Desarrollo y validación preliminar de un cuestionario de razonamiento estadístico en estudiantes de ciencias del deporte
DOI:
https://doi.org/10.47197/retos.v81.119251Keywords:
Delphi method, statistical reasoning, surveys and questionnaires, psychometrics, validationAbstract
Introduction: Statistical reasoning is critical for evidence-based decision-making in the sports sciences. However, there is a lack of psychometrically valid instruments for this population.
Objective: To develop and provide evidence of content validity, internal structure, and reliability for a questionnaire designed to assess statistical reasoning among sports science students.
Methods: A psychometric validation study was conducted, incorporating a three-stage Delphi consensus (n=13, experts) for item generation. Content validity was quantified using the item-level content validity index (IVC-I), the general content validity index (IVC-G), and modified Kappa (K*). A sample of (n=99) students (21.9 ± 2.04 years) completed the instrument. An exploratory factor analysis was performed using a robust estimate of diagonally weighted least squares. Reliability was determined using Cronbach’s alpha and the intraclass correlation coefficient (ICC).
Results: Content validity was excellent (CVI-G: 0.93; K* > 0.84). Exploratory factor analysis indicated a parsimonious two-factor structure comprising 10 items, which explained 62.4% of the total variance. Internal consistency was acceptable (α = 0.746), and test-retest reliability was adequate (ICC = 0.820; 95% CI: 0.672–0.813). Conclusions: The REI-Sports questionnaire demonstrates solid psychometric properties of validity and reliability for assessing statistical reasoning in sports science students. Further studies are needed to confirm its factor structure and applicability in other contexts.
References
Beatty, P. C., & Willis, G. B. (2007). Research Synthesis: The Practice of Cognitive Interviewing. Public Opinion Quarterly, 71(2), 287–311. https://doi.org/10.1093/poq/nfm006
Begum, M., Crossley, J., Strömbäck, F., Akrida, E., Alpizar-Chacon, I., Evans, A., Gross, J. B., Haglund, P., Lonati, V., Satyavolu, C., & Thorgeirsson, S. (2025). A Pedagogical Framework for Developing Abstraction Skills. 2024 Working Group Reports on Innovation and Technology in Computer Science Education, 258–299. https://doi.org/10.1145/3689187.3709613
Borg, D. N., Bach, A. J. E., O’Brien, J. L., & Sainani, K. L. (2022). Calculating sample size for reliability stud-ies. PM&R, 14(8), 1018–1025. https://doi.org/10.1002/pmrj.12850
Cantón-Chirivella, E., Blázquez-Perera, I., García-Mas, A., Núñez Prats, A., & Peris-Delcampo, D. (2025). Instrumentos de evaluación en psicología del deporte en español: triangulación de métodos en la identificación. Retos, 73, 950–972. https://doi.org/10.47197/retos.v73.117257
Carranza-Bautista, D., & Giakoni-Ramírez, F. (2025). Validación psicométrica SECO-3D: un instrumento para la evaluación integral de congresos académicos en ciencias de la actividad física y deporte. Retos, 72, 25–36. https://doi.org/10.47197/retos.v72.116552
Ceballos-Bernal, E. A., & Correa-Bautista, J. E. (2025). Efectividad de una intervención educativa basada en escenarios interactivos para mejorar actitudes hacia la estadística deportiva: un estudio cua-si-experimental. Retos, 72, 470–481. https://doi.org/10.47197/retos.v72.116894
Chan, S. W., & Ismail, Z. (2014). Developing Statistical Reasoning Assessment Instrument for High School Students in Descriptive Statistics. Procedia Social and Behavioral Sciences, 116, 4338–4343. https://doi.org/10.1016/j.sbspro.2014.01.943
Chance, B., Ben-Zvi, D., Garfield, J., & Medina, E. (2007). The Role of Technology in Improving Student Learning of Statistics. Technology Innovations in Statistics Education, 1(1). https://doi.org/10.5070/T511000026
Chance, B., del Mas, R., & Garfield, J. (2004). Reasoning about Sampling Distributions. In The Challenge of Developing Statistical Literacy, Reasoning and Thinking (pp. 295–323). Springer Nether-lands. https://doi.org/10.1007/1-4020-2278-6_13
Conway, B., Gary Martin, W., Strutchens, M., Kraska, M., & Huang, H. (2019). The Statistical Reasoning Learning Environment: A Comparison of Students’ Statistical Reasoning Ability. Journal of Sta-tis-tics Education, 27(3), 171–187. https://doi.org/10.1080/10691898.2019.1647008
Corbin, C. B. (2021). Conceptual physical education: A course for the future. Sport and Health Science, 10 (3), 308–322. https://doi.org/10.1016/j.jshs.2020.10.004
DeJonckheere, M., & Vaughn, L. M. (2019). Semistructured interviewing in primary care research: a balance of relationship and rigour. Family Medicine and Community Health, 7(2). https://doi.org/10.1136/fmch-2018-000057
