Relationship between Randomness and Coefficient Alpha: A Monte Carlo Simulation Study

ABSTRACT

Cronbach’s Alpha coefficient is the most popular method of examining reliability. It is typically used when the researcher has several Likert-type items that are summed or averaged to make a composite score. Distribution of alpha coefficient has been subjected of many studies. In this study relationship between randomness and Cronbach alpha coefficient were investigated and in this context, present study was examined the question“What is the distribution of the coefficient alpha when a Likert-type scale is answered randomly?” Data were generated in the form of five point Likert-type items and Monte Carlosimulation was run for 5000 times for different item numbers.

Cronbach’s Alpha coefficient is the most popular method of examining reliability. It is typically used when the researcher has several Likert-type items that are summed or averaged to make a composite score. Distribution of alpha coefficient has been subjected of many studies. In this study relationship between randomness and Cronbach alpha coefficient were investigated and in this context, present study was examined the question“What is the distribution of the coefficient alpha when a Likert-type scale is answered randomly?” Data were generated in the form of five point Likert-type items and Monte Carlosimulation was run for 5000 times for different item numbers.

Cite this paper

R. Bindak, "Relationship between Randomness and Coefficient Alpha: A Monte Carlo Simulation Study,"*Journal of Data Analysis and Information Processing*, Vol. 1 No. 2, 2013, pp. 13-17. doi: 10.4236/jdaip.2013.12003.

R. Bindak, "Relationship between Randomness and Coefficient Alpha: A Monte Carlo Simulation Study,"

References

[1] Y. Baykul, “Measurement in Education and Psychology: Classical Test Theory and Its Application,” Osym Press, Ankara, 2000.

[2] D. L. Steiner, “Starting at the Beginning: An Introduction to Coefficient Alpha and Internal Consistency,” Journal of Personality Assessment, Vol. 80, No. 1, 2003, pp. 99- 103. doi:10.1207/S15327752JPA8001_18

[3] L. J. Cronbach, “My Current Thoughts on Coefficient Alpha and Successor Procedures,” Educational and Psychological Measurement, Vol. 64, No. 3, 2004, pp. 391- 418. doi:10.1177/0013164404266386

[4] R. A. Peterson, “A Meta-Analysis of Cronbach’s Cofficient Alpha,” Journal of Consumer Research, Vol. 21, No. 2, 1994, pp. 381-391. doi:10.1086/209405

[5] H. ?encan, “Reliability and Validity for Measurement in the Behavioral and Social,” Seckin, Ankara, 2005.

[6] M. B. Miller, “Cofficient Alpha: A Basic Introduction from the Perspectives of Classical Test Theory and Structural Equation Modeling,” Structural Equation Modeling, Vol. 2, No. 3, 1995, pp. 255-273. doi:10.1080/10705519509540013

[7] L. J. Cronbach, “Coefficient Alpha and the Internal Structure of Tests,” Psychometrika, Vol. 16, No. 3, 1951, pp. 297-334. doi:10.1007/BF02310555

[8] A. Maydeu-Olivares, D. L. Coffman and W. M. Hartmann, “Asymptotically Distribution-Free (ADF) Interval Estimation of Coefficient Alpha,” Psychological Methods, Vol. 12, No. 2, 2007, pp. 157-176. doi:10.1037/1082-989X.12.2.157

[9] M. A. Padilla, J. Divers and M. Newton, “Coefficient Alpha Bootstrap Confidence Interval under Nonnormality,” Applied Psychological Measurement, Vol. 36, No. 5, 2012, pp. 331-348. doi:10.1177/0146621612445470

[10] J. L. Romano, J. D. Kromrey and S. T. Hibbard, “A Monte Carlo Study of Eight Confidence Interval Methods for Coefficient Alpha,” Educational and Psychological Measurement, Vol. 70, No. 3, 2012, pp. 376-393. doi:10.1177/0013164409355690

[11] S. Tan, “Misuses of KR-20 and Cronbach’s Alpha Reliability Coefficients,” Education and Science, Vol. 34, No. 152, 2009, pp. 101-112.

