Cross-spectrum analysis is a commonly used technique for the detection of phase and amplitude noise of a signal in the presence of interfering uncorrelated noise. Recently, we demonstrated that the phase-inversion (anti-correlation) effect due to amplitude noise leakage can cause complete or partial collapse of the cross-spectral function. In this paper, we discuss the newly discovered effect of anti-correlated thermal noise that originates from the common-mode power divider (splitter), an essential component in a cross-spectrum noise measurement system. We studied this effect for different power splitters and discuss its influence on the measurement of thermal-noise limited oscillators. We provide theory, simulation and experimental results. In addition, we expand this study to reveal how the presence of ferrite-isolators and amplifiers at the output ports of the power splitters can affect the oscillator noise measurements. Finally, we discuss a possible solution to overcome this problem.