Item Deletions Based on Difficulty Values and Discriminating Values

Authors

  • Satyendra Chakrabartty Indian Ports Association; Indian Statistical Institute

DOI:

https://doi.org/10.56916/ejip.v2i4.455

Keywords:

Item deletion, Difficulty value, Discriminating value, Coefficient of variation, Reliability

Abstract

Background: Deletion of items from MCQ tests or Likert type scales may be necessary due to various reasons. Methods: Considering entire data the paper gives new measures of difficulty and discriminating value of items as well as test along with their relationships including relationship with test reliability (. Discriminating value of test () and item ( are expressed as coefficient of variation (CV) of test scores and item scores respectively. Results: Non-linear relationship between and   derived. As number of persons giving correct answer to an item increases,   curve increases and  curve decreases and intersect at a point (say. Items lying outside the interval [  where SD is standard deviation of or  can be deleted. Choosing acceptance region as [] may result in discarding too few items. For Likert scale, items with high values of CV may be deleted. Relationship of reliability and discriminating values helps to find effect of such deletions. Conclusions: Proposed method of item deletions based on difficulty values and discriminating values offers significant benefits and is recommended. However, the approach may be compared with deletion of items by “alpha if the item is deleted”. Future studies suggested.

References

Avanoor V. and Mahendran P. (2018). Executive Function Rating Scale [EFRS]: A Study among Learning Disabled. Tool development: Item Generation and Item Analysis. International Journal of Indian Psychology, Vol. 6, (2), DIP: 18.01.031/20180602, DOI: 10.25215/0602.031

Chakrabartty, S.N. (2022). Disability and Quality of Life. Health Science Journal, Vol. 16, No. 12; 1 – 6

Chakrabartty, S. N. (2021). Assessment of item and test parameters: Cosine similarity approach. International Journal of Psychology and Educational Studies, 8(3), 28-38.

https://dx.doi.org/10.52380/ijpes.2021.8.3.190

Chakrabartty, S.N. (2022). Measurements in mental tests through person space. Current Psychology, 41 (1). DOI: 10.1007/s12144-020-01033-3

Chakrabartty, S.N. (2020). Discriminating Value of Item and Test. International Journal of Applied Mathematics and Statistics, 59(3), 61 - 78

Chauhan,P.R., Ratrhod, S. P., Chauhan, B. R., Chauhan, G. R., Adhvaryu, A. and Chauhan, A.P. (2013). Study of difficulty level and discriminating ındex of stem type multiple choice questions of anatomy in Rajkot, BIOMIRROR, 4(06), 1-4 / bm- 1214182613

Denga, D.I. (1987). Educational measurement, continuous assessment and psychological testing. Calabar Rapid Educational Publishers.

Erhart M, Hagquist C, Auquier P, Rajmil L, Power M, Ravens-Sieberer U; European KIDSCREEN Group (2010). A comparison of Rasch item-fit and Cronbach's alpha item reduction analysis for the development of a Quality of Life scale for children and adolescents. Child Care Health Dev. 36(4):473-84. doi: 10.1111/j.1365-2214.2009.00998.x.

Green, S. B., Lissitz, R. W., & Mulaik, S. A. (1977). Limitations of coefficient alpha as an index of test unidimensionality. Educational and Psychological Measurement,37(4), 827–838. https://doi.org/10.1177/001316447703700403

Feltz C.J, Miller G.E. (1996). An asymptotic test for the equality of coefficients of variation from k populations. Stat Med. 15(6):646-58. doi: 10.1002/(sici)1097-0258(19960330) 15:6<647: aid-sim184>3.0.co;2-p.

Ferrando, P. J. (2012): Assessing the discriminating power of item and test scores in the linear factor-analysis model. Psicológica, 33(1), 111-134.

Hankins M. (2007). Questionnaire discrimination: (re)-introducing coefficient Delta. BMC Medical Research Methodology. 7(1):19. doi: 10.1186/1471-2288-7-19.

