Abstract Sampling methods are often accompanied by sampling errors in collecting data. They are associated with design the chosen sample which can be handled in some way or another based on theoretically known styles in this field or by using the comprehensive census type. However, the people concerned with preparing and implementing statistical work face non random errors. Which are not less dangerous than errors connected with sampling methods. Whether what has been chosen partially of the population or by containing all items. These non random errors weakens the collected data efficiency. Because it is difficult to discover or to known: That is due to non-technical methods to handle them. In this paper focuses on the estimation of non-response of multi-auxiliary information of a finite population and infinite population. A comparison study is made between three methods of estimation using multi-auxiliary information; these methods are multi-mean imputation, multi-ratio method of imputation and multi-power transformation method of imputation, through randomized response technique. The relative efficiency was used to conclude the best methods by using empirically study (real data and simulation).