Which one of the following tests can be used to study ordinal date from two independence samples from a population that is not noraml distributed?
**Core Concept**
The question is asking about a statistical test used to compare two independent groups when the data is not normally distributed, specifically when the data is ordinal. Ordinal data is ranked or ordered, but the intervals between the ranks may not be equal. In such cases, non-parametric tests are preferred.
**Why the Correct Answer is Right**
The correct answer is the Wilcoxon rank-sum test, also known as the Mann-Whitney U test. This test is a non-parametric alternative to the independent samples t-test, which assumes normal distribution of the data. The Wilcoxon rank-sum test works by ranking all the observations from both groups combined and then summing the ranks for each group. The test statistic is then calculated based on the sum of ranks for each group. This test is suitable for ordinal data and does not assume normality of the data. The Wilcoxon rank-sum test is a versatile test that can be used to compare two independent groups, and it is a good alternative to the independent samples t-test when the data is not normally distributed.
**Why Each Wrong Option is Incorrect**
**Option A:** The Kruskal-Wallis H test is a non-parametric test used to compare more than two independent groups. It is not suitable for comparing two groups, making it an incorrect choice.
**Option B:** The Chi-squared test is used to compare categorical data, which is not the case here. The data is ordinal, not categorical, so the Chi-squared test is not the correct choice.
**Option C:** The independent samples t-test assumes normal distribution of the data, which is not the case here. This test is not suitable for ordinal data, making it an incorrect choice.
**Clinical Pearl / High-Yield Fact**
When working with ordinal data, it's essential to choose a non-parametric test, such as the Wilcoxon rank-sum test, to avoid assumptions of normality. Remember that non-parametric tests are often more robust and less sensitive to outliers than their parametric counterparts.
**Correct Answer:** B.