Thirty-six items tapping different types of cheating behavior were used to measure attitude toward cheating, and responses to questions were obtained via a randomized response technique. The new method was used to explain differences among students' attitudes using different kinds of background information.

Keywords

Index terms: ANOVA attitudes cheating item response theory randomized response data

Get full access to this article

View all access options for this article.

References

Albert, J.H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics , 17, 251-269.

Anderman, E.M. , & Midgley, C. (2004). Changes in self-reported academic cheating across the transition from middle school to high school. Contemporary Educational Psychology, 29, 499-517.

Baker, F.B. (1992). Item response theory: Parameter estimation techniques . New York: Marcel Dekker.

Box, G.E.P. , & Tiao, G.C. (1973). Bayesian inference in statistical analysis. Reading, MA: Addison-Wesley.

Cizek, G.J. (1999). Cheating on tests: How to do it, detect it, and prevent it. Mahwah, NJ: Lawrence Erlbaum.

Davis, S.F. , Grover, C.A. , Becker, A.H. , & McGregor, L.N. (1992). Academic dishonesty: Prevalence, determinants, techniques, and punishments. Teaching of Psychology , 9, 16-20.

De Boeck, P., & Wilson, M. (Eds.). (2004). Explanatory item response models. New York: Springer .

Donovan, J.J. , Dwight, S.A. , & Hurtz, G.M. (2003). An assessment of the prevalence, severity, and verifiability of entry-level applicant faking using the randomized response technique. Human Performance, 16, 81-106.

Fowler, F. (2002). Survey research methods (3rd ed.). Thousand Oaks, CA: Sage .

10.

Fox, J.A. , & Tracy, P.E. (1986). Randomized response. Beverly Hills, CA: Sage.

11.

Fox, J.-P. (2005). Randomized item response theory models. Journal of Educational and Behavioral Statistics, 30, 189-212.

12.

Fox, J.-P. , & Glas, C.A.W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66, 269-286.

13.

Gelman, A. , Carlin, J.B. , Stern, H.S. , & Rubin, D.B. (1995). Bayesian data analysis. London : Chapman & Hall.

14.

Glas, C.A.W. (1989). Extensions of the partial credit model. Psychometrika, 54, 635-659.

15.

Horvitz, D.G. , Shah, B.V. , & Simmons, W.R. (1967). The unrelated question randomized response model . In Proceedings of the Social Statistics Section (pp. 65-72). Washington, DC: American Statistical Association.

16.

Lord, F.M. , & Novick, M.R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

17.

McCullagh, P. , & Nelder, J.A. (1989). Generalized linear models. New York: Chapman & Hall/ CRC.

18.

Mislevy, R.J. , & Bock, R.D. (1990). BILOG 3. Item analysis and test scoring with binary logistic models (2nd ed.) [Computer software and manual]. Mooresville, IN: Scientific Software.

19.

Murdock, T.B. , Miller, A. , & Kohlhardt, J. (2004). Effects of classroom context variables on high school students' judgments of the acceptability and likelihood of cheating . Journal of Educational Psychology, 96, 765-777.

20.

Newstead, S. E., Franklyn-Stokes, A., & Armstead, P. (1996). Individual differences in student cheating. Journal of Educational Psychology, 88, 229-241.

21.

Patz, R.J. , & Junker, B.W. (1999a). Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses. Journal of Educational and Behavioral Statistics, 24, 342-366.

22.

Patz, R.J. , & Junker, B.W. (1999b). A straightforward approach to Markov chain Monte Carlo methods for item response models. Journal of Educational and Behavioral Statistics, 24, 146-178.

23.

Raftery, A.E. (1995). Bayesian model selection in social research. Social Methodology, 25, 111-163.

24.

Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-282.

25.

Rost, J. (1991). A logistic mixture distribution model for polychotomous item responses. British Journal of Mathematical and Statistical Psychology, 44, 75-92.

26.

Rupp, A.A. , Dey, D.K. , & Zumbo, B.D. (2004). To Bayes or not to Bayes, from whether to when: Applications of Bayesian methodology to modeling. Structural Equation Modeling, 11, 424-451.

27.

Scheers, N.J. , & Dayton, C.M. (1987). Improved estimation of academic cheating behavior using the randomized response technique. Research in Higher Education, 26, 61-69.

28.

van der Heijden, P.G.M. , van Gils, G. , Bouts, J. , & Hox, J.J. (2000). A comparison of randomized response, computer-assisted self-interview, and face-to-face direct questioning: Eliciting sensitive information in the context of welfare and unemployment benefit. Sociological Methods & Research, 28, 505-537.

29.

Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association , 60, 63-69.

30.

Whitley, B.E. (1998). Factors associated with cheating among college students: A Review. Research in Higher Education, 39, 235-274.