The impact of visualization on flexible Bayesian reasoning

• Katharin, Böcherer-Linder ^[1] ; Andreas, Eichler ^[2] ; Markus, Vogel ^[3]
  1. [1] University of Education Freiburg

     University of Education Freiburg

     Stadtkreis Freiburg im Breisgau, Alemania

     
  2. [2] University of Kassel

     University of Kassel

     Kreisfreie Stadt Kassel, Alemania

     
  3. [3] University of Education

     University of Education

     Pakistán

     

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• Localización: Avances de investigación en educación matemática: AIEM, ISSN-e 2254-4313, Nº. 11, 2017, págs. 25-46
• Idioma: inglés
• DOI: 10.35763/aiem.v1i11.169
• Títulos paralelos:
  • L’influence de la visualisation sur le raisonnement bayésien flexible
  • El impacto de la visualización sobre el razonamiento Bayesiano flexible
  • O impacto da visualização no raciocínio Bayesiano flexíve
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Hay un amplio consenso en que la visualización de la información estadística puede apoyar el razonamiento bayesiano. El trabajo se enfoca en la comprensión conceptual de las situaciones que implican razonamiento bayesiano e investiga si el diagrama en árbol o el cuadrado unidad son más apropiados para apoyar la comprensión de la influencia de las tasas base, que son introducidas como parte flexible del razonamiento bayesiano. Como gráfico estadístico, el cuadrado unidad refleja la influencia de las tasas base no sólo de forma numérica, sino también geométrica. En consecuencia, en dos experimentos con estudiantes de grado (N = 148 y N = 143) se obtuvieron mejores resultados con el cuadrado unidad que con el diagrama en árbol para comprender la influencia de las tasas base.Nuestros resultados contribuyen a la discusión sobre cómo visualizar las situaciones bayesianas y tiene consecuencias prácticas para la enseñanza y el aprendizaje de la estadística.

  • português

    É amplamente consensual que a visualização da informação estatística pode apoiar o raciocínio bayesiano. Este artigo foca-se na compreensão conceptual de situações que envolvem raciocínio Bayesiano e investiga se o diagrama de árvore ou o quadrado unitário é mais apropriado para apoiar a compreensão da influência da taxa de base que é introduzida como parte do raciocínio bayesiano flexível. Como gráfico estatístico, o quadrado unitário reflete a influência da taxa de base não apenas de forma numérica mas também geométrica. Consequentemente, em duas experiências com estudantes universitários (N = 148 e N = 143), obtiveram-se melhores desempenhos com o quadrado unitário do que com o diagrama em árvore, no que se refere à compreensão da influência da taxa de base. Os nossos resultados podem informar a discussão sobre como visualizar situações bayesianas e têm consequências práticas para o ensino e aprendizagem da estatística.

  • English

    There is wide consensus that visualizations of statistical information can support Bayesian reasoning. This article focusses on the conceptual understanding of Bayesian reasoning situations and investigates whether the tree diagram or the unit square is more appropriate to support the understanding of the influence of the base rate, which is introduced as being a part of flexible Bayesian reasoning. As a statistical graph, the unit square reflects the influence of the base rate not only in a numerical but also in a geometrical way. Accordingly, in two experiments with undergraduate students (N = 148 and N = 143) the unit square outperformed the tree diagram referring to the understanding of the influence of the base rate. Our results could inform the discussion about how to visualize Bayesian situations and has practical consequences for the teaching and learning of statistics.

  • français

    Selon un large consensus, la visualisation de l’information statistique peut aider le raisonnement bayésien. Cet article porte sur la compréhension conceptuelle des situations qui impliquent le raisonnement bayésien et il cherche à déterminer si le diagramme arborescent ou le carré d’unité est plus approprié pour aider à la compréhension de l’influence de la fréquence de base, qui est introduite comme étant une partie du raisonnement bayésien flexible. En tant que graphique statistique, le carré d’unité reflète l’influence de la fréquence de base pas seulement de manière numérique mais aussi de manière géométrique. Par conséquent, dans deux expériences avec des étudiants (N = 148 et N = 143) le carré d’unité a été plus efficace que le diagramme arborescent pour la compréhension de l’influence de la fréquence de base. Nos résultats contribuent à la discussion sur la visualisation des situations bayésiennes et ont des conséquences pratiques pour l’enseignement et l’apprentissage des statistiques

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