Browsing by Subject "Introductory statistics"

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    Evaluating the use of the different models of collaborative tests in an online introductory statistics course.
    (2012-07) Bjornsdottir, Audbjorg
    The purpose of this study was to explore how collaborative tests could be implemented successfully in online introductory statistics courses. The research questions set forth were (1) What is the impact of using collaborative tests in an online statistics course on students´ learning? (2) What is the effect of using collaborative tests on students’ attitudes towards statistics? and (3) How does using a required consensus on collaborative tests vs. a nonconsensus approach affect group discussions? Three collaborative tests were implemented in two online sections of the EPSY- 3264 Basic and Applied Statistics course offered at the University of Minnesota. The two sections were identical in terms of the instructor, assignments, assessments, and lecture notes used. The only difference between the two sections was in terms of the format of the collaborative tests that were used. In the consensus section, students worked together in groups and submitted one answer per group. In the nonconsensus section, students worked on the test together in groups but submitted tests individually. Students were randomly assigned to a consensus (n=32) or a nonconsensus (n=27) section of the course. The Comprehensive Assessment of Important Outcomes in Statistics (CAOS) test was used to measure students´ learning, both at the beginning and at the end of the course. The Survey Of Attitudes Toward Statistics (SATS-36) instrument was used to measure students’ change in attitudes towards statistics. Another instrument designed by the instructor to measure students’ perspective towards collaborative testing was also used. Students’ discussions during the three collaborative tests were reviewed using the Pozzi, Manca, Persico, & Sarti, (2007) framework to evaluate and monitor computersupported collaborative learning. Discussions were coded using three dimensions, iv (Social, Teaching and Cognitive) and their indicators from the framework and then converted to quantitative variables that were used in the data analysis. No significant relationship was found between different sections and students’ scores on the CAOS. There was no significant difference in students’ attitudes towards statistics between the two sections. However, for both sections, students’ attitudes increased in terms of their intellectual knowledge, skills, and interest towards statistics after taking the three collaborative tests. The effects of using a required consensus on collaborative tests vs. a nonconsensus approach on group discussions did not seem to be significantly different. The two formats of the collaborative tests that were used seemed to support students’ discussion more in terms of the Cognitive dimension compared to the Social and Teaching dimensions. Overall, the results suggest that the difference between using two different formats of collaborative tests is not significant. However, the results support what research on collaborative tests in face-to-face courses have demonstrated before such as an increase in students’ attitudes towards learning (e.g., Giraud & Enders, 2000; Ioannou & Artion, 2010). Instructors and researchers should continue to use and experiment with collaborative tests in online introductory statistics courses. The study here is just the beginning in terms of conducting empirical research into what teaching methods and assessments should be used in an effort to create quality and effective online statistics courses.
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    Student Understanding of the Hypothetical Nature of Simulations in Introductory Statistics
    (2021-08) Brown, Jonathan
    Simulations have played an increasing role in introductory statistics courses, as both content and pedagogy. Empirical research and theoretical arguments generally support the benefits of learning statistical inference with simulations, particularly in place of traditional formula-based methods with which introductory students typically struggle. However, the desired learning benefits of simulations have not been consistently observed in all circumstances. Moreover, students in introductory courses have exhibited several types of misconceptions specific to simulations. One theme common to several of these misconceptions is conflating the hypothetical nature of simulations with the real world. These misconceptions, however, have only been discussed in the context of null-hypothesis significance testing (NHST), typically with a randomization-test simulation. Misconceptions about bootstrapping for the purposes of statistical estimation, a common component of simulation-based curricula, have remained unexplored.The purpose of this study was to explore introductory statistics students’ real-world interpretations of hypothetical simulations. The research questions driving this study were the following: (1) To what extent are there quantitative differences in student understanding of the hypothetical nature of simulations when working with null-hypothesis significance testing vs. estimation? and (2) What typical themes emerge that indicate students are conflating the hypothetical nature of simulations with the real world? The Simulation Understanding in Statistical Inference and Estimation (SUSIE) instrument was created to evaluate student interpretations about the properties of simulations throughout the entire statistical analysis process. The final instrument consisted of eighteen constructed-response items interspersed throughout descriptions of two different statistical research contexts. One context presented the randomization test for the purpose of NHST, and the second context presented bootstrapping for the purpose of statistical estimation. The instrument was developed, piloted, and updated over eight months and then administered to 193 introductory statistics students from one of two simulation-based curricula. Responses to the instrument were quantitatively scored for accuracy and qualitatively classified for clear examples of conflating the hypothetical nature of simulations with the real world. Quantitative scores were analyzed with descriptive statistics, inferential statistics, and several linear models. Qualitative classifications were analyzed by identifying the primary themes emerging from the responses to each item. Results from the quantitative analysis suggest that there was no meaningful difference in the aggregate performance between interpreting the randomization simulation vs. the bootstrap simulation (average within-participant instrument section score difference = 0 points, 95% CI: -0.3 to 0.2 points, out of a possible 18 points). However, there was evidence of some differences in performance in parallel items between the NHST and estimation instrument sections. This indicates that participants inconsistently struggled with correctly interpreting the randomization test for NHST vs. bootstrapping for estimation, across the steps of a statistical analysis. Moreover, performance on the instrument overall (average total score = 9.0 points, SD = 3.7 points) and on a per-item basis indicates that several topics were difficult for participants. Bolstering this outcome, results from the qualitative analysis indicate that the participants held a large variety of misconceptions about simulations that pertain to real-world properties and that these misconceptions may vary by the type of simulation used. This includes thinking that simulations can improve several real-world aspects of studies, can increase the sample size of a study after the data are collected, and are a sufficient replacement for a real-world process such as study replication. Implications from these results suggest the need for real-world conflations to be better addressed in the classroom, a clearer framework to define conflations, and new assessment to efficiently identify the prevalence of conflations and how they emerge when learning statistics with simulations.