Wilcoxon Signed Rank Test Critical Values Table

The Wilcoxon Signed Rank Test Critical Values Table is a key tool for interpreting the results of the Wilcoxon Signed Rank Test, a non-parametric statistical test used to compare two related samples. Here’s a breakdown of the table and its explanation:

What it contains:

  • Sample size (n): This refers to the number of paired observations in your data.
  • Significance level (α): This represents the probability of rejecting the null hypothesis (H0) when it’s actually true, typically set at 0.05 (5%) or 0.01 (1%).
  • Critical values: These are specific thresholds for your Wilcoxon signed-rank statistic (W) based on n and α.

How to use it:

  1. Calculate your Wilcoxon signed-rank statistic (W): This involves ranking the absolute differences between paired observations, considering their signs, and summing the positive ranks.

  2. Look up the critical value based on your sample size (n) and chosen significance level (α): Each combination of n and α has a corresponding critical value in the table.

  3. Compare your calculated W to the critical value:

    • Two-tailed test: If your W is less than or equal to the critical value, reject the null hypothesis (H0) and conclude that there is a significant difference between the paired samples.
    • One-tailed test: Double your chosen α and use the table accordingly. Reject H0 if W is less than or equal to the adjusted critical value for the desired direction of change (e.g., only positive differences).