چكيده به لاتين
Today, the problem of determining the sample size is an important and significant subject in statistics science. In general, methods for determining the sample size are divided into two categories: 1) Classical (Frequentist) method, 2) Bayesian method. Such that Bayesian method is also divided into Inferential Bayesian and Fully Bayesian (decision theory) approaches. To date, the problem of determining the sample size has been done with the two aforementioned methods. In this research, along with introducing Shannon's Information and Lindley's Information, we present an optimal approach to determine the optimal sample size in binary trials, and the variables we are examining here have a binomial distribution. Our aim is to examine the sample size for the difference between the two ratios of the relating binomial distributions (p_1,p_2). The optimal sample size is obtained using the Shannon method by maximizing the ENGS (expected net gain of sampling), and in the Lindley method, we calculate the optimal sample size by maximizing the net utility function. By using the two aforementioned methods, the computational complexities decreases significantly in order to determine the sample size in compare to prior methods and these methods are more suitable.
Keywords:
Lindley Information, Shannon Information, Binomial Distribution, Utility Function, Decision Theory, Inferential Bayesian Method, Fully Bayesian Method, Expected Net Gain of Sampling.
