How many ways can you answer a 10 question True False test if you answer each question with a true or false?

In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.

The first question could be answered either true or false. . If you answered true on the first question, you could answer either true or false on the second question. . If you answered false on the first question you could answer either true or false on the second question. . So after two questions you have four possible situations: . True & then True True & then False False & then True False & then False . Now for each of those 4 possibilities, you could answer either true or false on the third question. So after 3 questions you would have 8 possible test answers ... 4 * 2. . And for each of the 8 possible answer situations on the third question, you can answer either true or false on the fourth question. This will give you 8 * 2 = 16 possible answers after the fourth question. . By now you have probably noticed the pattern. Each additional question increases the number of possible answer configurations by a factor of 2. . This pattern is reflected by the equation: . Number of different tests = 2^n . where n represents the number of questions on the test. . If there were just 1 question on the test there would be 2^1 possible answers (either true or false). If there were 2 questions on the test, the number of possible answer combinations would be 2^2 or 4. Similarly for 3 questions there would be 2^3 = 8 possible combinations. . Extending on this pattern, for a 10 question test there would be 2^10 possible combinations of answers. And 2^10 = 1024 possible answer combinations. That means that the teacher could possibly receive 1024 tests that are all different by at least one answer. . Hope this provides you with a way of figuring out a process for solving questions

such as this one.

• Adams, W. K., & Wieman, C. E. (2011). Development and validation of instruments to measure learning of expert-like thinking. International Journal of Science Education, 33(9), 1289–1312. https://doi.org/10.1080/09500693.2010.512369.

  Article  Google Scholar 

• Alnabhan, M. (2002). An empirical investigation of the effects of three methods of handling guessing and risk taking on the psychometric indices of a test. Social Behavior and Personality, 30, 645–652.

  Article  Google Scholar 

• Angelo, T. A. (1998). Classroom assessment and research: An update on uses, approaches, and research findings. San Francisco: Jossey-Bass.

  Google Scholar 

• Ávila, C., & Torrubia, R. (2004). Personality, expectations, and response strategies in multiple-choice question examinations in university students: A test of Gray’s hypotheses. European Journal of Personality, 18(1), 45–59. https://doi.org/10.1002/per.506.

  Article  Google Scholar 

• Baker, F. B., & Kim, S.-H. (2004). Item response theory: Parameter estimation techniques (2nd ed.). New York: Marcel Dekker.

  Book  Google Scholar 

• Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), 5–31. https://doi.org/10.1007/s11092-008-9068-5.

  Article  Google Scholar 

• Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29–51. https://doi.org/10.1007/BF02291411.

  Article  Google Scholar 

• Bolt, D. M., Cohen, A. S., & Wollack, J. A. (2001). A mixture item response model for multiple-choice data. Journal of Educational and Behavioral Statistics, 26(4), 381–409.

  Article  Google Scholar 

• Briggs, D., Alonzo, A., Schwab, C., & Wilson, M. (2006). Diagnostic assessment with ordered multiple-choice items. Educational Assessment, 11(1), 33–63. https://doi.org/10.1207/s15326977ea1101_2.

  Article  Google Scholar 

• Burnham, K. P., & Anderson, D. R. (2002). Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). New York: Springer-Verlag Retrieved from https://www.springer.com/us/book/9780387953649.

  Google Scholar 

• Burton, R. F. (2002). Misinformation, partial knowledge and guessing in true/false tests. Medical Education, 36(9), 805–811.

  Article  Google Scholar 

• Chiu, T.-W., & Camilli, G. (2013). Comment on 3PL IRT adjustment for guessing. Applied Psychological Measurement, 37(1), 76–86. https://doi.org/10.1177/0146621612459369.

  Article  Google Scholar 

• Couch, B. A., Hubbard, J. K., & Brassil, C. E. (2018). Multiple–true–false questions reveal the limits of the multiple–choice format for detecting students with incomplete understandings. BioScience, 68(6), 455–463. https://doi.org/10.1093/biosci/biy037.

  Article  Google Scholar 

• Couch, B. A., Wood, W. B., & Knight, J. K. (2015). The molecular biology capstone assessment: A concept assessment for upper-division molecular biology students. CBE-Life Sciences Education, 14(1), ar10. https://doi.org/10.1187/cbe.14-04-0071.

  Article  Google Scholar 

• Couch, B. A., Wright, C. D., Freeman, S., Knight, J. K., Semsar, K., Smith, M. K., et al. (2019). GenBio-MAPS: A programmatic assessment to measure student understanding of vision and change core concepts across general biology programs. CBE—Life Sciences Education, 18(1), ar1. https://doi.org/10.1187/cbe.18-07-0117.

  Article  Google Scholar 

• Cronbach, L. J. (1941). An experimental comparison of the multiple true-false and multiple multiple-choice tests. Journal of Educational Psychology, 32(7), 533.

