Which nonparametric test is used to assess an ordered pattern of medians across independent groups?

Which nonparametric test is used to assess an ordered pattern of medians across independent groups?

• A. Jonckheere-Terpstra test
• B. Mann-Whitney test
• C. Kolmogorov-Smirnov test
• D. Kruskal-Wallis test

Answer: (A)

When you want to know if medians follow an increasing (or decreasing) pattern across several independent groups, you need a test that specifically targets a monotone trend. The Jonckheere-Terpstra test does exactly that. It compares all pairs of observations from different groups in the order of the groups and looks for a consistent pattern where values tend to be higher in higher-ordered groups. If there’s a true trend, the statistic will be large and the p-value small. This is more appropriate than a two-group test like Mann-Whitney, which isn’t designed to handle multiple ordered groups. It’s also different from Kolmogorov-Smirnov, which focuses on overall distribution differences rather than a directional trend in medians. And it differs from Kruskal-Wallis, which tests for any distribution differences across groups but doesn’t test a specific ordered pattern in medians. So, for an ordered pattern of medians across independent groups, the Jonckheere-Terpstra test is the best choice.

When you want to know if medians follow an increasing (or decreasing) pattern across several independent groups, you need a test that specifically targets a monotone trend. The Jonckheere-Terpstra test does exactly that. It compares all pairs of observations from different groups in the order of the groups and looks for a consistent pattern where values tend to be higher in higher-ordered groups. If there’s a true trend, the statistic will be large and the p-value small.

This is more appropriate than a two-group test like Mann-Whitney, which isn’t designed to handle multiple ordered groups. It’s also different from Kolmogorov-Smirnov, which focuses on overall distribution differences rather than a directional trend in medians. And it differs from Kruskal-Wallis, which tests for any distribution differences across groups but doesn’t test a specific ordered pattern in medians.

So, for an ordered pattern of medians across independent groups, the Jonckheere-Terpstra test is the best choice.