Which statistical test is best used for data that is abnormally distributed and has small sample sizes when comparing independent measures?

The Mann-Whitney U test is particularly suited for situations involving abnormally distributed data and small sample sizes when comparing independent measures. This non-parametric test does not assume that the data is drawn from normally distributed populations, making it a robust choice when traditional parametric tests, such as the t-test for independent means, may not be appropriate. The Mann-Whitney U test ranks the data and analyzes these ranks, which allows it to be effective even when the underlying distribution of the data does not meet the assumptions of normality required for parametric tests.

In contrast, the t-test for independent means relies on the assumption of normality and is generally less reliable with small sample sizes and non-normally distributed data. The t-test for dependent means is specifically for paired observations, so it does not apply in the case of independent measures. ANOVA is suitable for comparing means across multiple groups or conditions but also assumes normality and may not perform well with small or abnormally distributed datasets. Therefore, the Mann-Whitney U test stands out as the most fitting choice under these specific circumstances.