Statistika Non Parametrik: Tes Wilcoxon (Test Median).

Introduction

This tutorial will guide you through the Wilcoxon test, a non-parametric statistical method used to analyze data from one-shot case studies. The Wilcoxon test is particularly useful when the data does not meet the assumptions of parametric tests and is aimed at comparing medians from two related groups. This guide will outline the steps necessary to perform the Wilcoxon test effectively.

Step 1: Prepare Your Data

Before conducting the Wilcoxon test, ensure your data is properly organized.

• Data Collection: Gather your single set of data points. This could be measurements, responses, or any relevant observations from your study.
• Organize Data: Arrange the data in a structured format, such as a spreadsheet, to facilitate analysis.

Step 2: Determine the Hypotheses

Formulate your null and alternative hypotheses.

• Null Hypothesis (H0): The median of the population is equal to a specified value or the medians of two paired groups are equal.
• Alternative Hypothesis (H1): The median of the population is not equal to the specified value or the medians of two paired groups are different.

Step 3: Choose the Wilcoxon Test Type

Decide which version of the Wilcoxon test to use based on your data structure.

• Wilcoxon Signed-Rank Test: Use this when comparing two related samples or repeated measurements on a single sample.
• Wilcoxon Rank-Sum Test: Use this when comparing two independent samples.

Step 4: Calculate the Test Statistic

Perform the calculations needed for the Wilcoxon test.

1. Rank the Data:

   • Assign ranks to the differences between paired observations.
   • Ignore zeros and assign average ranks for ties.

2. Sum the Ranks:

   • Calculate the sum of positive ranks and the sum of negative ranks.

3. Determine the Test Statistic (W):

   • Use the smaller of the two sums (positive or negative) as your test statistic.

Step 5: Determine the Critical Value

Identify the critical value for your test.

• Use Wilcoxon distribution tables or statistical software to find the critical value based on your sample size and significance level (commonly 0.05).

Step 6: Make a Decision

Draw conclusions based on your calculated test statistic and critical value.

• If W is less than or equal to the critical value: Reject the null hypothesis (indicating a significant difference).
• If W is greater than the critical value: Do not reject the null hypothesis (indicating no significant difference).

Conclusion

The Wilcoxon test is a powerful tool for analyzing data from one-shot case studies, especially when assumptions for parametric tests are not met. By following the steps outlined above, you can effectively conduct the Wilcoxon test and interpret the results to make informed decisions based on your data. As a next step, consider exploring statistical software packages that can automate these calculations for you.