Before revision:  These tests require us to overcome an identification problem  when the measures of central tendency are equal or in a local neighborhood of each other, as is the case for (exactly or nearly) symmetric and unimodal distributions.
After revision:  These tests require us to overcome an identification problem that arises when the measures of central tendency are equal or in a local neighborhood of each other, as is the case for (exactly or nearly) symmetric and unimodal distributions.