How general is the natural frequency effect? The case of joint probabilities

• DOI: 10.3389/fpsyg.2024.1296359
• Publication Date: 2024-04-10T08:41:35Z
• Authors: Nathalie Stegmüller; Karin Binder; Stefan Krauss
• Keywords: ddc:510; joint probabilities, Bayesian reasoning, natural frequencies, visualization, net diagram; Bayesian reasoning; net diagram; 510 Mathematik; joint probabilities; BF1-990; 03 medical and health sciences; 0302 clinical medicine; Psychology; natural frequencies; visualization

Natural frequencies are known to improve performance in Bayesian reasoning. However, their impact situations with two binary events has not yet been completely examined, as most researchers the last 30 years focused only on conditional probabilities. Nevertheless, consist of 16 elementary probabilities and so we widen scope focus joint In this article, theoretically elaborate importance probabilities, for example, like Linda problem. Furthermore, implemented a study 2×5×2 design factors information format (probabilities vs. natural frequencies), visualization type (“Bayesian text” tree diagram double net 2×2 table), context (mammography economics problem). Additionally, all four “joint questions” (i.e., <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">A</mml:mi><mml:mo>∩</mml:mo><mml:mi mathvariant="normal">B</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mi stretchy="false">(</mml:mo><mml:mover accent="true"><mml:mi mathvariant="normal">A</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo>∩</mml:mo><mml:mi mathvariant="normal">A</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo>∩</mml:mo><mml:mover mathvariant="normal">B</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo mathvariant="normal">A</mml:mi><mml:mo>∩</mml:mo><mml:mover stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> were asked for. The main factor interest was whether there is effect five types named above. Surprisingly, advantage found and, strikingly, interacted type. Specifically, while people’s understanding seems be worse than corresponding (and, thus, frequency holds true), opposite true 2 × table. Hence, compared typical tasks cannot same way when probability or asked.