The Histogram Test method is a popular technique in analog-to-digital converter (ADC) testing. The presence of additive noise in the test setup or in the ADC itself can potentially affect the accuracy of the test results. In this study, we demonstrate that additive noise causes a bias in the terminal based estimation of the gain but not in the estimation of the offset. The estimation error is determined analytically as a function of the sinusoidal stimulus signal amplitude and the noise standard deviation. We derive an exact but computationally difficult expression as well as a simpler closed form approximation that provides an upper bound of the bias of the terminal based gain. The estimators are validated numerically using a Monte Carlo procedure with simulated and experimental data.