In studying the sensitive attributes of the human populations, obtaining the accurate results is difficult. In these cases, if the privacy of respondent hasn't been considered, the obtained results include refusal and response bias. To overcome to this problem, Warner (1965) proposed randomized response technique (RRT) based on the interviewer awareness of the respondent true status. In this thesis, we study the methods help us to increase the efficiency of the RRT. This thesis describes ways to maximize the efficiency of randomized response designs. When randomized response designs become more efficient their value as a tool to study sensitive topics will increase. This positive effect on the validity of the results was found both when the estimates of a randomized response condition were compared to known population estimates and when the results of a randomized response condition were compared to other data collection methods. In chapter one we briefly give a review on the most important methods in RRT. Two new randomized response models are introduced in chapter two. Chapter 3 deals with methods to estimate the proportion of the truthful answers, by which we can modify the attribute estimator. Constructing optimal RRT by considering the level of the privacy protection is discussed in chapter 4. In chapter 5, we propose new method that change structure of randomization and has higher efficiency relative to Warner method. RRT in matched paired data and estimating proportion of tax evasion are explained in chapter 6 7, respectively.