WILCOXON SIGNED RANK TEST

WILCOXON SIGNED RANK TEST

• Definition: Non-parametric alternative to the paired t-test for paired data.

• Usage: Appropriate for continuous variables under paired observations.

HYPOTHESES

• Null Hypothesis (H0): The difference between paired observations in the population is zero.

• Alternative Hypothesis (Ha): The difference is not equal to zero.

RESEARCH EXAMPLE

• Context: Evaluating a truancy program for 30 teenagers.

• Data Points: Number of school days missed before and after the program (prior mean: 42.47 days, post mean: 23.63 days).

• Research Question: Does the program impact days missed?

DATA ANALYSIS

• Difference Calculation: Days Absent (Difference) = Time 2 - Time 1; Mean difference = 18.33 days.

• Skewness: -0.56; indicates non-normal distribution, unsuitable for paired t-test.

• Test Selection: Use Wilcoxon Signed Rank Test.

WILCOXON SIGNED RANK TEST CALCULATIONS

• W-value: 88

• Z-value: -2.9721

• P-value: 0.00298; significant at p < 0.05.

• Critical Value for W (N=30): 137.

EFFECT SIZE

• Formula: r = z / √n

• Interpretation:

  • r < 0.3: Small effect

  • 0.3 < r < 0.5: Medium effect

  • r > 0.5: Large effect

RESULTS SUMMARY

• Conclusion: Significant reduction in absenteeism post-program (z = -2.97, p = 0.003); average decrease of 18.83 days; effect size r = 0.54.

• Decision: Reject the null hypothesis.