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oai:figshare.com:article/34046226 2026-10-02T08:04:48Z category_32816 portal_2 item_type_3 month_year_10_2026

Data, analyses and material associated with the manuscript “Believability and Conditional Inference in Mathematics Undergraduates: A Replication and Extension” Lara Alcock (1384308) Matthew Inglis (1384290) Education logic reasoning mathematics believability Mathematics uses many conditionals, sentences of the form ‘if p then q’. For a true conditional, inferences from p to q and from not-q to not-p are valid; inferences from q to p and from not-p to not-q are invalid. Logically, this applies regardless of content. However, Alcock, Davies and Inglis (in press) found that content influences mathematics undergraduates’ reasoning. They reported that these students respond more normatively to inferences from true mathematical conditionals that are highly believable than from those that are less believable; also, that there are considerable individual differences. We replicate this work with a larger and more diverse sample, finding a similar overall believability effect but a different pattern of individual differences. We extend the work by relating conditional inference responses to prior performance in mathematics and to students’ cultural backgrounds. Finally, we offer a fuller theoretical account for why believability affects conditional inference in mathematics. Codebook:(i) Data are in 2024_Replication.csvVariables:Version - Participant numberLanguage - Participant's reported first languageLang code - 1 = English, 2 = Chinese, 0 = otherMaths - A level mathematics gradeM points - A level mathematics pointsF Maths - A level further mathematics gradeFM points - A level further mathematics pointsPoints - Total A level mathematics points (mathematics + further mathematics)Q1-Q4 - MP, DA, AC and MT items for the (math believable) conditional “If n is a multiple of 6, then n is a multiple of 3.” 1 = accept, 0 = rejectQ5-Q8 - MP, DA, AC and MT items for the (math believable) conditional “If x is less than 2, then s is less than 5.” 1 = accept, 0 = rejectQ9-Q12 - MP, DA, AC and MT items for the (math unbelievable) conditional “If quadrilateral Q has a reflex angle, then it will tesselate.” 1 = accept, 0 = rejectQ13-Q16 - MP, DA, AC and MT items for the (math unbelievable) conditional “If sin x is greater than 0, then cos x is less than 1.” 1 = accept, 0 = rejectQ17-Q20 - MP, DA, AC and MT items for the (causal believable) conditional “If car ownership increases, then traffic congestion will get worse.” 1 = accept, 0 = rejectQ21-Q24 - MP, DA, AC and MT items for the (causal believable) conditional “If nurses' salaries are improved, then recruitment of nurses will increase.” 1 = accept, 0 = rejectQ25-Q28 - MP, DA, AC and MT items for the (causal unbelievable) conditional “If divorce is made more difficult, then the number of marriages will decrease.” 1 = accept, 0 = rejectQ29-Q32 - MP, DA, AC and MT items for the (causal unbelievable) conditional “If foreign investment is encouraged, then the UK car industry will revive.” 1 = accept, 0 = rejectQ33-Q36 - MP, DA, AC and MT items for the (causal unbelievable) conditional “If the letter is C, then the number is 7.” 1 = accept, 0 = rejectQ37-Q40 - MP, DA, AC and MT items for the (causal unbelievable) conditional “If the letter is N, then the number is 2.” 1 = accept, 0 = rejectInc All - Whether completed all conditional inference items. 1 = yes, 0 = noInc 90 - Whether completed 90% of conditional inference items. 1 = yes, 0 = noMPMB - Acceptances out of 2 for MP items for mathematical believable conditionalsDAMB - Acceptances out of 2 for DA items for mathematical believable conditionalsACMB - Acceptances out of 2 for AC items for mathematical believable conditionalsMTMB - Acceptances out of 2 for MT items for mathematical believable conditionalsMPMU - Acceptances out of 2 for MP items for mathematical unbelievable conditionalsDAMU - Acceptances out of 2 for DA items for mathematical unbelievable conditionalsACMU - Acceptances out of 2 for AC items for mathematical unbelievable conditionalsMTMU - Acceptances out of 2 for MT items for mathematical unbelievable conditionalsMPCB - Acceptances out of 2 for MP items for causal believable conditionalsDACB - Acceptances out of 2 for DA items for causal believable conditionalsACCB - Acceptances out of 2 for AC items for causal believable conditionalsMTCB - Acceptances out of 2 for MT items for causal believable conditionalsMPCU - Acceptances out of 2 for MP items for causal unbelievable conditionalsDACU - Acceptances out of 2 for DA items for causal unbelievable conditionalsACCU - Acceptances out of 2 for AC items for causal unbelievable conditionalsMTCU - Acceptances out of 2 for MT items for causal unbelievable conditionalsMPA - Acceptances out of 2 for MP items for abstract conditionalsDAA - Acceptances out of 2 for DA items for abstract conditionalsACA - Acceptances out of 2 for AC items for abstract conditionalsMTA - Acceptances out of 2 for MT items for abstract conditionals (ii) Tasks are in2024_Replication_intstructions.tex, 2024_Replication_intstructions.pdf, 2024_Replication_abstract.tex, 2024_Replication_abstract.pdf, 2024_Replication_causal.tex, 2024_Replication_causal.pdf, 2024_Replication_math.tex, 2024_Replication_math.pdf, (iii) Main analyses are in 2024_Replication.omv and 2024_Replication.html (iv) Additional cluster analyses are in 2024_Replication_4clusters.html and 2024_Replication_5clusters.html (v) Preregistration is in 2024_Replication_prereg.pdf<table><tr><td>© the authors</td></tr></table> 2026-10-02T08:04:48Z Dataset Dataset 10.17028/rd.lboro.34046226.v1 https://figshare.com/articles/dataset/Data_analyses_and_material_associated_with_the_manuscript_Believability_and_Conditional_Inference_in_Mathematics_Undergraduates_A_Replication_and_Extension_/34046226 CC BY-NC 4.0