The effects of non-sampling errors on measures of association in $2 \times 2$ contingency tables are evaluated by the application of models due to the U. S. Bureau of the Census. This is achieved by first expressing the appropriate sample estimates in the form of Taylor series approximations involving cell probabilities, and then applying the model in a term by term fashion. In this way, the relative effects of sampling errors and response errors on the variability of an estimated measure of association may be interpreted in terms of a sampling variance component and a response variance component. Finally, some indication is given as to how re-survey information can be used to estimate these quantities
The Effect of Non-Sampling Errors on Measures of Association in $2 \times 2$ Contingency Tables
Koch, GG. (1969). The Effect of Non-Sampling Errors on Measures of Association in $2 \times 2$ Contingency Tables. Journal of the American Statistical Association, 64(327), 852-863.