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Benford's Law: textbook exercises and multiple-choice testbanks.

ABSTRACT: Benford's Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1%, and the least common is 9, with an expected frequency of 4.6%. Currently, the most common application of Benford's Law is in detecting number invention and tampering such as found in accounting-, tax-, and voter-fraud. We demonstrate that answers to end-of-chapter exercises in physics and chemistry textbooks conform to Benford's Law. Subsequently, we investigate whether this fact can be used to gain advantage over random guessing in multiple-choice tests, and find that while testbank answers in introductory physics closely conform to Benford's Law, the testbank is nonetheless secure against such a Benford's attack for banal reasons.

SUBMITTER: Slepkov AD

PROVIDER: S-EPMC4331362 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Benford's Law: textbook exercises and multiple-choice testbanks.

Slepkov Aaron D AD Ironside Kevin B KB DiBattista David D

PloS one 20150217 2

Benford's Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1%, and the least common is 9, with an expected frequency of 4.6%. Currently, the most common application of Benford's Law is in detecting number invention and tampering such as found in accounting-, tax-, and ...[more]

PMID: 25689468

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Project description:Background and aimsRecently formed allopolyploid species represent excellent subjects for exploring early stages of polyploid evolution. The hexaploid Cardamine schulzii was regarded as one of the few nascent allopolyploid species formed within the past ?150 years that presumably arose by autopolyploidization of a triploid hybrid, C. × insueta; however, the most recent investigations have shown that it is a trigenomic hybrid. The aims of this study were to explore the efficiency of progenitor-specific microsatellite markers in detecting the hybrid origins and genome composition of these two allopolyploids, to estimate the frequency of polyploid formation events, and to outline their evolutionary potential for long-term persistence and speciation.MethodsFlow-cytometric ploidy-level screening and genotyping by progenitor-specific microsatellite markers (20 microsatellite loci) were carried out on samples focused on hybridizing populations at Urnerboden, Switzerland, but also including comparative material of the parental species from other sites in the Alps and more distant areas.Key resultsIt was confirmed that hybridization between the diploids C. amara and C. rivularis auct. gave rise to triploid C. × insueta, and it is inferred that this has occurred repeatedly. Evidence is provided that C. schulzii comprises three parental genomes and supports its origin from hybridization events between C. × insueta and the locally co-occurring hypotetraploid C. pratensis, leading to two cytotypes of C. schulzii: hypopentaploid and hypohexaploid. Each cytotype of C. schulzii is genetically uniform, suggesting their single origins.ConclusionsPersistence of C. schulzii has presumably been achieved only by perennial growth and clonal reproduction. This contrasts with C. × insueta, in which multiple origins and occasional sexual reproduction have generated sufficient genetic variation for long-term survival and evolutionary success. This study illustrates a complex case of recurrent hybridization and polyploidization events, and highlights the role of triploids that promoted the origin of trigenomic hybrids.

Dataset Information

Benford's Law: textbook exercises and multiple-choice testbanks.

Publications

Benford's Law: textbook exercises and multiple-choice testbanks.

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