TY - JOUR

T1 - Sample size and power calculations for left-truncated normal distribution

AU - Ren, Shiquan

AU - Chu, Haitao

AU - Lai, Shenghan

N1 - 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.

PY - 2008/1

Y1 - 2008/1

N2 - 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.

AB - 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.

KW - Central Limit Theorem

KW - Health insurance cost data

KW - Left-truncated normal distribution

KW - Power

KW - Saddlepoint approximation

KW - Sample size

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U2 - 10.1080/03610920701693876

DO - 10.1080/03610920701693876

M3 - Article

AN - SCOPUS:38949177375

VL - 37

SP - 847

EP - 860

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 6

ER -