“…Testing these predictions requires manipulating probabilities. Reasoning researchers have manipulated probabilities in many ways, using pretested content (Oaksford, Chater, & Grainger, 1999; Oaksford et al, 2000), frequency formats (Gigerenzer & Hoffrage, 1995) combined with concrete visualizations (stacks of cards; Oaksford, Chater, Grainger, & Larkin, 1997, 1999), contingency tables, or “probabilistic truth tables” (Evans, Handley, & Over, 2003; Oberauer & Wilhelm, 2003), as in causal judgment (Ward & Jenkins, 1965), a procedure that has also been reversed so participants construct the contingency table given a conditional (Oaksford & Moussakowski, 2004; Oaksford & Wakefield, 2003; Oberauer, 2006; Over, Hadjichristidis, Evans, Handley, & Sloman, 2007), and sequential tasks where trial frequency reflects the probabilities (Fugard, Pfeifer, Mayerhofer, & Kleiter, 2011; Oaksford & Moussakowski, 2004; Oaksford & Wakefield, 2003), and where learning effects are observed (for critiques, see Jubin & Barrouillet, 2019; Oberauer, Weidenfeld, & Hörnig, 2004). In these experiments, we used experiential learning of probabilities, which leads to improved performance in judgment and decision making, and which has not used before in reasoning research.…”