Comparative Analysis of Pain Relief Scores Across Three Dose Levels

Research Question:

Does pain relief vary significantly across different dose levels (low, medium, high)?

Statistical Analysis:

The statistical analysis was performed to compare pain relief scores across three different dose levels (low, medium, and high). Given the ordinal nature of the pain relief scores and the absence of assumptions about the normality of the data, the Kruskal-Wallis test was used to assess whether there were significant differences in pain relief scores across the three dose levels.

Post-hoc Dunn’s test with Bonferroni correction was performed to identify which specific dose groups differed from one another.

A significance level of 0.05 was used for all statistical tests. P-values less than 0.05 were considered statistically significant.

All statistical analyses were conducted using R (version 4.1.0). The Kruskal-Wallis test was implemented using the function kruskal.test(), and post-hoc pairwise comparisons were carried out using the dunn.test() function from the dunn.test package.

Results:

The Kruskal-Wallis test was conducted to compare pain relief scores across three dose levels: low, medium, and high. The results of the test indicated a significant difference in pain relief scores across the three dose groups, with a Kruskal-Wallis chi-squared statistic of 112.34 (df = 2), and a p-value < 0.01.

Post-Hoc Test Results:

The pairwise comparisons performed with Dunn’s test revealed significant differences in pain relief scores between all pairs of dose levels:

• Low vs. Medium: The Low dose group exhibited significantly lower pain relief scores compared to the Medium dose group (Z = -5.79, p < 0.0001).

• Low vs. High: The Low dose group also showed significantly lower pain relief scores compared to the High dose group (Z = -10.58, p < 0.0001).

• Medium vs. High: Finally, the Medium dose group had significantly lower pain relief scores compared to the High dose group (Z = -4.79, p < 0.0001).

The significant differences observed in all pairwise comparisons suggest that increasing the dose improves pain relief. Therefore, the High dose appears to be the most effective in reducing pain, followed by the Medium dose, while the Low dose provides the least pain relief.

Figure 2. The cumulative distribution of pain relief scores shows that individuals receiving higher doses (medium and high) report greater levels of pain relief, as indicated by the more pronounced shift in the cumulative probability curve towards higher pain relief scores.

Conclusion:

The Kruskal-Wallis test revealed significant differences in pain relief scores across the three dose levels (low, medium, and high), indicating that dose level is a significant factor influencing pain relief. Post-hoc pairwise comparisons further confirmed that the higher doses (medium and high) resulted in significantly greater pain relief compared to the low dose. These findings suggest a dose-dependent response, where increased dosage leads to more effective pain management.