Estimation of Response Bias from Both Samples in Double Sampling with Unequal Probabilities

In this study, we consider estimation of response bias based on information from both the initial and the subsample in double sampling with inclusion probabilities in contrast to estimation of the response bias based on information from the subsample only. The condition, under which either of the two estimators can be preferred to the other is determined. The relative significance of the contribution of the correlated factors to the total response variance compared to the contribution by the other factors of response variation noted earlier by Hansen under a different sample design is confirmed. The effect of the replication of the survey for K>1 times.