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An Eye-Tracking Study of Statistical Reasoning With Tree Diagrams and 2 × 2 Tables

Georg Bruckmaier, Karin Binder, Stefan Krauss, Han-Min Kufner
2019 Frontiers in Psychology  
Changing the information format from probabilities into frequencies as well as employing appropriate visualizations such as tree diagrams or 2 × 2 tables are important tools that can facilitate people's  ...  In the present study, we attempt to replicate this effect and also examine, by the method of eye tracking, why probabilistic 2 × 2 tables and tree diagrams do not facilitate reasoning with regard to Bayesian  ...  ACKNOWLEDGMENTS We would like to thank the university students for participating in our study.  ... 
doi:10.3389/fpsyg.2019.00632 pmid:31156488 pmcid:PMC6530428 fatcat:mkdaahjrdzhbtosmrqorqynxom

Mirroring Sankey Diagrams for Visual Comparison Tasks

Zana Vosough, Dietrich Kammer, Mandy Keck, Rainer Groh
2018 Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications  
Flow diagrams are a powerful tool to understand the structure in hierarchical data sets.  ...  In order to illustrate our concepts, we selected Product Lifecycle Costing as application domain in which comparison tasks play an important role.  ...  In this paper, we propose a new solution to extend another explicit representation, Sankey Diagrams for comparison of two tree structures.  ... 
doi:10.5220/0006651203490355 dblp:conf/grapp/VosoughKKG18 fatcat:vg6pfm6cyvddtgkicsszjiphfm

Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations

Andreas Eichler, Katharina Böcherer-Linder, Markus Vogel
2020 Frontiers in Psychology  
In particular, we compared two pairs of visualization with similar numerical information (tree diagram vs. unit square, and double-tree diagram vs. 2 × 2-table) concerning their impact on people's erroneous  ...  For example, compared to the unit square, a tree diagram does not explicitly visualize the set-subset relations that are relevant in a Bayesian situation.  ...  solution more frequently than those who use a tree diagram.  ... 
doi:10.3389/fpsyg.2020.01897 pmid:32973606 pmcid:PMC7472875 fatcat:yhdhrrnz6famjm74mnu3iwkx2y

Interactive Learning Environment Supporting Visualization in the Teaching of Probability

Stanislav Lukáč, Tadeáš Gavala
2019 International Journal of Information and Communication Technologies in Education  
In the case of incorrect answer, solutions of the additional tasks using tree diagram or a tangram are recommended to the students.  ...  Solving different task sequences using the selected types of visualization allows more learning paths for students.  ...  ACKNOWLEDGEMENTS The paper was created with support of the VEGA project no. 1/0265/17: Formative assessment in science, mathematics and informatics.  ... 
doi:10.2478/ijicte-2019-0005 fatcat:p72w6lxwnjeuflx5ogdnicxg3m

A New Visualization for Probabilistic Situations Containing Two Binary Events: The Frequency Net

Karin Binder, Stefan Krauss, Patrick Wiesner
2020 Frontiers in Psychology  
Because tree diagrams or double-trees (which are largely unknown in school) are node-branch structures, these two visualizations (in contrast to the 2 × 2 table) can even simultaneously display probabilities  ...  In teaching statistics in secondary schools and at university, two visualizations are primarily used when situations with two dichotomous characteristics are represented: 2 × 2 tables and tree diagrams  ...  on tasks using double-tree and net diagram are remarkably high given the fact that neither of these two visualizations has been explained in advance.  ... 
doi:10.3389/fpsyg.2020.00750 pmid:32528335 pmcid:PMC7264419 fatcat:nojnsja5yzbkjasiaeizdw653y

Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making

Karin Binder, Stefan Krauss, Georg Bruckmaier, Jörg Marienhagen, Aamir Ahmad
2018 PLoS ONE  
"text and tree diagram in combination"), whereas in Study 2 (N = 198 participants), we varied the kinds of tree diagrams ("complete tree" vs. "highlighted tree" vs. "pruned tree").  ...  In Study 1 (N = 190 participants), we systematically varied the presentation of statistical information ("only textual information" vs. "only tree diagram" vs.  ...  Strategy 2: Visualizing Bayesian reasoning tasks There is another strategy for improving Bayesian reasoning in the 1-test case, namely, visualizing the statistical information.  ... 
doi:10.1371/journal.pone.0195029 pmid:29584770 pmcid:PMC5871005 fatcat:7krwfbwc45grdl5abpgwmgw2f4

Evaluation of Traditional, Orthogonal, and Radial Tree Diagrams by an Eye Tracking Study

M. Burch, N. Konevtsova, J. Heinrich, M. Hoeferlin, D. Weiskopf
2011 IEEE Transactions on Visualization and Computer Graphics  
Furthermore, by applying trajectory analysis techniques we uncovered that participants cross-checked their task solution more often in the radial than in the non-radial layouts.  ...  Eye tracking was used to identify visual exploration behaviors of participants that were asked to solve a typical hierarchy exploration task by inspecting a static tree diagram: finding the least common  ...  ACKNOWLEDGMENTS This work was funded in part by the German Research Foundation (DFG) within the Priority Program "Scalable Visual Analytics" (SPP 1335).  ... 
doi:10.1109/tvcg.2011.193 pmid:22034365 fatcat:yqsgfoprfjgptctha3bq5v4xmq

