How to Analyze Wilcoxon Matched-Pairs Signed-Ranks Test - Non Parametric

The Wilcoxon Matched-Pairs Signed-Ranks Test is a non-parametric analysis designed to determine whether two dependent samples come from populations with identical or different distributions. This test serves as an alternative to the Paired T-Test, especially when the assumption of normality cannot be met. Using SmartstatXL, this test provides a robust statistical solution for data analysis under these conditions.

Case Example

Sourced from: Handbook of Parametric and Nonparametric Statistical Procedures, Fifth Edition By David J. Sheskin

Example 18.1

A psychologist conducts research to determine whether people display more emotionality when exposed to sexually explicit words compared to when exposed to neutral words. Each of the ten subjects is shown a list of 16 randomly arranged words, projected one at a time onto a screen for five seconds. Eight of the words on the list are sexually explicit, and the other eight are neutral. As each word is projected, the subject is instructed to softly speak the word to themselves. While doing this, sensors attached to the subject's palm record galvanic skin responses (GSR), which the psychologist uses as a measure of emotionality. The psychologist calculates two scores for each subject, one for each experimental condition: Condition 1: GSR/Explicit—The average GSR score for the eight sexually explicit words; Condition 2: GSR/Neutral—The average GSR score for the eight neutral words. The GSR/Explicit and GSR/Neutral scores for the ten subjects are as follows. (The higher the score, the higher the level of emotionality.) Subject 1 (9, 8); Subject 2 (2, 2); Subject 3 (1, 3); Subject 4 (4, 2); Subject 5 (6, 3); Subject 6 (4, 0); Subject 7 (7, 4); Subject 8 (8, 5); Subject 9 (5, 4); Subject 10 (1, 0). Do the subjects display emotional differences with respect to the two categories of words?

Analysis Steps

Here are the steps for the Wilcoxon Matched-Pairs Signed-Ranks Test and the PostHoc Test using SmartstatXL, Excel Add-in:

1. Activate the worksheet (Sheet) that will be analyzed.
2. Place the cursor on the dataset (to create the dataset, see the Data Preparation method). The dataset can be arranged in two layouts:
3. Grouped by level/grade (comparison between levels)
4. Grouped by variable (comparison between variables)
   
5. If the active cell is not on the dataset, SmartstatXL will automatically attempt to identify the dataset.
6. Activate the SmartstatXL Tab
7. Click on the Non-Parametric menu. SmartstatXL will display a dialog box to confirm whether the dataset is correct or not (usually, the cell address of the dataset is automatically selected correctly).
   
8. If it's correct, Click on the Next Button
9. Next, the following Non-Parametric Test Dialog Box will appear:
   
10. If the layout of the data used is based on variable comparison, the following dialog box will appear:
    
11. Finally, press the "OK" button.

Analysis Results

The following is the Output Analysis of the Wilcoxon Matched-Pairs Signed-Ranks Test:

Statistical Summary

From the analysis using the Wilcoxon Signed Ranks Test, we aim to find out whether there is a significant difference in the emotional levels of subjects when exposed to sexually explicit words compared to neutral words.

Let's interpret these analysis results:

1. Proposed Hypotheses:
   1. H0 (Null Hypothesis): There is no median difference between the two conditions.
   2. H1 (Alternative Hypothesis): There is a median difference between the two conditions.
2. Statistical Results:
   1. W+ (positive ranks) is 40.500, and W- (negative ranks) is 4.500.
   2. The T-value is 4.500.
   3. The Z-value (without adjustments for ties) is 2.073, while the Z-value (with adjustments for ties) is 2.149.
   4. The p-value (probability) is 0.032.
   5. The critical value for this test is 1.960.
3. Interpretation:
   1. Since the Z-value (2.149) is greater than the critical value (1.960), and the p-value (0.032) is less than 0.05, we reject the null hypothesis (H0). This means there is sufficient evidence to state that there is a significant difference in the emotional levels of subjects when exposed to sexually explicit words compared to neutral words.

Conclusion:

Based on the Wilcoxon Signed Ranks Test analysis, there is a significant difference in the emotional levels of subjects when exposed to sexually explicit words compared to neutral words at the 0.05 significance level.

Average Comparison

Table of average values, Mean Rank, Sum Rank, and PostHoc Test

From the table, we can see the comparison between the two conditions based on average values:

1. Data Description:
   • Condition 1: With an average of 4.70.
   • Condition 2: With an average of 3.10.
2. Subset Interpretation:
   • Condition 1 has a subset label "b," while Condition 2 has a subset label "a." This indicates that there is a significant difference between the two conditions based on their average values.

Conclusion:

Based on the average comparison, subjects show a higher level of emotionality (as measured through GSR) when exposed to sexually explicit words (Condition 1 with an average of 4.70) compared to neutral words (Condition 2 with an average of 3.10).

When we compare these results with the previous Wilcoxon Signed Ranks Test analysis, both are consistent in indicating that there is a significant difference in the emotional response of subjects between the two conditions.