A New Approach to Determine the Pilot Sample Size in Two-Stage Sampling

ABSTRACT

In a two-stage sampling design, one gathers data in at most two steps. In the first step, known as Stage 1, one records a set of pilot observations of size m. Then, one proceeds to the second step, known as Stage 2, to gather all remaining observations if needed. Next, based on the observations combined from both Stages 1 and 2, one proceeds with the required inference procedure(s) that demand implementation of a two-stage sampling design in the first place. In this article, we introduce an easy-to-implement criterion through the Fisher information for the determination of a pilot sample size. Both versatility and practicality of this approach are substantiated with the help of a series of interesting and substantive examples. In the last example, we have given an ad-hoc and yet intuitive version of the approach since in this situation we are unable to proceed with the Fisher information in the first place.

Key Words:

• Behrens-Fisher analog
• Best population
• Confidence interval
• Fisher information
• Fixed-width
• Indifference zone
• Initial sample size
• Maximal risk
• Negative exponential distribution
• Normal distribution
• Point estimation

Mathematics Subject Classification:

• 62L05
• 62L12
• 62F07

Acknowledgments

Two referees gave substantial remarks on an earlier version. One referee especially included a lengthy list of editorial pointers. Their comments have helped immensely by improving the overall clarity. I express my deepest gratitude to these colleagues.