Sample size algorithm for randomized response model with dichotomized response

ABSTRACT

The sample size calculation plays an important role in many areas, particularly for applications in the biomedical and social sciences. Large-sample size is wasting of time and resources. Small-sample provides unreliable answer. In the literature, the aim of sample size calculation is to either detecting the difference among groups statistically or assessing the precision of estimate. Other than these two main goals of sample size determination, the objective of this article is to provide the sample size formulae for randomized/nonrandomized response models such that the estimates of sensitive probabilities falling inside the normal interval [0, 1] are guaranteed under a certain confidence. The sample size algorithm is introduced because of no closed form solution for sample size. A higher confidence probability, a greater sample size should be included into the study. Vice versa, larger sample sizes generally lead to increase the chance of the estimated probability falling in [0, 1]. An example is given to illustrate the use of the proposed algorithm.

KEYWORDS:

• Sample Size Algorithm
• Confidence Probability
• Precision
• Randomized Response Model

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05
• 62P99

Acknowledgments

This research was supported by a research grant from the Ministry of Science and Technology in Taiwan (Grant No. MOST 104-2118-M-033 -002).