A Simple Statistical Estimation of One’s Performance in an MCQ Examination, Based Upon Mock Test Results, Using Binomial Distribution of Probability

Abstract

A simple statistical model is proposed regarding the estimation of one’s overall performance in an MCQ examination along with the calculation of probability of obtaining a certain percentage of marks in the same. Using the data obtained from the results of a sufficiently large number of mock examinations, conducted prior to the main examination, certain parameters quantifying one’s knowledge or preparation for the examination has been calculated. Based on those parameters, the probability of obtaining a certain percentage of marks has been computed using the theory of binomial probability distribution. The dependence of this probability function on various parameters has been depicted graphically. A parameter, called the performance index, has been defined in terms of the expectation value and standard deviation of marks computed from probability distribution. Using this parameter, a new parameter called the relative performance index has been defined. This index estimates one’s performance with respect to the best possible performance. The variation of relative performance index with respect to the preparation index has been shown graphically for different parameter values quantifying various aspects regarding the examination and the examinee.

Share and Cite:

S. Roy and P. Majumdar, "A Simple Statistical Estimation of One’s Performance in an MCQ Examination, Based Upon Mock Test Results, Using Binomial Distribution of Probability," Open Journal of Statistics, Vol. 2 No. 4, 2012, pp. 452-459. doi: 10.4236/ojs.2012.24057.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] D. K. Srinivasa and B. V. Adkoll, “Multiple Choice Questions: How to Construct and How to Evaluate?” Indian Journal of Pediatrics, Vol. 56, No. 1, 1989, pp. 69- 74.
[2] M. Tarrant and J. Ware, “Impact of Item-Writing Flaws in Multiple-Choice Questions on Student Achievement in High-Stakes Nursing Assessments,” Medical Education, Vol. 42, No. 2, 2008, pp. 198-206. doi:10.1111/j.1365-2923.2007.02957.x
[3] P. Costa, P. Olivera and M. E. Ferrao, “Equalizac?ao de Escalas com o Modelo de Resposta as Item de Dois Parametros,” In: M. Hill, et al., Eds., Estatistica-da Teoria a` Pratica, Actas do XV Congresso Annual da Sociedade Portuguesa de Estatistica, Edic?es SPE, 2008, pp. 155-166.
[4] P. Steif and J. Dantzler, “Astatics Concept Inventory: Development and Psychometric Analysis,” Journal of Engineering Education, Vol. 33, 2005, pp. 363-371.
[5] P. Steif and M. A. Handsen, “Comparisons between Performances in a Statics Concept Inventory and Course Examinations,” International Journal of Engineering Education, Vol. 22, No. 3, 2006, pp. 1070-1076.
[6] E. Ventouas, D. Triantis, P. Tsiakas and C. Stergiopoulos, “Comparison of Examination Methods Based on Multiple Choice Questions,” Computers & Education, Vol. 54, No. 2, 2010, pp. 455-461. doi:10.1016/j.compedu.2009.08.028
[7] D. Nicol, “E-Assessment by Design: Using Multiple- Choice Tests to Good Effect,” Journal of Further & Higher Education, Vol. 31, No. 1, 2007, pp. 53-64. doi:10.1080/03098770601167922
[8] L. Thompson, “The Uses and Abuses of Multiple Choice Testing in a University Setting,” Annotated Bibliography Prepared for the University Centre for Teaching and Learning, University of Canterbury, Canterbury, 2005.
[9] P. Nightingale, et al., “Assessing Learning in Universities,” Professional Development Centre, University of New South Wales, 1996, pp. 151-157.
[10] J. Heywood, “Assessment in Higher Education: Student Learning, Teaching Programmes and Institutions,” Jessica Kingsley Publishers, London, 2000.
[11] N. Falchikov, “Improving Assessment through Student Involvement: Practical Solutions for Aiding Learning in Higher and Further Education,” Routledge Falmer, London, 2005.
[12] D. Krathwohl, “A Revision of Bloom’s Taxonomy: An Overview,” Theory into Practice, Vol. 41, No. 4, 2002, pp. 212-218. doi:10.1207/s15430421tip4104_2
[13] S. Brown, “Institutional Strategies for Assessment,” In S. Brown and A. Glasner, Eds., Assessment Matters in Higher Education, SRHE and Open University Press, Buckingham, 1999, pp. 3-13.
[14] M. Culwick, “Designing and Managing MCQs,” University of Leisester, The Castle Toolkit, 2002.
[15] S. Kvale, “Contradictions of Assessment for Learning in Institutions of Higher Education,” In: D. Boud and N. Falchikov, Eds., Rethinking Assessment in Higher Education: Learning for the Longer Term, Routledge, London, 2007, pp. 57-71.
[16] M. Paxton, “A Linguistic Perspective on Multiple Choice Questioning,” Assessment and Evaluation in Higher Education, Vol. 25, No. 2, 2000, pp. 109-119. doi:10.1080/713611429
[17] G. Gibbs and C. Simpson, “Conditions under Which Assessment Supports Students’ Learning,” Learning and Teaching in Higher Education, Vol. 1, No. 1, 2004, pp. 3- 29.
[18] K. Scouller, “The Influence of Assessment Method on Students’ Learning Approaches: Multiple-Choice Question Examination versus Assignment Essay,” Higher Education, Vol. 35, No. 4, 1998, pp. 453-472. doi:10.1023/A:1003196224280
[19] L. Ding and R. Beichner, “Approaches to Data Analysis of Multiple Choice Questions,” Physical Review Special Topics—Physics Education Research, Vol. 5, 2009, Article ID: 020103.
[20] N. G. Das, “Statistical Methods,” Tata McGraw-Hill Publishing Company Ltd., New Delhi, 2008.
[21] A. M. Goon, M. K. Gupta and B. Das Gupta, “Fundamentals of Statistics,” The World Press Pvt. Ltd., Kolkata, 1971.
[22] M. R. Spiegel, et al., “Schaum’s Outlines of Statistics,” 3rd Edition, McGraw Hill, New York, 1999.
[23] M. R. Spiegel, et al., “Schaum’s Outlines of Probability and Statistics,” 3rd Edition, McGraw Hill, New York, 2009.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.