By level of evidence do you mean thedisparity between the values of p or z found when calculating the test statistic vs the value determined in the rejection rule at different levels? So there would be more evidence against the null hypothesis say if the rule was to reject if p < 0.01 and the p-value was found to be 0.009 than if the rule to reject wasp < 0.05 and the p-value was 0.045?