## 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 language | English (US) |
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Pages (from-to) | 847-860 |

Number of pages | 14 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 37 |

Issue number | 6 |

DOIs | |

State | Published - Jan 2008 |

### Bibliographical note

Funding Information:Dr. Ren and Professor Lai were supported by grants from the National Institute on Drug Abuse (DA12777) of USA, the National Natural Science Foundation (70103007) of China and National Social Science Foundation (02CTJ001) of China.

## Keywords

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