Ban bar graphs
Bar graphs must be banned in neuroscience & psychology research
Bar graphs are inadequate to portray results because they hide inter-participant differences. Informative illustrations of the results should let readers assess the distributions of effects. This is important to check for the presence of outliers or skewness, which could lead to weak statistical power. For between-participant designs, only a sub-group of participants might differ from another group. For paired designs, distributions of pairwise differences should be illustrated, so that readers can appreciate effect sizes and their distributions across participants.
If a paper reports bar graphs and non-significant statistical analyses of the mean, not much can be concluded: there might be differences in other aspects than the mean; mean differences might exist, but the assumptions of the test could have been violated. Without informative illustrations of the results, it is impossible to tell.
These references provide examples of more informative figures:
Wilcox, R.R. (2006) Graphical methods for assessing effect size: Some alternatives to Cohen's d. Journal of Experimental Education, 74, 353-367.
Allen, E.A., Erhardt, E.B. & Calhoun, V.D. (2012) Data visualization in the neurosciences: overcoming the curse of dimensionality. Neuron, 74, 603-608.
For an overview of robust methods, to go beyond ANOVAs on means:
Wilcox, R.R. (2012) Introduction to robust estimation and hypothesis testing. Academic Press.
Wilcox, R.R. & Keselman, H.J. (2003) Modern Robust Data Analysis Methods: Measures of Central Tendency. Psychological Methods, 8, 254-274.