When conducting statistical tests, a p-value greater than 0.05 indicates that the results could have occurred by chance and are not statistically significant. While a p-value below 0.05 provides strong evidence against the null hypothesis, a p-value above 0.05 does not necessarily prove the null hypothesis is true. Researchers should avoid making definitive conclusions when p > 0.05 and consider other factors like effect size, sample size, and clinical significance rather than relying solely on statistical significance.