Methods and apparatus for analyzing a test sample using complementary techniques, such as x-ray fluorescence (XRF) and optical emission spectroscopy (OES), are disclosed for registering two or more test instruments, in relation to the test sample, such that each of the instruments analyzes substantially the same region as is analyzed by the other instrument(s), and for communicating analytical results between or among the instruments, or between the instruments and another component, to enable one or more of the instruments, or the other component, to combine the results and, thereby, more completely and accurately determine the composition of the test sample. Such registration and communication enables, for example, separate XRF and OES instruments to collectively determine the composition of the test sample, including the absolute amounts of light and heavy elements in the test material.