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Teste de Soma de Postos de Wilcoxon
O teste de soma de postos de Wilcoxon, também conhecido como teste U de Mann-Whitney, é um teste não paramétrico usado para determinar se há uma difer…
Wilcoxon rank-sum, ou Mann-Whitney U, é um teste não paramétrico usado para determinar a diferença entre duas populações comparando suas medianas.
Aplica-se estritamente a duas amostras aleatórias simples independentes com tamanhos de amostra iguais ou desiguais.
Considere o tempo de resposta de captura de presas em duas espécies diferentes de aranhas.
Aqui, a hipótese nula afirma que o tempo médio de resposta das duas espécies é o mesmo. A hipótese alternativa afirma o contrário.
Os valores nessas duas amostras são classificados, considerando-os como um único conjunto de pontos de dados. No entanto, a soma da classificação é calculada de forma independente.
Quando classificações altas ou baixas são encontradas principalmente em uma amostra do que na outra, as duas amostras podem ter medianas diferentes.
A estatística de teste z é calculada usando as seguintes equações para testar a hipótese.
O teste de soma de classificação de Wilcoxon é bicaudal. Portanto, a estatística de teste deve ser comparada com os valores críticos positivos e negativos, normalmente em 5%.
Uma vez que, no presente exemplo, a estatística de teste está além da faixa desses valores críticos, as medianas das duas amostras são significativamente diferentes.
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Q1: What is the Wilcoxon rank-sum test used for?
The Wilcoxon rank-sum test, also called the Mann-Whitney U test, is a nonparametric test that determines whether two independent populations have different medians. It compares the distributions of two independent samples without assuming normal distribution. This test is particularly useful when data are ordinal or when assumptions for parametric tests like the two-sample t-test are violated.
Q2: How are data ranked in the Wilcoxon rank-sum test?
Data from both samples are combined into a single ranked list, with each value assigned a rank from smallest to largest. Tied values receive the average of the ranks for those positions. The ranks are then separated back into their respective groups, and the sum of ranks is calculated for each group independently to determine the test statistic.
Q3: What does it mean if high or low ranks cluster in one sample?
When high or low ranks predominantly fall into one sample rather than being distributed evenly, this suggests the two samples may have different medians. This clustering pattern indicates a systematic difference in the underlying distributions of the two populations, which the test statistic evaluates for statistical significance.
Q4: When should you use a z-score approximation versus critical value tables?
For small sample sizes, typically when n is less than 20, critical values for U are obtained from statistical tables. For larger samples, a z-score approximation is applied, assuming a normal distribution. This approximation becomes more reliable and efficient as sample size increases, making it the preferred approach for larger datasets.
Q5: What are the key requirements for the Wilcoxon rank-sum test?
The test requires two independent samples that are randomly drawn from their populations. Data must be ordinal or capable of being converted to an ordinal scale so values can be ranked. There is no assumption that samples are normally distributed, making this test robust for non-normal data and a suitable alternative to parametric tests.
Q6: Why is the Wilcoxon rank-sum test two-tailed?
The Wilcoxon rank-sum test is two-tailed because the alternative hypothesis states that the distributions of the two populations are different, without specifying direction. The test statistic is compared against both positive and negative critical values, typically at the 5% significance level, to determine if a significant difference exists in either direction.
Q7: What limitations should you consider when using this test?
While the Wilcoxon rank-sum test is robust to outliers, it is prone to higher type-I error when data are biased, heteroscedastic (having different variance), or when sample distributions are extremely far from normal. Despite these limitations, the test remains reliable for most ordinal and non-normally distributed data in practical applications.