  Article  Google Scholar 

• Crouch, C. H., & Mazur, E. (2001). Peer instruction: Ten years of experience and results. American Journal of Physics, 69(9), 970–977. https://doi.org/10.1119/1.1374249.

  Article  Google Scholar 

• de Ayala, R. J. (2008). The theory and practice of item response theory (1st ed.). New York: The Guilford Press.

  Google Scholar 

• Diamond, J., & Evans, W. (1973). The correction for guessing. Review of Educational Research, 43(2), 181–191.

  Article  Google Scholar 

• Dudley, A. (2006). Multiple dichotomous-scored items in second language testing: Investigating the multiple true–false item type under norm-referenced conditions. Language Testing, 23(2), 198–228. https://doi.org/10.1191/0265532206lt327oa.

  Article  Google Scholar 

• Eagan, K., Stolzenberg, E. B., Lozano, J. B., Aragon, M. C., Suchard, M. R., & Hurtado, S. (2014). Undergraduate teaching faculty: The 2013–2014 HERI faculty survey. Los Angeles: Higher Education Research Institute, UCLA Retrieved from https://www.heri.ucla.edu/monographs/HERI-FAC2014-monograph-expanded.pdf.

  Google Scholar 

• Ellis, A. P. J., & Ryan, A. M. (2003). Race and cognitive-ability test performance: The mediating effects of test preparation, test-taking strategy use and self-efficacy. Journal of Applied Social Psychology, 33(12), 2607–2629. https://doi.org/10.1111/j.1559-1816.2003.tb02783.x.

  Article  Google Scholar 

• Ericsson, K. A., Krampe, R. T., & Tesch-romer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3), 363–406.

  Article  Google Scholar 

• Fox, J. (2010). Bayesian item response modeling. New York: Springer.

  Book  Google Scholar 

• Frary, R. B. (1988). Formula scoring of multiple-choice tests (correction for guessing). Educational Measurement: Issues and Practice, 7(2), 33–38. https://doi.org/10.1111/j.1745-3992.1988.tb00434.x.

  Article  Google Scholar 

• Frey, B. B., Petersen, S., Edwards, L. M., Pedrotti, J. T., & Peyton, V. (2005). Item-writing rules: Collective wisdom. Teaching and Teacher Education: An International Journal of Research and Studies, 21(4), 357–364.

  Article  Google Scholar 

• Frisbie, D. A. (1992). The multiple true-false item format: A status review. Educational Measurement: Issues and Practice, 11(4), 21–26.

  Article  Google Scholar 

• Frisbie, D. A., & Sweeney, D. C. (1982). The relative merits of multiple true-false achievement tests. Journal of Educational Measurement, 19(1), 29–35. https://doi.org/10.1111/j.1745-3984.1982.tb00112.x.

  Article  Google Scholar 

• Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1(3), 515–534.

  Article  Google Scholar 

• Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24(6), 997–1016. https://doi.org/10.1007/s11222-013-9416-2.

  Article  Google Scholar 

• Haladyna, T. M., Downing, S. M., & Rodriguez, M. C. (2002). A review of multiple-choice item-writing guidelines for classroom assessment. Applied Measurement in Education, 15(3), 309–333. https://doi.org/10.1207/S15324818AME1503_5.

  Article  Google Scholar 

• Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park: SAGE Publications, Inc.

• Handelsman, J., Miller, S., & Pfund, C. (2007). Scientific teaching. New York: W. H. Freeman and Co.

  Google Scholar 

• Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. The Physics Teacher, 30(3), 141–158.

  Article  Google Scholar 

• Hubbard, J. K., & Couch, B. A. (2018). The positive effect of in-class clicker questions on later exams depends on initial student performance level but not question format. Computers & Education, 120, 1–12. https://doi.org/10.1016/j.compedu.2018.01.008.

  Article  Google Scholar 

• Javid, L. (2014). The comparison between multiple-choice (mc) and multiple true-false (mtf) test formats in Iranian intermediate EFL learners’ vocabulary learning. Procedia - Social and Behavioral Sciences, 98, 784–788. https://doi.org/10.1016/j.sbspro.2014.03.482.

  Article  Google Scholar 

• Kalas, P., O’Neill, A., Pollock, C., & Birol, G. (2013). Development of a meiosis concept inventory. CBE-Life Sciences Education, 12(4), 655–664. https://doi.org/10.1187/cbe.12-10-0174.

  Article  Google Scholar 

• Kim (Yoon), Y. H., & Goetz, E. T. (1993). Strategic processing of test questions: The test marking responses of college students. Learning and Individual Differences, 5(3), 211–218. https://doi.org/10.1016/1041-6080(93)90003-B.

  Article  Google Scholar 

• Kreiter, C. D., & Frisbie, D. A. (1989). Effectiveness of multiple true-false items. Applied Measurement in Education, 2(3), 207–216.