Huang, Rui-Ting, Yu, Chung-Long,Tang, Tzy-Wen and Chang, Sheng-Chun (2021). A study of the use of mobile learning technology in Taiwan for language learning, Innovations in Education and Teaching International, 58:1, 59-71. DOI: 10.1080/14703297.2019.1628798

Kehoe, Jerard (1994). Basic Item Analysis for Multiple-Choice Tests. Practical Assessment, Research, and Evaluation. Vol. 4 , Article 10. DOI: https://doi.org/10.7275/07zg-h235

Krishnamoorthy, K., & Lee, M. (2013). Improved tests for the equality of normal coefficients of variation. Computational Statistics, 29 (1 – 2), 215 – 232. DOI:10.1007/s00180-013-0445-2

Lorenzo-Seva, U. and Ferrando,P. J.(2021): MSA: The Forgotten Index for Identifying Inappropriate Items Before Computing Exploratory Item Factor Analysis. Methodology, 17(4), 296–306 https://doi.org/10.5964/meth.7185

Marwick, B. and Krishnamoorthy, K. (2019): CV equality: Tests for the Equality of Coefficients of Variation from Multiple Groups. R software package version 0.1.3. https://github.com/benmarwick/cvequality

Masters, G. N. (1982). A Rasch Model for Partial Credit Scoring. Psychometrika; 47, 149–174. doi: 10.1007/BF02296272

McDonald, R.P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates Publishers.

Muñiz, J., & Fonseca-Pedrero, E. (2019): Diez pasos para la construcción de un test. Psicothema, 31(1), 7-16. https://doi.org/10.7334/psicothema2018.291

Ogasawara, H. (2006): Approximations to the distribution of the sample coefficient alpha under non-normality. Behaviormetrika; 33(1), 3–26. https://doi.org/10.2333/bhmk.33.3

Parkerson HA, Noel M, Pagé MG, Fuss S, Katz J, Asmundson GJ (2013). Factorial Validity of the English-Language Version of the Pain Catastrophizing Scale–Child Version, The Journal of Pain, 14 (11), 1383-1389, https://doi.org/10.1016/j.jpain.2013.06.004

Popham, J. W. (2008). Classroom assessment: What teachers need to know. Boston, MA: Allyn & Bacon.

Pronk T, Molenaar D, Wiers RW, Murre J. (2022). Methods to split cognitive task data for estimating split-half reliability: A comprehensive review and systematic assessment. Psychon Bull Rev. 29(1):44-54. 10.3758/s13423-021-01948-3

Rao C, Kishan Prasad H L, Sajitha K, Permi H, Shetty J. (2016). Item analysis of multiple choice questions: Assessing an assessment tool in medical students. Int J Educ Psychol Res, 2 (4):201-204. DOI: 10.4103/2395-2296.189670

Raykov, T. (2008). Alpha if item deleted: a note on loss of criterion validity in scale development if maximizing coefficient alpha. Br. J. Math. Stat. Psychol.61, 275–285. doi: 10.1348/000711007X188520

Raykov, T. (2007). Reliability if deleted, not “alpha if deleted”: Evaluation of scale reliability following component deletion. British Journal of Mathematical and Statistical Psychology, 60, 201-216.

Shakil, M. (2008).Assessing student performance using test item analysis and its relevance to the state exit final exams of MAT0024 classes: An action research project. Polygons, 2, 1 – 35.

Sim, Si–Mui and Rasiah, R. I.(2006). Relationship between ıtem difficulty and discrimination ındices in true/false type multiple choice questions of a para-clinical multidisciplinary paper, Annals of the Academy of Medicine, 35(2), 67-71.

Sokal, R.R. and Rohlf, F.J. (1995). Biometry: The Principles and Practice of Statistics in Biological Research (3rd Ed.), W.H. Freeman and Co., New York

Ten Berge J.M.F. & Hofstee W.K. (1999). Coefficient alpha and reliabilities of unrotated and rotated components. Psychometrika, 64(1):83–90. doi:10.1007/BF02294321

Downloads

Published

2023-09-23

How to Cite

Chakrabartty, S. (2023). Item Deletions Based on Difficulty Values and Discriminating Values. Edukasiana: Jurnal Inovasi Pendidikan, 2(4), 285–293. https://doi.org/10.56916/ejip.v2i4.455

Issue

Section

Articles