In this paper, we aim at analyzing how pre-service and in-service mathematics teachers make a judgment about comparing two groups which requires several important concepts. The research questions include: (1) Which concepts are applied to make a judgment about comparing two groups? (2) How are the counter-examples made? In our study, teachers were asked to make a judgment about comparing two groups individually and then explained their judgments in class. The result shows that most teachers prefer using concept of mean to represent the outline of the whole distribution. And the strategies of successfully making counter-examples include thinking with (1) proportion-based, (2) properties-oriented, (3) statistics-modified, and (4) unfixing a sub-group. Implications and further research will be suggested in relation to roles of making counter-examples for learning statistical thinking.