Wilcoxon Signed-Rank Test Calculator
Perform a non-parametric hypothesis test to compare two related samples.
Input Data
Enter comma-separated numeric values.
Enter comma-separated numeric values, paired with Sample 1.
Enter a value between 0 and 1.
Test Results
| Test Statistic (W) | |
| P-value | |
| Conclusion | ( at α = ) |
Understanding the Test
The Wilcoxon Signed-Rank Test is used to determine if there is a statistically significant difference between two related groups. Here’s a brief overview of how it works:
- Calculate Differences: For each pair of data points, the difference is calculated.
- Rank Absolute Differences: The absolute values of these differences are then ranked from smallest to largest. Differences of zero are discarded and the sample size is reduced accordingly.
- Assign Signs: Each rank is given the sign of the original difference.
- Calculate Test Statistic (W): The Wilcoxon test statistic, denoted as W, is the smaller of the sum of the positive ranks and the absolute sum of the negative ranks.
- Determine P-value: The p-value is calculated based on the test statistic and the sample size. It indicates the probability of observing a test statistic as extreme as, or more extreme than, the one calculated if there is no actual difference between the groups.
A low p-value (typically less than the significance level α) suggests that you should reject the null hypothesis, indicating a significant difference between the two related samples.
About the Wilcoxon Signed-Rank Test
The Wilcoxon Signed-Rank Test is a non-parametric statistical test used to compare two related samples, matched samples, or repeated measurements on a single sample. It is used as an alternative to the paired t-test when the population cannot be assumed to be normally distributed. This test assesses whether the population mean ranks of differences between paired observations are centered around zero.
Key Concepts:
- Non-parametric Test: Does not rely on assumptions about the shape or parameters of the probability distribution of the population.
- Paired Data: Used when observations are paired or related (e.g., before and after measurements on the same subjects).
- Null Hypothesis: States there is no difference between the two related groups.
- Alternative Hypothesis: States there is a difference between the two related groups (can be one-tailed or two-tailed).
- Significance Level (α): The probability of rejecting the null hypothesis when it is true (Type I error). Common values are 0.05 or 0.01.
- P-value: The probability of obtaining test results at least as extreme as the results actually observed, assuming the null hypothesis is correct.
This calculator helps you quickly perform a Wilcoxon Signed-Rank Test and interpret the results, making it easier to analyze paired data in various fields such as psychology, medicine, and engineering.
Learn more about the Wilcoxon Signed-Rank Test on resources like Wikipedia and statistical textbooks.