Ami Feder, Mariya Lozin, Nadav Neumann, Michal Pinhas
{"title":"指数表达式的数值比较:基数部分的显著性","authors":"Ami Feder, Mariya Lozin, Nadav Neumann, Michal Pinhas","doi":"10.3758/s13423-024-02571-8","DOIUrl":null,"url":null,"abstract":"<p><p>Exponential expressions represent series that grow at a fast pace such as carbon pollution and the spread of disease. Despite their importance, people tend to struggle with these expressions. In two experiments, participants chose the larger of two exponential expressions as quickly and accurately as possible. We manipulated the distance between the base/power components and their compatibility. In base-power compatible pairs, both the base and power of one expression were larger than the other (e.g., 2<sup>3</sup> vs. 3<sup>4</sup>), while in base-power incompatible pairs, the base of one expression was larger than the base in the other expression but the relation between the power components of the two expressions was reversed (e.g., 3<sup>2</sup> vs. 2<sup>4</sup>). Moreover, while in the first experiment the larger power always led to the larger result, in the second experiment we introduced base-result congruent pairs as well. Namely, the larger base led to the larger result. Our results showed a base-power compatibility effect, which was also larger for larger power distances (Experiments 1-2). Furthermore, participants processed the base-result congruent pairs faster and more accurately than the power-result congruent pairs (Experiment 2). These findings suggest that while both the base and power components are processed when comparing exponential expressions, the base is more salient. This exemplifies an incorrect processing of the syntax of exponential expressions, where the power typically has a larger mathematical contribution to the result of the expression.</p>","PeriodicalId":20763,"journal":{"name":"Psychonomic Bulletin & Review","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical comparisons of exponential expressions: The saliency of the base component.\",\"authors\":\"Ami Feder, Mariya Lozin, Nadav Neumann, Michal Pinhas\",\"doi\":\"10.3758/s13423-024-02571-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Exponential expressions represent series that grow at a fast pace such as carbon pollution and the spread of disease. Despite their importance, people tend to struggle with these expressions. In two experiments, participants chose the larger of two exponential expressions as quickly and accurately as possible. We manipulated the distance between the base/power components and their compatibility. In base-power compatible pairs, both the base and power of one expression were larger than the other (e.g., 2<sup>3</sup> vs. 3<sup>4</sup>), while in base-power incompatible pairs, the base of one expression was larger than the base in the other expression but the relation between the power components of the two expressions was reversed (e.g., 3<sup>2</sup> vs. 2<sup>4</sup>). Moreover, while in the first experiment the larger power always led to the larger result, in the second experiment we introduced base-result congruent pairs as well. Namely, the larger base led to the larger result. Our results showed a base-power compatibility effect, which was also larger for larger power distances (Experiments 1-2). Furthermore, participants processed the base-result congruent pairs faster and more accurately than the power-result congruent pairs (Experiment 2). These findings suggest that while both the base and power components are processed when comparing exponential expressions, the base is more salient. This exemplifies an incorrect processing of the syntax of exponential expressions, where the power typically has a larger mathematical contribution to the result of the expression.</p>\",\"PeriodicalId\":20763,\"journal\":{\"name\":\"Psychonomic Bulletin & Review\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Psychonomic Bulletin & Review\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://doi.org/10.3758/s13423-024-02571-8\",\"RegionNum\":3,\"RegionCategory\":\"心理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PSYCHOLOGY, EXPERIMENTAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Psychonomic Bulletin & Review","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.3758/s13423-024-02571-8","RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PSYCHOLOGY, EXPERIMENTAL","Score":null,"Total":0}
Numerical comparisons of exponential expressions: The saliency of the base component.
Exponential expressions represent series that grow at a fast pace such as carbon pollution and the spread of disease. Despite their importance, people tend to struggle with these expressions. In two experiments, participants chose the larger of two exponential expressions as quickly and accurately as possible. We manipulated the distance between the base/power components and their compatibility. In base-power compatible pairs, both the base and power of one expression were larger than the other (e.g., 23 vs. 34), while in base-power incompatible pairs, the base of one expression was larger than the base in the other expression but the relation between the power components of the two expressions was reversed (e.g., 32 vs. 24). Moreover, while in the first experiment the larger power always led to the larger result, in the second experiment we introduced base-result congruent pairs as well. Namely, the larger base led to the larger result. Our results showed a base-power compatibility effect, which was also larger for larger power distances (Experiments 1-2). Furthermore, participants processed the base-result congruent pairs faster and more accurately than the power-result congruent pairs (Experiment 2). These findings suggest that while both the base and power components are processed when comparing exponential expressions, the base is more salient. This exemplifies an incorrect processing of the syntax of exponential expressions, where the power typically has a larger mathematical contribution to the result of the expression.
期刊介绍:
The journal provides coverage spanning a broad spectrum of topics in all areas of experimental psychology. The journal is primarily dedicated to the publication of theory and review articles and brief reports of outstanding experimental work. Areas of coverage include cognitive psychology broadly construed, including but not limited to action, perception, & attention, language, learning & memory, reasoning & decision making, and social cognition. We welcome submissions that approach these issues from a variety of perspectives such as behavioral measurements, comparative psychology, development, evolutionary psychology, genetics, neuroscience, and quantitative/computational modeling. We particularly encourage integrative research that crosses traditional content and methodological boundaries.