Delmas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing Student´s Conceptual Understanding After a First Course in Statistics. Statistics Education Research Journal, 6(2), 28–58. https://doi.org/10.52041/serj.v6i2.483
Dunn, T. J., Baguley, T., & Brunsden, V. (2014). From alpha to omega: A practical solution to the perva-sive problem of internal consistency estimation. British Journal of Psychology, 105(3), 399–412. https://doi.org/10.1111/bjop.12046
Evans, A. D., Roberts, K. P., Price, H. L., & Stefek, C. P. (2010). The use of paraphrasing in investigative interviews. Child Abuse & Neglect, 34(8), 585–592. https://doi.org/10.1016/j.chiabu.2010.01.008
Fan, X. (1998). Item Response Theory and Classical Test Theory: An Empirical Comparison of their Item/ Person Statistics. Educational and Psychological Measurement, 58(3), 357–381. https://doi.org/10.1177/0013164498058003001
Friedrich, S., Antes, G., Behr, S., Binder, H., Brannath, W., Dumpert, F., Ickstadt, K., Kestler, H. A., Lederer, J., Leitgöb, H., Pauly, M., Steland, A., Wilhelm, A., & Friede, T. (2022). Is there a role for statistics in artificial intelligence? Advances in Data Analysis and Classification, 16(4), 823–846. https://doi.org/10.1007/s11634-021-00455-6
Gagnier, J. J., Lai, J., Mokkink, L. B., & Terwee, C. B. (2021). COSMIN reporting guideline for studies on measurement properties of patient-reported outcome measures. Quality of Life Research, 30(8), 2197–2218. https://doi.org/10.1007/s11136-021-02822-4
Galanis, P. (2018). The Delphi method. Archives of Hellenic Medicine, 35(4). https://doi.org/10.4324/9781315728513-10
Garfield, & Ben-Zvi, D. (2008). Developing Students’ Statistical Reasoning. Springer Netherlands. https://doi.org/10.1007/978-1-4020-8383-9
Garfield, J. (2002). The Challenge of Developing Statistical Reasoning. Journal of Statistics Education, 10(3). https://doi.org/10.1080/10691898.2002.11910676
Garfield, J., & Ahlgren, A. (1988). Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research. Journal for Research in Mathematics Education, 19(1), 44–63. https://doi.org/10.5951/jresematheduc.19.1.0044
Garfield, J. B. (2003). Assessing Statistical Reasoning. Statistics Education Research Journal, 2(1), 22–38. https://doi.org/10.52041/serj.v2i1.557
Garfield, J., & DelMas, R. (2010). A Web Site That Provides Resources for Assessing Students’ Statistical Literacy, Reasoning and Thinking. Teaching Statistics, 32(1), 2–7. https://doi.org/10.1111/j.1467-9639.2009.00373.x
Garfield, J., & Gal, I. (1999). Teaching and Assessing Statistical Reasoning”. En L. V. Stiff (Ed.), Develop-ing Mathematical Reasoning in Grade K-12 (pp. 207–219). National Council of Teachers of Mathematics.
Gaviria-Bedoya, J. A., Villa-Ochoa, J. A., & González-Gómez, D. (2025). Situated statistical reasoning as-sessment for postgraduate health sciences students: Design and validation. ZDM - Mathematics Education, 57(7), 1329–1342. https://doi.org/10.1007/s11858-025-01753-5
He, D., & Lao, H. (2018). Paper-and-pencil assessment. En The SAGE encyclopedia of educational re-search, measurement, and evaluation. SAGE Publications. https://doi.org/10.4135/9781506326139.n496
Heemskerk, L., Norman, G., Chou, S., Mintz, M., Mandin, H., & McLaughlin, K. (2008). The effect of ques-tion format and task difficulty on reasoning strategies and diagnostic performance in Internal Medicine residents. Advances in Health Sciences Education, 13(4), 453–462. https://doi.org/10.1007/s10459-006-9057-8
Hinkin, T. (1995). A review of scale development practices in the study of organizations. Journal of Management, 21(5), 967–988. https://doi.org/10.1016/0149-2063(95)90050-0
Hussain, M., Zhu, W., Zhang, W., Abidi, S. M. R., & Ali, S. (2019). Using machine learning to predict student difficulties from learning session data. Artificial Intelligence Review, 52(1), 381–407. https://doi.org/10.1007/s10462-018-9620-8
Kamp, K., Wyatt, G., Dudley-Brown, S., Brittain, K., & Given, B. (2018). Using cognitive interviewing to improve questionnaires: An exemplar study focusing on individual and condition-specific fac-tors. Applied Nursing Research, 43, 121–125. https://doi.org/10.1016/j.apnr.2018.06.007
Kellerhuis, B. E., Jenniskens, K., Kusters, M. P. T., Schuit, E., Hooft, L., Moons, K. G. M., & Reitsma, J. B. (2025). Expert panel as reference standard procedure in diagnostic accuracy studies: a system-atic scoping review and methodological guidance. Diagnostic and Prognostic Research, 9(1), 12. https://doi.org/10.1186/s41512-025-00195-7