[12] M. Tavakol and R. Dennick, “Making Sense of Cronbach’s Alpha,” International Journal of Medical Education, Vol. 2, 2003, pp. 53-55. doi:10.5116/ijme.4dfb.8dfd

[13] N. Schmitt, “Uses and Abuses of Coefficient Alpha,” Psychological Assessment, Vol. 8, No. 4, 1996, pp. 350-353. doi:10.1037/1040-3590.8.4.350

[14] G. D. Sideridis, “Examination of the Biasing Properties of Cronbach Coefficient Alpha under Conditions of Varying Shapes of Data Distribution: A Monte Carlo Simulation,” Perceptual and Motor Skills, Vol. 89, No. 3, 1999, pp. 899-902. doi:10.2466/pms.1999.89.3.899

[15] A. Leontitsis and J. Pagge, “A Simulation Approach on Cronbach’s Alpha Statistical Significance,” Mathematics and Computers in Simulation, Vol. 73, 2007, pp. 336-340. doi:10.1016/j.matcom.2006.08.001

[16] H. Yurdugül, “Minimum Sample Size for Cronbach’s Coefficient Alpha: A Monte-Carlo Study,” Hacettepe University Journal of Education, Vol. 35, 2008, pp. 397-405.

[1] Y. Baykul, “Measurement in Education and Psychology: Classical Test Theory and Its Application,” Osym Press, Ankara, 2000.

[2] D. L. Steiner, “Starting at the Beginning: An Introduction to Coefficient Alpha and Internal Consistency,” Journal of Personality Assessment, Vol. 80, No. 1, 2003, pp. 99- 103. doi:10.1207/S15327752JPA8001_18

[3] L. J. Cronbach, “My Current Thoughts on Coefficient Alpha and Successor Procedures,” Educational and Psychological Measurement, Vol. 64, No. 3, 2004, pp. 391- 418. doi:10.1177/0013164404266386

[4] R. A. Peterson, “A Meta-Analysis of Cronbach’s Cofficient Alpha,” Journal of Consumer Research, Vol. 21, No. 2, 1994, pp. 381-391. doi:10.1086/209405

[5] H. ?encan, “Reliability and Validity for Measurement in the Behavioral and Social,” Seckin, Ankara, 2005.

[6] M. B. Miller, “Cofficient Alpha: A Basic Introduction from the Perspectives of Classical Test Theory and Structural Equation Modeling,” Structural Equation Modeling, Vol. 2, No. 3, 1995, pp. 255-273. doi:10.1080/10705519509540013

[7] L. J. Cronbach, “Coefficient Alpha and the Internal Structure of Tests,” Psychometrika, Vol. 16, No. 3, 1951, pp. 297-334. doi:10.1007/BF02310555

[8] A. Maydeu-Olivares, D. L. Coffman and W. M. Hartmann, “Asymptotically Distribution-Free (ADF) Interval Estimation of Coefficient Alpha,” Psychological Methods, Vol. 12, No. 2, 2007, pp. 157-176. doi:10.1037/1082-989X.12.2.157

[9] M. A. Padilla, J. Divers and M. Newton, “Coefficient Alpha Bootstrap Confidence Interval under Nonnormality,” Applied Psychological Measurement, Vol. 36, No. 5, 2012, pp. 331-348. doi:10.1177/0146621612445470

[10] J. L. Romano, J. D. Kromrey and S. T. Hibbard, “A Monte Carlo Study of Eight Confidence Interval Methods for Coefficient Alpha,” Educational and Psychological Measurement, Vol. 70, No. 3, 2012, pp. 376-393. doi:10.1177/0013164409355690

[11] S. Tan, “Misuses of KR-20 and Cronbach’s Alpha Reliability Coefficients,” Education and Science, Vol. 34, No. 152, 2009, pp. 101-112.

[12] M. Tavakol and R. Dennick, “Making Sense of Cronbach’s Alpha,” International Journal of Medical Education, Vol. 2, 2003, pp. 53-55. doi:10.5116/ijme.4dfb.8dfd

[13] N. Schmitt, “Uses and Abuses of Coefficient Alpha,” Psychological Assessment, Vol. 8, No. 4, 1996, pp. 350-353. doi:10.1037/1040-3590.8.4.350

[14] G. D. Sideridis, “Examination of the Biasing Properties of Cronbach Coefficient Alpha under Conditions of Varying Shapes of Data Distribution: A Monte Carlo Simulation,” Perceptual and Motor Skills, Vol. 89, No. 3, 1999, pp. 899-902. doi:10.2466/pms.1999.89.3.899

[15] A. Leontitsis and J. Pagge, “A Simulation Approach on Cronbach’s Alpha Statistical Significance,” Mathematics and Computers in Simulation, Vol. 73, 2007, pp. 336-340. doi:10.1016/j.matcom.2006.08.001

[16] H. Yurdugül, “Minimum Sample Size for Cronbach’s Coefficient Alpha: A Monte-Carlo Study,” Hacettepe University Journal of Education, Vol. 35, 2008, pp. 397-405.