Before revision:  For instance, our results imply that identifying a defective pair in a set of m points in the plane always requires \Omega(m^{ 4 / 7 }) rectangle-tests , and there exist configurations of m points for which O(m^{2/3}) rectangle-tests are sufficient, whereas to identify a single defective point in the plane, \Theta(m^{1/2}) tests are always necessary and sometimes sufficient.
After revision:  For instance, our results imply that identifying a defective pair in a set of m points in the plane always requires \Omega(m^{ 4 / 7 }) tests , and there exist configurations of m points for which O(m^{2/3}) rectangle-tests are sufficient, whereas to identify a single defective point in the plane, \Theta(m^{1/2}) tests are always necessary and sometimes sufficient.