Sample size and power calculations for left-truncated normal distribution

Shiquan Ren, Haitao Chu, Shenghan Lai

Research output: Contribution to journalArticlepeer-review

Abstract

Sample size calculation is an important component in designing an experiment or a survey. In a wide variety of fields - including management science, insurance, and biological and medical science - truncated normal distributions are encountered in many applications. However, the sample size required for the left-truncated normal distribution has not been investigated, because the distribution of the sample mean from the left-truncated normal distribution is complex and difficult to obtain. This paper compares an ad hoc approach to two newly proposed methods based on the Central Limit Theorem and on a high degree saddlepoint approximation for calculating the required sample size with the prespecified power. As shown by use of simulations and an example of health insurance cost in China, the ad hoc approach underestimates the sample size required to achieve prespecified power. The method based on the high degree saddlepoint approximation provides valid sample size and power calculations, and it performs better than the Central Limit Theorem. When the sample size is not too small, the Central Limit Theorem also provides a valid, but relatively simple tool to approximate that sample size.

Original languageEnglish (US)
Pages (from-to)847-860
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Volume37
Issue number6
DOIs
StatePublished - Jan 2008

Keywords

  • Central Limit Theorem
  • Health insurance cost data
  • Left-truncated normal distribution
  • Power
  • Saddlepoint approximation
  • Sample size

ASJC Scopus subject areas

  • Statistics and Probability

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