Mann-Whitney U Test Calculator
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The Mann-Whitney U test is a non-parametric test used to determine whether there is a significant difference between the distributions of two independent samples. It is often used as an alternative to the t-test when the data do not meet the assumptions of normality.
Background
The test, developed by Henry Mann and Donald Whitney, is useful in situations where the sample sizes are small, or the data are ordinal. It compares the ranks of data rather than their actual values, making it robust against outliers and non-normal distributions.
Calculation Process
- Combine the data from both groups and rank them.
- Calculate the sum of ranks for each group.
- Use the rank sums to compute the U value.
- Determine the p-value using the normal approximation method for larger sample sizes.
Example Calculation
Consider two small groups with the following data:
- Group 1: 12, 18, 24
- Group 2: 8, 16, 28
Calculate the U value and compare it against critical values to determine if the difference between the groups is statistically significant.
Importance
The Mann-Whitney U test is widely used in various fields, such as medicine, psychology, and business, to compare two independent groups when the data do not meet the assumptions required for parametric tests. It helps researchers make informed decisions based on non-normally distributed data.