The problem: Conventional graphs often include error bars around the group means. Regardless of what these bars depict, they are uninformative as to whether a difference between the groups is statistically significant.
The solution: This article suggests plotting the null bar or null zone: that is, the range or area in which the means of the two groups fall if the null hypothesis of no difference cannot be rejected. The bar and zone are simply derived from the confidence interval around the difference, obtained from the t-test.