Which statistical test is particularly useful when dealing with small sample sizes and non-normal distributions?

The Wilcoxon signed-rank test is particularly useful for situations involving small sample sizes and non-normal distributions because it is a non-parametric test. Non-parametric tests do not assume that the data follow a specific distribution, which is especially important when the sample size is small and does not meet the normality assumption required for parametric tests like the t-test.

In cases where the sample size is small, data may not have enough power to validate the assumptions of normality. The Wilcoxon signed-rank test looks at the differences between paired observations and ranks these differences without normality requirements, making it more robust in these scenarios. This flexibility allows researchers to draw meaningful conclusions from their data even when they cannot meet the strict assumptions of parametric tests.

On the other hand, tests such as the t-test for independent means and the t-test for dependent means require the assumption of normally distributed data, which may not hold true in small samples or non-normal conditions. ANOVA also relies on similar assumptions about data distribution and is not the best fit for non-normal distributions, especially in small sample sizes. The Wilcoxon signed-rank test stands out in its applicability under these specific conditions, making it the preferred choice.