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Identifying Student Difficulties in Conditional Probability within Statistical Reasoning

Fabby, Carol
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1636381029526366

Abstract Details

2021, PhD, University of Cincinnati, Education, Criminal Justice, and Human Services: Educational Studies.
Having the ability to make informed decisions about health, financial investments, and even the weather are all important to our everyday lives. However, most people receive no formal education on how to read and understand data presented in formats such as data tables and graphs. Research within the field of statistical reasoning demonstrates a lack of reasoning abilities persists through misconceptions about conditional probabilities, the topic of interest to make informed decisions based on data. The purpose of this research was to assess statistical reasoning abilities involving conditional probabilities, how individuals make decisions based on various representations of statistical data, and if bias influences decisions involving data. Participants in this study consisted of 154 students enrolled in the algebra-based sections and 496 students enrolled in the calculus-based sections of an introductory physics laboratory course during Spring semester 2016 at the University of Cincinnati main campus. In this multiple methods study design, students completed a statistical reasoning assessment developed for this research. The assessment questions used real-world scenarios for the purpose of identifying student difficulties in the interpretation and application of conditional probabilities in multiple tasks involving decision making. Two parallel versions of the quantitative assessment were used to compare students’ responses on various aspects of students’ reasoning, including different representations of data, different types of probability questions, and how bias influenced data analysis and decision making. Qualitative data were gathered through student interviews to gain insight into the reasoning behind students’ decisions on the assessment questions. The results of this study identified seven key difficulties hindering students from reaching the correct response on the assessment questions. Two difficulties were based on bias: social and motivational. Five difficulties were based on data: distracted by trends or patterns, inability to read data, inability to understand percentages in a data table, inability to do a probability, and improper normalization. Analysis using single-factor ANOVAs reveals one main effect observed in three comparisons: the type of data (no data or combined limited and full data) students used to answer all sets of assessment questions in the six scenarios, F = 37.641, p = 0.000 ; from the type of data (no data, limited data, full data) in the six scenarios, F = 4.142, p = 0.043; and F = 4.022, p = 0.046, when using the same data types from all question sets in five of the six scenarios, excluding the tree scenario. This shows whether and how data were included with the assessment questions influenced students’ decision-making abilities. As the question types became more involved and the data provided became more complex, there was a difference in how students answered the questions.
Kathleen Koenig, Ph.D (Committee Chair)
Mark| W. Plano Clark, Ph.D (Committee Member)
Jonathan| Breiner|, Ph.D (Committee Member)
Lei Bao, Ph.D (Committee Member)
Physics; Science Education
conditional probability; statistical reasoning; decision making; bias; college-age students; scientific reasoning

Recommended Citations

Citations

  • Fabby, C. (2021). Identifying Student Difficulties in Conditional Probability within Statistical Reasoning [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1636381029526366

    APA Style (7th edition)

  • Fabby, Carol. Identifying Student Difficulties in Conditional Probability within Statistical Reasoning. 2021. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1636381029526366.

    MLA Style (8th edition)

  • Fabby, Carol. "Identifying Student Difficulties in Conditional Probability within Statistical Reasoning." Doctoral dissertation, University of Cincinnati, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1636381029526366

    Chicago Manual of Style (17th edition)

ucin1636381029526366
185
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This open access ETD is published by University of Cincinnati and OhioLINK.