Using diagrams as tools for the solution of non-routine mathematical problems

Marilena Pantziara, Athanasios Gagatsis, Iliada Elia
2009 Educational Studies in Mathematics  
The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems.  ...  Diezman & English, 2001) which documented some students' difficulties to use diagrams efficiently for the solution of problems.  ...  Students' solution strategies in the problems with diagrams and without diagrams With regard to question 3, students used a variety of strategies to solve the problems in Test A.  ... 
doi:10.1007/s10649-009-9181-5 fatcat:ihczrimnmbgdlbofu6gqjrg7sa

How to Improve Performance in Bayesian Inference Tasks: A Comparison of Five Visualizations

Katharina Böcherer-Linder, Andreas Eichler
2019 Frontiers in Psychology  
In addition to this numerical format, we used five visualizations: a 2 × 2-table, a unit square, an icon array, a tree diagram, and a double-tree diagram.  ...  We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies.  ...  The connection of both strategies resulted in a performance of about 60% in different Bayesian reasoning tasks.  ... 
doi:10.3389/fpsyg.2019.00267 pmid:30873061 pmcid:PMC6401595 fatcat:6e45kqol2ze4teavbyococncbm

Natural frequency trees improve diagnostic efficiency in Bayesian reasoning

Karin Binder, Stefan Krauss, Ralf Schmidmaier, Leah T Braun
2021 Advances in Health Sciences Education  
In an empirical study we varied information format (probabilities vs. natural frequencies) and visualization (text only vs. tree only) for four contexts. 111 medical students participated in this study  ...  Improving correctness and efficiency in Bayesian tasks might help to decrease overdiagnosis in daily clinical practice, which on the one hand cause cost and on the other hand might endanger patients' safety  ...  Acknowledgements We are thankful to Valentina Jung (Institut für Didaktik und Ausbildungsforschung in  ... 
doi:10.1007/s10459-020-10025-8 pmid:33599875 fatcat:nvplj32hazbwfbuzah7n6qmiva

Types of visual-spatial representations and mathematical problem solving

Mary Hegarty, Maria Kozhevnikov
1999 Journal of Educational Psychology  
Participants solved mathematical problems and reported on their solution strategies.  ...  relationship between use of visual-spatial representations and success in mathematical problem solving.  ...  A visual-spatial representation was scored as primarily schematic if the student drew a diagram, used gestures showing the spatial relations between objects in a problem in explaining their solution strategy  ... 
doi:10.1037//0022-0663.91.4.684 fatcat:visx72lylbcsroa4o7ufjdbiay

Types of visual-spatial representations and mathematical problem solving

Mary Hegarty, Maria Kozhevnikov
1999 Journal of Educational Psychology  
Participants solved mathematical problems and reported on their solution strategies.  ...  relationship between use of visual-spatial representations and success in mathematical problem solving.  ...  A visual-spatial representation was scored as primarily schematic if the student drew a diagram, used gestures showing the spatial relations between objects in a problem in explaining their solution strategy  ... 
doi:10.1037/0022-0663.91.4.684 fatcat:koy3w572kbh2xdwdlujyskhlxq

Cognitive Analysis on Prospective Mathematics Teachers' Reasoning Using Area and Tree Diagrams

Belén Giacomone, Pablo Beltrán-Pellicer, Juan D. Godino
2019 International journal of innovation in science and mathematics education (IJISME)  
However, the structure of the system of practices that have to be carried out to solve the problem in the tree diagram are better aligned with this kind of reasoning.  ...  Taking this challenge as an objective, this paper analyses the answers of 30 prospective teachers of primary education to a typical mathematics problem on fractions using area and tree diagrams.  ...  Acknowledgements Research carried out as part of the research project EDU2016-74848-P (FEDER, AEI), FQM-126 Group (Regional Government of Andalusia), and Project S36_17D-Research in Mathematics Education  ... 
doi:10.30722/ijisme.27.02.002 fatcat:q3y7eeuu5vanplpxy6i6wq3vgu

Why Can Only 24% Solve Bayesian Reasoning Problems in Natural Frequencies: Frequency Phobia in Spite of Probability Blindness

Patrick Weber, Karin Binder, Stefan Krauss
2018 Frontiers in Psychology  
Nevertheless, on average three quarters of participants in their meta-analysis failed to obtain the correct solution for such a task in frequency format.  ...  In a recent meta-analysis, McDowell and Jacobs (2017) showed that presenting a task in natural frequency format increases performance rates to 24% compared to only 4% when the same task is presented in  ...  first task) or presented a tree diagram (in the second task).  ... 
doi:10.3389/fpsyg.2018.01833 pmid:30369891 pmcid:PMC6194348 fatcat:pqgeuhzcz5hadn5cmkfmadjqua

Visual Patterns Associated to Abstract Trees

Uwe Kastens, Carsten Schmidt
2006 Electronical Notes in Theoretical Computer Science  
It generates editors from high level specifications: A language is specified by identifying certain patterns in the language structure, selecting a visual representation from a set of precoined solutions  ...  A complete visual structure editor is generated from such a specification. It represents visual programs by attributed abstract trees.  ...  The diagram in Fig. 5 shows the structure of four variants of language implementations. They differ in two aspects: • textual vs. visual language • input submitted in files vs. interactive input.  ... 
doi:10.1016/j.entcs.2005.12.010 fatcat:c3tns2ln3fd35p546ml2qkd7tq
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