What does 'w(T)' represent in the Wilcoxon test?

In the context of the Wilcoxon test, 'w(T)' refers to the test statistic calculated during the analysis. The Wilcoxon test is a non-parametric statistical method used to assess whether there is a significant difference between paired or matched samples. Unlike parametric tests that rely on assumptions about the population distribution, the Wilcoxon test analyzes the ranks of the data rather than the raw values.

The test statistic, in this case 'w(T)', is derived from the ranks of the differences between paired observations, focusing on the sums of the ranks for positive and negative differences. It helps determine if the observed differences are statistically significant. Therefore, recognizing 'w(T)' as the test statistic is essential for interpreting the results of the Wilcoxon test properly, as it provides the basis for comparing the computed value against critical values from the Wilcoxon distribution, which informs the conclusion about the null hypothesis.

Understanding the role of 'w(T)' as the test statistic is critical in utilizing the Wilcoxon test effectively for analyzing ordinal or non-normally distributed interval data.