Kincaid, J. P., Fishburne, Jr., Robert P., R., Richard L., C., & Brad S. (1975). Derivation of New Readability Formulas (Automated Readability Index, Fog Count and Flesch Reading Ease Formula) for Na-vy Enlisted Personnel. Naval technical training command. https://doi.org/10.21236/ADA006655
JASP Team. (2024). JASP (Versión 0.19.3) [Software de computación]. https://jasp-stats.org/
Li, C.-H. (2016a). Confirmatory factor analysis with ordinal data: Comparing robust maximum likeli-hood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936–949. https://doi.org/10.3758/s13428-015-0619-7
Li, C.-H. (2016b). The performance of ML, DWLS, and ULS estimation with robust corrections in struc-tural equation models with ordinal variables. Psychological Methods, 21(3), 369–387. https://doi.org/10.1037/met0000093
Lu, H.-F. (2023). Statistical learning in sports education: A case study on improving quantitative analy-sis skills through project-based alearning. Journal of Hospitality, Leisure, Sport & Tourism Edu-cation, 32, 100417. https://doi.org/10.1016/j.jhlste.2023.100417
Marco, A. (2023). A Pen and Paper Introduction to Statistics. Chapman and Hall/CRC. https://doi.org/10.1201/9781003398820
McGrath, A. L. (2014). Content, Affective, and Behavioral Challenges to Learning: Students’ Experiences Learning Statistics. International Journal for the Scholarship of Teaching and Learning, 8(2). https://doi.org/10.20429/ijsotl.2014.080206
Nasa, P., Jain, R., & Juneja, D. (2021). Delphi methodology in healthcare research: How to decide its ap-propriateness. World Journal of Methodology, 11(4), 116–129. https://doi.org/10.5662/wjm.v11.i4.116
Niederberger, M., Schifano, J., Deckert, S., Hirt, J., Homberg, A., Köberich, S., Kuhn, R., Rommel, A., & Sonnberger, M. (2024). Delphi studies in social and health sciences-Recommendations for in-terdisciplinary standardized reporting (DELPHISTAR). Results of a Delphi study. Plos One, 19(8), e0304651. https://doi.org/10.1371/journal.pone.0304651
Patalay, P., Hayes, D., & Wolpert, M. (2018). Assessing the readability of the self-reported Strengths and Difficulties Questionnaire. BJPsych Open, 4(2), 55–57. https://doi.org/10.1192/bjo.2017.13
Perner, P. (2008). Case‐based reasoning and the statistical challenges. Quality and Reliability Engineer-ing International, 24(6), 705–720. https://doi.org/10.1002/qre.951
Polit, D. F., & Beck, C. T. (2006). The content validity index: Are you sure you know what’s being re-ported? critique and recommendations. Research in Nursing & Health, 29(5), 489–497. https://doi.org/10.1002/nur.20147
Sabbag, A., Zieffler, A., & Ng, C. (2025). Can We Distinguish Statistical Literacy and Statistical Reasoning? Statistics Education Research Journal, 24(1). https://doi.org/10.52041/serj.v24i1.587
Schwob, M., Duan, Y., Cantoni, B., Flores-Lopez, B., & G. Walker, S. (2025). Exercises in Statistical Rea-soning. Chapman and Hall/CRC. https://doi.org/10.1201/9781003493471
Sepdanius, E., Binti Sanuddin, N. D., Bin Mohd Nor, M. A., Mohd Sidi, M. A. Bin, Erhan Orhan, B., Aman, M. S., & Afriani, R. (2025). Validity and reliability of a sport participant psychosocial well-being in-strument: a preliminary study. Retos, 64, 754–766. https://doi.org/10.47197/retos.v64.110789
Shoozan, A., & Mohamad, M. (2024). Application of Interview Protocol Refinement Framework in Sys-tematically Developing and Refining a Semi-structured Interview Protocol. SHS Web of Confer-ences, 182. https://doi.org/10.1051/shsconf/202418204006
Silva, P. N., & Sarnecka, B. W. (2025). What Do Your Students Struggle with? A Survey of Statistics In-structors. Journal of Statistics and Data Science Education, 1–12. https://doi.org/10.1080/26939169.2025.2455560
Szigriszt, F. (2001). Sistemas predictivos de legibilidad del mensaje escrito: fórmula de lecturabilidad de la lengua española [Tesis doctoral, Universidad Complutense, Madrid.]. https://eprints.ucm.es/id/eprint/4134/
Traynor, A., & Christopherson, S. C. (2024). Using Content Relevance and Representativeness Indices in Instrument Revision. Applied Measurement in Education, 37(2), 132–147. https://doi.org/10.1080/08957347.2024.2347518
Wild, C. J., & Pfannkuch, M. (1999). Statistical Thinking in Empirical Enquiry. International Statistical Review, 67(3), 223–248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x
Zieffler, A., Garfield, J., Alt, S., Dupuis, D., Holleque, K., & Chang, B. (2008). What Does Research Suggest About the Teaching and Learning of Introductory Statistics at the College Level? A Review of Literature. Journal of Statistics Education, 16(2), 122. https://doi.org/10.1080/10691898.2008.11889566
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