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Manufacturer application note. The oversampling and Averaging section discusses uncorrelated noise and dither; Table 1 gives fourfold sample-count increases per extra output bit. No individual author is established by the consulted HTML page.

oversampling takes samples faster than the minimum rate required by the desired signal bandwidth. With suitable uncorrelated conversion noise, digital filtering removes noise outside that bandwidth before decimation. Independent-error averaging improves standard deviation as $N^{-1/2}$; fourfold averaging ideally gains one bit of amplitude resolution. Repetition of an unchanged biased code does not produce the same benefit.

A small constant input can repeatedly produce the same analogue-to-digital converter code, so averaging those codes cannot reveal its position within a conversion interval. dither makes adjacent codes toggle; their relative frequencies then encode changes smaller than one conversion step. With adequate oversampling, low-pass filtering and averaging reduce the added, sufficiently uncorrelated noise while retaining the slow signal.

For independent sample errors, the averaged standard deviation scales as $N^{-1/2}$; ideally four times as many samples gain about one effective bit. For example a constant input $0.2\Delta$ rounded to levels separated by $\Delta$ would always return zero. Adding uniform dither on $[-\Delta /2,\Delta /2]$ gives output $\Delta$ with probability $0.2$ and zero otherwise: the expected average is $0.2\Delta$, with error $0.4\Delta /\sqrt{N}$. The benefit concerns the filtered estimate, not a more accurate individual conversion. Excessive dither wastes range, and averaging does not correct calibration bias, correlated drift or arbitrary converter nonlinearity.^[ref]