When normally distributed additive noise is present on the test setup, it leads to a bias on the values of estimated gain and offset error of analog-to-digital converters when estimated using the Histogram Test Method. It is shown that the offset estimation is unbiased while the gain estimation can have up to 5% bias for values of signal-tonoise ratio as low as 10 dB. It is also shown that this bias is not dependent on the number of samples acquired. An approximate analytical expression, in closed form, is proposed for rapid estimation of gain error. It considers the signal-to-noise ratio as well as the amount of overdrive used. The analytical derivations made are validated using simulated data using a Monte Carlo procedure. The same procedure is used with experimental data obtained with a real data acquisition system to validate the results obtained.