We consider statistical methods for nonresponse problem in social and economic sample surveys. To create a complete data set, which does not include item nonresponse data, imputation methods are generally used. In this paper, we introduce some imputation methods and compare them with one another. Also, we consider some problems, which occur when an imputed data set is treated as a response data set. Due to the imputed values, the true variance of the estimator after imputation is increased by the imputation variance. However, since usual naive variance estimator constructed from the imputed data set does not estimate the imputation variance, the true variance of the estimator after imputation tends to be underestimated. Theoretical reason is investigated and serious results are explained through a simulation study. Finally, some adjusted variance estimation methods to compensate for underestimation are presented and discussed.