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An Eye-Tracking Study of Statistical Reasoning With Tree Diagrams and 2 × 2 Tables
Article
Bruckmaier, Georg, Binder, Karin
, Krauss, Stefan
and Kufner, Han-Min
(2019)
An Eye-Tracking Study of Statistical Reasoning With Tree Diagrams and 2 × 2 Tables.
Frontiers in Psychology 10, p. 632.
DOI to cite this document: 10.5283/epub.40626
Abstract
Changing the information format from probabilities into frequencies as well as employing appropriate visualizations such as tree diagrams or 2 x 2 tables are important tools that can facilitate people's statistical reasoning. Previous studies have shown that despite their widespread use in statistical textbooks, both of those visualization types are only of restricted help when they are provided ...
Changing the information format from probabilities into frequencies as well as employing appropriate visualizations such as tree diagrams or 2 x 2 tables are important tools that can facilitate people's statistical reasoning. Previous studies have shown that despite their widespread use in statistical textbooks, both of those visualization types are only of restricted help when they are provided with probabilities, but that they can foster insight when presented with frequencies instead. In the present study, we attempt to replicate this effect and also examine, by the method of eye tracking, why probabilistic 2 x 2 tables and tree diagrams do not facilitate reasoning with regard to Bayesian inferences (i.e., determining what errors occur and whether they can be explained by scan paths), and why the same visualizations are of great help to an individual when they are combined with frequencies. All ten inferences of N = 24 participants were based solely on tree diagrams or 2 x 2 tables that presented either the famous "mammography context" or an "economics context" (without additional textual wording). We first asked participants for marginal, conjoint, and (non-inverted) conditional probabilities (or frequencies), followed by related Bayesian tasks. While solution rates were higher for natural frequency questions as compared to probability versions, eye-tracking analyses indeed yielded noticeable differences regarding eye movements between correct and incorrect solutions. For instance, heat maps (aggregated scan paths) of distinct results differed remarkably, thereby making correct and faulty strategies visible in the line of theoretical classifications. Moreover, the inherent structure of 2 x 2 tables seems to help participants avoid certain Bayesian mistakes (e.g., "Fisherian" error) while tree diagrams seem to help steer them away from others (e.g., "joint occurrence"). We will discuss resulting educational consequences at the end of the paper.
Involved Institutions
Details
| Item type | Article | ||||||
| Journal or Publication Title | Frontiers in Psychology | ||||||
| Publisher | Frontiers | ||||||
| Place of Publication | LAUSANNE | ||||||
| Volume | 10 | ||||||
| Page Range | p. 632 | ||||||
| Date | 15 May 2019 | ||||||
| Date of publication | 02 Aug 2019 08:29 | ||||||
| Institutions | Mathematics > Prof. Dr. Stefan Krauss | ||||||
| Identification Number |
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| Keywords | NATURAL FREQUENCIES; CONDITIONAL-PROBABILITY; ECOLOGICAL RATIONALITY; DIAGNOSTIC INFERENCES; SAMPLING APPROACH; WORD-PROBLEMS; STRATEGIES; MOVEMENTS; RISK; REPRESENTATION; Bayesian reasoning; eye tracking; 2 x 2 table; tree diagram;; probabilities | ||||||
| Dewey Decimal Classification | 300 Social sciences > 370 Education 500 Science > 510 Mathematics | ||||||
| Status | Published | ||||||
| Refereed | Yes, this version has been refereed | ||||||
| Created at the University of Regensburg | Partially | ||||||
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-406269 | ||||||
| Item ID | 40626 |
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