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For measurements of the Mueller matrix and other polarization effect matrices in a birefringent optical system, such as an optical fiber, we demonstrate by theoretical analysis and simulation that two input polarization states that are mutually orthogonal in Stokes space statistically have the maximum probability to achieve the optimum measurement accuracy. But in a single test, evident deviation from perpendicularity can be observed for achieving the minimum measurement error. For measurements of both polarization effect matrices and polarization effect vectors, we find that all measurement errors have a bathtub-shaped relationship with the angle between two input polarization states in the range from . This means a limited offset from perpendicularity will only slightly and statistically increase the measurement error in a single test.