Partition of the sample space of the two dimensional outcome space defined by p
. The shaded two areas are the true non-null areas for the two individual tests respectively. The rejected regions by both tests are highlighted in bold rectangles at the four corners of the outcome space. Only the lower-left corner is the non-null region from both tests and therefore should be rejected by IUT. The other three corners are type 1 error region for IUT because at least one individual test is making type 1 error.