Tamanho da amostra, risco e fator de confiança

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Em mais uma dica sobre amostras / amostragem, veremos alguns aspectos importantes sobre esse tema. Então, vamos ao que interessa?

Primeiro, é importante compreender sobre o tamanho da amostra. Imagine que temos uma pilha de mil livros. Preciso fazer algumas análises sobre essa população gigantesca. Assim, em face da dificuldade de examinar todos os mil materiais (sou uma única pessoa), decido que aplicarei a amostragem – selecionarei apenas parte dos livros e, ao término da minha análise, extrapolarei minhas conclusões sobre essa porção à toda a população de 1.000 livros.

Porém, a pergunta que fica é: quantos livros devo pegar desse montante? A resposta é: depende. É que a decisão passa pelo risco que estou disposto a incorrer – será que a análise referente a 30 livros é suficiente para que eu não tire conclusões erradas sobre os 970 restantes?

Ora, a minha intenção é, ao descobrir informações da amostra, olhar para o restante da pilha de books que não passou pelo meu exame e dizer que a ele também se aplica as minhas conclusões. Logo, o tamanho da amostra está relacionado a esse fator. Se eu for um auditor corajoso (apenas uma brincadeira), isto é, estiver disposto a aceitar um risco maior, posso preparar uma amostra menor. Se eu for um ser medroso e conservador aumento o tamanho da minha amostra.

Repare em uma questão errada da CESPE / CEBRASPE que afronta essa lógica (ao dizer que tamanho da amostra e risco são diretamente proporcionais – são, em verdade, inversamente proporcionais, como expliquei acima):

QUESTÃO ERRADA: Quanto maior o risco que o auditor está disposto a aceitar, maior deve ser o tamanho da amostra.

Negativo. Maior o risco, menor a amostra (sou corajoso).

A Valor Consulting explica: “O auditor deve determinar o tamanho de amostra suficiente para reduzir o risco de amostragem a um nível mínimo aceitável. O nível de risco de amostragem que o auditor está disposto a aceitar afeta o tamanho da amostra exigido. Quanto menor o risco que o auditor está disposto a aceitar, maior deve ser o tamanho da amostra”.

Agora, uma questão certa da CESPE / CEBRASPE:

QUESTÃO CERTA: No que diz respeito à amostragem estatística em auditoria, o tamanho da amostra exigida é afetado pelo nível de risco de amostragem que o auditor está disposto a aceitar. Com base no exposto, afirma-se que: quanto menor o risco que o auditor está disposto a aceitar, maior deve ser o tamanho da amostra.

É isso mesmo! O fator de confiança tem essa relação quanto ao tamanho da amostra.

Mais uma questão nesses moldes:

QUESTÃO CERTA: Determinado Estado da Federação mantém programa de Cidadania Fiscal por meio do qual a emissão de notas e cupons fiscais pode ser feita com a inclusão do número de CPF do consumidor final. Após cadastro no programa, é possível que esses contribuintes diretos obtenham descontos no imposto sobre a propriedade de veículos automotores – IPVA devido. Em auditoria interna da base de dados de resgates de pontos na forma de descontos no IPVA, realizou-se um teste para apurar a distância geográfica entre os estabelecimentos em que foram realizadas as compras dos bens e serviços de onde se originou a pontuação resgatada, o endereço registrado no cadastro do programa e o domicílio do proprietário constante da anotação no Departamento Estadual de Trânsito. O objetivo pretendido era indicar possíveis erros, fraudes ou simulações. Após inspeção gráfica dos dados, o auditor promoveu a exclusão de uma série de observações que, a seu juízo, não poderiam estar corretas. Ao fim, chegou-se a uma relação de pessoas jurídicas como emissoras de documentação fiscal com afastamento geográfico suspeito entre sede e local de utilização dos pontos derivados. Sobre o caso e considerando a amostragem em auditoria, é correto afirmar: se o auditor desejar aumentar o risco amostragem, deve diminuir o tamanho da amostra.

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Inclusive, isso é o que diz a NBC TA 530:

A10. O nível de risco de amostragem que o auditor está disposto a aceitar afeta o tamanho da amostra exigido. Quanto menor o risco que o auditor está disposto a aceitar, maior deve ser o tamanho da amostra.

Observe essa outra questão:

QUESTAO CERTA: A NBC TA 530 estabelece, em seu item 5, que risco de amostragem é o risco de que a conclusão do auditor, com base em amostra” pudesse “ser diferente se toda a população fosse sujeita ao mesmo procedimento de auditoria. O risco de amostragem pode levar a conclusões errôneas. De acordo com a referida NBC, o nível de risco de amostragem que o auditor está disposto a aceitar: afeta o tamanho da amostra exigido, sendo que, quanto menor o risco que o auditor está disposto a aceitar, maior deve ser o tamanho da amostra.

Veja, agora uma questão danadinha que viaja na maionese:

QUESTÃO ERRADA: o tamanho da amostra é um critério válido para distinguir entre as abordagens estatísticas e não estatísticas.

Nada disso, o tamanho da amostra não tem a ver com essa distinção citada.

Outra questão para reforçar:

QUESTÃO CERTA Na definição da amostra de auditoria, o auditor deve considerar as características da população e a finalidade do procedimento de auditoria aplicável. Nessas condições o auditor, ao determinar o tamanho de amostra, deve reduzir o risco de amostragem a um nível mínimo aceitável.

O auditor não é bobo, não é pessoal? Ele é corajoso, mas não bobo. Ele diminui o número de amostras para tornar a análise viável, mas nem tanto, jacaré!

Finalizando com outras da examinadora CEBRASPE:

QUESTÃO ERRADA: O nível de risco que o auditor está disposto a aceitar não afeta o tamanho da amostra exigido em razão da existência de outros controles a serem utilizados;

QUESTÃO CERTA: Conforme a NBC TA 530, o tamanho de uma amostra é afetado pelo nível do risco de amostragem que o auditor está disposto a aceitar dos resultados da amostra. Deste modo é correto afirmar que: quanto menor o risco, maior deve ser o tamanho da amostra.

QUESTÃO ERRADA: Quanto menor o risco de amostragem que o auditor está disposto a aceitar, menor deve ser o tamanho da amostra.

Negativo. Quanto menor o risco de amostragem, maior deverá ser a amostra.

QUESTÃO CERTA: Quanto maior a confiança do auditor em procedimentos substantivos (testes de detalhes ou procedimentos analíticos substantivos), menor pode ser o tamanho da amostra.

Resumo: tamanho da amostra tem a ver com o risco que eu estou disposto a aceitar.

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