隨機作答模式於不相關敏感性問題之應用研究

Applied Study of the Unrelated Sensitive Questions by Using Randomized Response Model

王智立(Chih-Li Wang) ； 許雅恬(Ya-Tien Hsu)

《Journal of Data Analysis》 5卷3期 (2010/06) Pp. 87-104

https://doi.org/10.6338/JDA.201006_5(3).0006

摘要

當在進行研究調查，研究的議題牽涉敏感特性時，受訪者在基於保護個人隱私的心態下，通常會採取拒答或不誠實作答。Warner（1965）隨機作答模式（Randomized Response），希望能藉由隨機作答模式降低受訪者心理的不安全感，進而得到較精確的母體比例估計。Chang and Liang（1996）提出的兩個不相關敏感性問題隨機作答程序，能同時對兩個敏感性母體進行推估。而Christofides（2003）則是提出另一隨機作答程序，以「數字」回答的方式代替Warner（1965）模式直接回答「是」或「否」之作答方式。此外，Kim & Warde（2004）更提出分層隨機作答程序，希望能藉由分層抽樣的方式，提高估計的效率。本文考慮將Chang and Liang（1996）提出的兩個不相關敏感性問題隨機作答程序與Christofides（2003）的隨機作答程序做一結合，並加入分層的概念，進而提出新的隨機作答模式，本文所提之新作答模式不僅可找出敏感性母體比例的不偏估計量及其變異數外，在進行效率比較之後，可以發現本文所提之新模式比Christofides（2003）模式有較好的估計效率。

關鍵字

敏感性問題 ； 隨機作答模式 ； 母體比例 ； 分層隨機抽樣

並列摘要

In a sample survey, if the topic of study is involved in sensitive characteristics, respondents usually refuse to reply or answer untruthfully. Warner (1965) proposed a procedure termed ”Randomized Response” to reduce the sense of insecurity of respondents and obtain an accurate population proportion estimator. Another procedure is for two unrelated sensitive questions proposed by Chang and Liang (1996). This procedure can estimate two population proportions at same time. Christofides (2003) proposed alternative randomized response. Respondents do not answer ”yes” or ”no” directly, reply ”distance” instead in the procedure. Besides, Kim & Warde (2004) proposed stratified randomized response to enhance the efficiency of estimator. This paper combines Chang and Liang (1996) with Christofides (2003) and proposes a new randomized response procedure considered strata. We also show the estimator of sensitive population proportion, the variance of estimator and simulate data. In addition, we also prove the procedure which we proposed has more efficient estimator than Christofides (2003).

並列關鍵字

Sensitive question ； Randomized Response ； Population proportion ； Stratified Random Sampling

參考文獻

Chang, H. J.,Liang, D. H.(1996).A randomized response procedure for two-unrelated sensitive questions.Journal of Information & Optimization Sciences.17,185-198.

Christofides, T. C.(2003).A generalized randomized response technique.Metrika.57,195-200.

Kim, J. M.,Warde, W. D.(2004).A stratified Warner's randomized response model.Journal of Statistical Planning and Inference.120,155-165.

Warner, S. L.(1965).Randomized response: A survey technique for eliminating evasive answer bias.Journal of American Statistical Association.60,63-69.