This statistical test is a non-parametric alternative to the independent samples t-test. It is employed to determine whether two independent groups have been sampled from the same population. Specifically, it assesses if the distributions of the two groups are equal. An example of its application would be comparing the test scores of students taught using two different methods, where the data does not meet the assumptions of a parametric t-test.
Its importance lies in its applicability when data are not normally distributed or when the sample sizes are small. This test offers a robust method for comparing two groups without making stringent assumptions about the underlying data distribution. Historically, it has been a valuable tool in fields such as psychology, education, and medical research, providing a means to analyze data that would otherwise be unsuitable for parametric analysis.