In the paper, the authors consider the performance of histogram-based analog to digital converter (ADC) testing under the assumption of input-equivalent wideband noise, which models either noise sources inside the device or unwanted disturbances corrupting the stimulus signal employed for carrying out the test. Theoretical relationships are presented which allow the design of the test parameters needed to meet a given test accuracy. Moreover, it is shown, that the histogram test is effective in providing information on the deterministic behavior of the tested device and that it can be made insensitive to the effects of input-equivalent noise. Finally, the obtained results are employed to determine the test performance in estimating the device effective number of bits, and simulations results are provided which validate the theoretical derivations.