Statistical heterogeneity has been dealt with in some meta-analyses by excluding "outliers" identified using graphical methods such as the Cochrane plot and the L'Abbe plot. However, this approach will not increase the credibility of a meta-analysis. This is because, firstly, eligible trials are excluded according to their results, not their designs. Secondly, excluding trials will further lower statistical power for heterogeneity testing. Thirdly, research evidence is under-used if the chance to explore the clinic and/or methodological heterogeneity are missed. In addition, this paper demonstrates that different methods may identify different trials as outliers and the conclusions of a meta-analysis may change by excluding different studies. Using published meta-analyses as examples, this paper compared the Cochrane plot and the L'Abbe plot for the investigation of heterogeneity between individual studies. As compared with other graphical methods, the L'Abbe plot is useful to identify not only the studies having different results from other studies, but also the study arms that are responsible for such differences. However, results of stochastic simulations demonstrate that random variation in the distance between a study point and the overall rate ratio line in a L'Abbe plot is associated with the number of subjects and the event rates. Purely because of random variation, studies with event rates of around 50% are more likely to be identified as outliers in a L'Abbe plot. A method is suggested to standardize the distance between study points and the overall RR line in a L'Abbe plot before making comparisons for investigating clinical and/or methodological heterogeneity. It is concluded that if they are used appropriately, the graphical plots are very useful in determining the focus of heterogeneity investigation in a meta-analysis.