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.