ranksum

Ranksum is a nonparametric statistical test used to determine whether two independent samples come from populations with equal distributions. It is commonly referred to as the Wilcoxon rank-sum test or the Mann-Whitney U test. The test compares the central tendency of two groups by ranking all observations together and evaluating whether the ranks of one group tend to be higher than those of the other.

Assumptions and scope: ranksum requires independent samples and data that are at least ordinal. It does not assume normality, making it suitable for non-normally distributed data or small samples. The test assesses differences in location (central tendency), but differences in shape or spread between distributions can influence the result. When ties occur, adjustments to the rank sums are applied.

Calculation and interpretation: all observations from both groups are pooled and ranked from smallest to largest. The sum of ranks for one group is used to compute the U statistic, which can be converted to a p-value through either an exact calculation (for small samples) or a normal approximation (for larger samples). The p-value indicates whether there is a statistically significant difference between the two groups. The test can be two-sided or one-sided, depending on the alternative hypothesis. Effect size can be reported with measures such as the rank-biserial correlation or related statistics derived from U.

Relation to other tests and usage: ranksum is a nonparametric alternative to the two-sample t-test when normality cannot be assumed. It is widely implemented in statistical software and is commonly used in fields like biomedicine and social sciences to compare two independent samples.