  Article  Google Scholar 

• National Research Council (NRC). (2012). Discipline-based education research: Understanding and improving learning in undergraduate science and engineering. Washington, D.C.: National Academies Press.

  Google Scholar 

• Nehm, R. H., & Reilly, L. (2007). Biology majors’ knowledge and misconceptions of natural selection. BioScience, 57(3), 263–272. https://doi.org/10.1641/B570311.

  Article  Google Scholar 

• Nehm, R. H., & Schonfeld, I. S. (2008). Measuring knowledge of natural selection: A comparison of the CINS, an open-response instrument, and an oral interview. Journal of Research in Science Teaching, 45(10), 1131–1160. https://doi.org/10.1002/tea.20251.

  Article  Google Scholar 

• Newman, D. L., Snyder, C. W., Fisk, J. N., & Wright, L. K. (2016). Development of the Central Dogma Concept Inventory (CDCI) assessment tool. CBE-Life Sciences Education, 15(2), ar9. https://doi.org/10.1187/cbe.15-06-0124.

  Article  Google Scholar 

• Parker, J. M., Anderson, C. W., Heidemann, M., Merrill, J., Merritt, B., Richmond, G., & Urban-Lurain, M. (2012). Exploring undergraduates’ understanding of photosynthesis using diagnostic question clusters. CBE-Life Sciences Education, 11(1), 47–57. https://doi.org/10.1187/cbe.11-07-0054.

  Article  Google Scholar 

• Piñeiro, G., Perelman, S., Guerschman, J. P., & Paruelo, J. M. (2008). How to evaluate models: Observed vs. predicted or predicted vs. observed? Ecological Modelling, 216(3), 316–322. https://doi.org/10.1016/j.ecolmodel.2008.05.006.

  Article  Google Scholar 

• Pomplun, M., & Omar, H. (1997). Multiple-mark items: An alternative objective item format? Educational and Psychological Measurement, 57(6), 949–962.

  Article  Google Scholar 

• Rasch, G. (1960). Probabilistic models for some intelligence and attainments tests. Copenhagen: Danish Institute for Educational Research.

• Rodriguez, M. C. (2005). Three options are optimal for multiple-choice items: A meta-analysis of 80 years of research. Educational Measurement: Issues and Practice, 24(2), 3–13. https://doi.org/10.1111/j.1745-3992.2005.00006.x.

  Article  Google Scholar 

• Semsar, K., Brownell, S., Couch, B. A., Crowe, A. J., Smith, M. K., Summers, M. M. et al. (2019). Phys-MAPS: A programmatic physiology assessment for introductory and advanced undergraduates. Advances in Physiology Education, 43(1), 15–27. https://doi.org/10.1152/advan.00128.2018.

• Smith, M. K., Wood, W. B., & Knight, J. K. (2008). The Genetics Concept Assessment: A new concept inventory for gauging student understanding of genetics. CBE-Life Sciences Education, 7(4), 422–430. https://doi.org/10.1187/cbe.08-08-0045.

  Article  Google Scholar 

• Stan Development Team. (2017). Stan modeling language users guide and reference manual, version 2.15.0 (version 2.15.0). http://mc-stan.org.

  Google Scholar 

• Stenlund, T., Eklöf, H., & Lyrén, P.-E. (2017). Group differences in test-taking behaviour: An example from a high-stakes testing program. Assessment in Education: Principles, Policy & Practice, 24(1), 4–20. https://doi.org/10.1080/0969594X.2016.1142935.

  Article  Google Scholar 

• Summers, M. M., Couch, B. A., Knight, J. K., Brownell, S. E., Crowe, A. J., Semsar, K., et al. (2018). EcoEvo-MAPS: An ecology and evolution assessment for introductory through advanced undergraduates. CBE—Life Sciences Education, 17(2), ar18. https://doi.org/10.1187/cbe.17-02-0037.

  Article  Google Scholar 

• Thissen, D., Steinberg, L., & Fitzpatrick, A. R. (1989). Multiple-choice models: The distractors are also part of the item. Journal of Educational Measurement, 26(2), 161–176. https://doi.org/10.1111/j.1745-3984.1989.tb00326.x.

  Article  Google Scholar 

• Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27(5), 1413–1432. https://doi.org/10.1007/s11222-016-9696-4.

  Article  Google Scholar 

• Vickrey, T., Rosploch, K., Rahmanian, R., Pilarz, M., & Stains, M. (2015). Research-based implementation of peer instruction: A literature review. CBE-Life Sciences Education, 14(1), es3. https://doi.org/10.1187/cbe.14-11-0198.

  Article  Google Scholar 

• Wood, W. (2004). Clickers: A teaching gimmick that works. Developmental Cell, 7(6), 796–798. https://doi.org/10.1016/j.devcel.2004.11.004.

  Article  Google Scholar 

Page 2

Skip to main content

From: Multiple-true-false questions reveal more thoroughly the complexity of student thinking than multiple-choice questions: a Bayesian item response model comparison