287 research outputs found

    Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen – kognitive Überlastung oder didaktische Unterstützung?

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    In stochastischen Situationen mit zwei dichotomen Merkmalen erlauben weder die schulüblichen Baumdiagramme noch Vierfeldertafeln die simultane Darstellung sämtlicher in der Situation möglicher Wahrscheinlichkeiten. Das im vorliegenden Beitrag vorgestellte Netz hat die Kapazität, alle vier möglichen Randwahrscheinlichkeiten, alle vier Schnittwahrscheinlichkeiten sowie alle acht bedingten Wahrscheinlichkeiten gleichzeitig darzustellen. Darüber hinaus ist – aufgrund der Knoten-Ast-Struktur des Netzes – die simultane Darstellung von Wahrscheinlichkeiten und absoluten Häufigkeiten mit dieser Visualisierung ebenfalls möglich. Bei der sukzessiven Erweiterung des typischen Baumdiagramms zunächst zum Doppelbaum und schließlich zum Netz sinkt der Inferenzgrad (d. h. weniger kognitive Schritte sind erforderlich) z. B. für Fragen nach bedingten Wahrscheinlichkeiten, aber gleichzeitig steigt die Komplexität der Darstellung und somit die extrinsische kognitive Belastung. Im vorliegenden Artikel erfolgt zunächst ein theoretischer Vergleich dieser Knoten-Ast-Strukturen. Eine anschließende Studie illustriert, dass sich die sukzessive Erweiterung bereits vollständig ausgefüllter Diagramme positiv auf die Performanz von N = 269 Schülerinnen und Schülern auswirkt. Obwohl Häufigkeitsdoppelbäume und Häufigkeitsnetze den Schülerinnen und Schülern gänzlich unbekannt waren, unterstützten diese Visualisierungen die Schülerinnen und Schüler bei der Bearbeitung der Aufgaben am meisten. In stochastic situations with two dichotomous events, neither typical tree diagrams nor 2 × 2 tables allow the simultaneous representation of all possible probabilities in the situation. The net diagram presented in this paper has the capacity to represent all four possible marginal probabilities, all four joint probabilities, and all eight conditional probabilities simultaneously. Furthermore, due to the node-branch structure of the frequency net, the simultaneous representation of probabilities and absolute frequencies is also possible with this visualization. With the successive extension of the typical tree diagram to the double tree and finally to the net diagram, the inference degree, e.g., for questions about conditional probabilities, decreases (i.e., less mental steps are required), however, at the same time the complexity of the representation increases and thus the extrinsic cognitive load. In the present article, a theoretical comparison of these node-branch-structures is made. Furthermore, we demonstrate with an empirical study that the successive extension of these node-branch structures, which were already completely worked out, positively affects the performance of N = 269 students. Although frequency double trees and frequency nets were entirely unfamiliar to the students, these visualizations provided the best support to the students in completing the tasks

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

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    For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer and Hoffrage, 1995). 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 probability format. 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 this paper, we present an empirical study on what participants typically do wrong when confronted with natural frequencies. We found that many of them did not actually use natural frequencies for their calculations, but translated them back into complicated probabilities instead. This switch from the intuitive presentation format to a less intuitive calculation format will be discussed within the framework of psychological theories (e.g., the Einstellung effect)

    Epigenome-Wide and Transcriptome-Wide Analyses Reveal Gestational Diabetes is Associated with Alterations in the Human Leukocyte Antigen Complex

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    Background: Gestational diabetes mellitus (GDM) affects approximately 10% of pregnancies in the United States and increases the risk of adverse health outcomes in the offspring. These adult disease propensities may be set by anatomical and molecular alterations in the placenta associated with GDM. Results: To assess the mechanistic aspects of fetal programming, we measured genome-wide methylation (Infinium HumanMethylation450 BeadChips) and expression (Affymetrix transcriptome microarrays) in placental tissue of 41 GDM cases and 41 matched pregnancies without maternal complications from the Harvard Epigenetic Birth Cohort. Specific transcriptional and epigenetic perturbations associated with GDM status included alterations in the major histocompatibility complex (MHC) region, which were validated in an independent cohort, the Rhode Island Child Health Study. Gene ontology enrichment among gene regulation influenced by GDM revealed an over-representation of immune response pathways among differential expression, reflecting these coordinated changes in the MHC region. This differential methylation and expression may be capturing shifts in cellular composition, reflecting physiological changes in the placenta associated with GDM. Conclusions: Our study represents the largest investigation of transcriptomic and methylomic differences associated with GDM, providing comprehensive insight into how GDM shapes the intrauterine environment, which may have implications for fetal (re)programming

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

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    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 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 × 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 × 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 × 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
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