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Um método estatístico para identificação de fraude em exames de larga escala com questões do tipo múltipla escolha
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| 1.02 MB | Adobe PDF |
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Abstract(s)
No Brasil, exames de larga escala são utilizados em concursos para admissão
a cargos públicos ou para ingresso em universidades. Existem organizações criminosas
especializadas em fraudar tais exames, causando enormes danos para a sociedade,
possibilitando que pessoas não qualificadas e desonestas ingressem nas universidades e
funções públicas, em detrimento de pessoas qualificadas e honestas.
Em busca de uma forma de provar cientificamente a ocorrência de fraude em
exames compostos por questões tipo múltipla-escolha, desenvolveu-se um método de análise
estatística da similaridade das respostas dos candidatos.
O método se baseia no fato de que as respostas dadas por uma população de
candidatos em determinado exame seguem uma distribuição probabilística, cujos parâmetros
podem ser estimados a partir de dados intrínsecos do exame. Compara-se o número de
respostas coincidentes obtidas entre cada par de candidatos com o número que seria
esperado, e calcula-se a probabilidade associada a essa ocorrência. Destacam-se os casos
cuja probabilidade de ocorrência é muito pequena, menor que um nível de significância préestabelecido.
O método foi desenvolvido de maneira a preservar a segurança, de modo a
garantir que todos os candidatos sinalizados como fraudadores tenham probabilidade
elevada de terem cometido a fraude, mesmo correndo o risco de eventualmente deixar de
indicar algum candidato culpado. Isso é feito através da escolha adequada do nível de
significância para os testes de hipóteses.
As limitações de aplicabilidade do método são analisadas através de
simulação de dados, determinando-se os limites dentro dos quais o método pode ser aplicado
de forma eficaz e fiável.
In Brazil, large-scale exams are used in selection processes for admission to public positions or universities. There are criminal organizations specialized in defrauding such exams, causing enormous damage to society, allowing unqualified and dishonest people to enter universities and public functions, instead of qualified and honest people. In search of a way to scientifically prove the occurrence of fraud in exams composed of multiple-choice questions, a statistical analysis method to determine the similarity of the candidates' answers was developed. The method is based on the fact that the answers given by a population of candidates in a given exam follow a probability distribution, whose parameters can be estimated from the intrinsic data of the exam. The number of coincident responses between each pair of candidates is compared with what would be expected, and the probability associated with this occurrence is calculated. Cases whose probability of occurrence is very small, less than a pre-established level of significance, stand out. The method was developed to preserve security, in a way that it guarantees that all candidates indicated as fraudsters have a high probability of having committed the fraud, even at the risk of eventually failing to nominate a guilty candidate. This is done by choosing the appropriate level of significance for the hypothesis tests. The limitations of applicability of the method is analyzed through data simulation, determining the limits within which the method can be applied effectively and reliably.
In Brazil, large-scale exams are used in selection processes for admission to public positions or universities. There are criminal organizations specialized in defrauding such exams, causing enormous damage to society, allowing unqualified and dishonest people to enter universities and public functions, instead of qualified and honest people. In search of a way to scientifically prove the occurrence of fraud in exams composed of multiple-choice questions, a statistical analysis method to determine the similarity of the candidates' answers was developed. The method is based on the fact that the answers given by a population of candidates in a given exam follow a probability distribution, whose parameters can be estimated from the intrinsic data of the exam. The number of coincident responses between each pair of candidates is compared with what would be expected, and the probability associated with this occurrence is calculated. Cases whose probability of occurrence is very small, less than a pre-established level of significance, stand out. The method was developed to preserve security, in a way that it guarantees that all candidates indicated as fraudsters have a high probability of having committed the fraud, even at the risk of eventually failing to nominate a guilty candidate. This is done by choosing the appropriate level of significance for the hypothesis tests. The limitations of applicability of the method is analyzed through data simulation, determining the limits within which the method can be applied effectively and reliably.
Description
Keywords
Distribuição Bernoulli com probabilidades variáveis Teorema de Liapounov Teorema do limite central para variáveis não identicamente distribuídas Identificação de fraude em exames tipo múltipla escolha Bernoulli Distribution with variable probabilities Liapounov Theorems Central limit theorem for non-identical variables Fraud identification in multiple-choice exam