Magnitude Comparisons of Discounted Prices: Are They Similar to Fractions?

The present study examines whether peoples mental representation of discounted prices, which have a part-whole relation-ship of the current price to the original price, is similar to that of fractions. Participants performed a fraction comparisontask and a deal comparison task on the same set of fractional magnitudes. In two experiments, we observed worse perfor-mance (error rate, RT of correct trials) on the deal comparison task. The distance effect, where magnitude comparisons aremade more slowly and less accurately the closer two magnitudes are, observed in the two tasks was best modeled usinglogarithmic distance between the fractional magnitudes as a predictor of performance

Magnitude Processing of Improper Fractions When Comparing Bundle Deals

People encounter improper fractions in real life contexts on a regular basis. One such example is with bundling at thegrocery store (2/$4 or two for$4). The present study seeks to understand how people process these bundle prices comparedto improper fractions. Participants completed a magnitude comparison task with different bundling formats (2/$4 vs.$4/2)and their fractional equivalents. We found a reliable difference between the bundle format (2/$4) seen in grocery storesand the most visually similar fraction (2/4). This difference shows that participants are not using a heuristic (larger fractionmeans cheaper per item) when comparing these bundle deals and instead do need to process them like improper fractions.Overall, we found that participants were better at comparing fractional magnitudes in a math context than in a financialcontext and that this effect of context also depended on format (2/4 vs. 4/2)

Magnitude Comparisons of Improper Fractions

Previous studies examining the mental representations of fractions have focused on fractions with magnitudes less thanone (e.g., 2/3). In the current study, we examine the mental representations of fractions with magnitudes greater than one,specifically those of improper fractions. Participants were asked to make magnitude comparisons of these improper frac-tions to a reference that was in an improper fraction, a mixed fraction, or a decimal format. Results show that magnitudesof improper fractions were more accurately accessed when they were compared to mixed fractions and decimals. Thissuggests that the reinterpretation of these improper fractions benefited magnitude processing. Distance effects on errorrate and response time were observed for all three reference formats and more consistently took the form of a Welfordfunction, which predicts worse performance above rather than below the reference. Possible explanations of these resultsare discussed

Performance of drawing scatterplots based on given correlations

Previous research assessing peopleÕs sense of correlation used scatterplots as stimuli and asked participants to estimate the correlation of said scatterplots. This method has consistently shown that people tend to underestimate the correlation of a scatterplot (e.g., guessing the correlation is 0.25 when the actual correlation is 0.5). However, it is unclear whether this underestimation is perceptual or reflective of having a poor internal representation of different correlations. We investigated this question by flipping the task: instead of estimating the correlation from a scatterplot, participants drew a scatterplot based on a given correlation. They drew 20 points to represent the correlation coefficients: 0, 0.25, 0.5, 0.75, and 1. While the drawn correlations of 0, 0.75 and 1 were quite accurate, the drawn correlations of 0.25 and 0.5 were much higher than the requested correlations. This pattern is consistent with previous research, suggesting the underestimation may not be perceptual