What do large p-values indicate about a disparity?

Large p-values suggest that the observed disparity between groups or treatments is likely due to random chance rather than a statistically significant effect. In hypothesis testing, a p-value represents the probability of obtaining results at least as extreme as the observed outcomes, assuming that the null hypothesis (which posits no effect or difference) is true. When the p-value is large, typically above a threshold (commonly 0.05), it indicates a lack of strong evidence against the null hypothesis, suggesting that the differences observed could easily happen under random variations without implying a real underlying effect. This understanding is critical in statistical analysis, as it helps analysts gauge the reliability and validity of their results in relation to chance occurrences.