# Mann Whitney U Test: Determining "First" Population

In summary, the Mann Whitney U Test is a non-parametric statistical test used to determine differences between two independent groups when the assumptions for parametric tests are not met. It works by ranking the data and comparing the sums of ranks for each group. It should be used when data is not normally distributed or when assumptions for parametric tests are not met. It differs from the t-test in that it makes no assumptions about the underlying distribution of the data and can be used for ordinal or non-normally distributed data. The results of the test can be interpreted by looking at the U statistic and p-value, with a p-value less than 0.05 indicating a significant difference between the groups.

The question relate to the Mann Whitney U test with two populations.

For the test statistic formula, there is a R1 term, which is the sum of the ranks of the "first" population. My question is, given any two populations, how do i decide which one is the "first" population?

The Mann Whitney U test essentially tests the absolute value of the difference in means of two populations. It doesn't matter which is the "first" and which is the "second" population.

## 1. What is the Mann Whitney U Test?

The Mann Whitney U Test is a non-parametric statistical test used to determine if there is a significant difference between two independent groups. It is also known as the Wilcoxon Rank-Sum test and can be used when the assumptions for parametric tests, such as the t-test, are not met.

## 2. How does the Mann Whitney U Test work?

The Mann Whitney U Test works by ranking the data from both groups together, then calculating the sum of ranks for each group. It then uses the U statistic to compare these sums and determine if there is a significant difference between the groups. The test assumes that the two groups have similar distributions and that the data is independent.

## 3. When should the Mann Whitney U Test be used?

The Mann Whitney U Test should be used when the data does not meet the assumptions for parametric tests, such as normality or equal variances. Additionally, it is appropriate when the data is ordinal or non-normally distributed. It is commonly used in social sciences, biology, and psychology research.

## 4. What is the difference between the Mann Whitney U Test and the t-test?

The Mann Whitney U Test is a non-parametric test, meaning it makes no assumptions about the underlying distribution of the data. The t-test, on the other hand, is a parametric test that assumes the data is normally distributed. Additionally, the Mann Whitney U Test can be used for two independent groups, while the t-test is used for comparing means of two groups.

## 5. How do you interpret the results of the Mann Whitney U Test?

The results of the Mann Whitney U Test will provide a U statistic and a p-value. The U statistic indicates the sum of ranks for one group and can be used to compare the two groups. The p-value represents the probability of obtaining these results by chance. If the p-value is less than the chosen significance level (usually 0.05), it can be concluded that there is a significant difference between the two groups.