title: Tests for an upper percentile of a lognormal distribution based on samples with multiple detection limits and sample-size calculation.
abstract: The problem of determining sample size for testing an upper percentile of a lognormal distribution based on samples with multiple detection limits is considered. Two tests, the signed likelihood ratio test and another test based on a pivotal statistic, are outlined. These tests are very satisfactory in controlling type I error rates and comparable in terms of powers. Procedures and R codes for calculating sample sizes for these tests to attain a specified power are given. It is noted that for guaranteeing a given power, increased sample size is necessary due to the presence of detection limits, and the required sample size goes up as the proportion of non-detects goes up. It is also noted that in the multiple detection limit scenario, sample-size determination does not require knowledge of the proportions of non-detects that are expected to be below the individual detection limits; rather, what is required is a knowledge of the overall percentage of non-detects that is to be expected in the entire sample. Sample-size calculation is illustrated using a practical situation.
authors.affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70508-1010, USA;
authors.forename: Kalimuthu
authors.initials: K
authors.lastname: Krishnamoorthy
authors.forename: Thomas
authors.initials: T
authors.lastname: Mathew
authors.forename: Zhao
authors.initials: Z
authors.lastname: Xu
mesh_terms: D000465:Algorithms; D004784:Environmental Monitoring / Q000379:methods*; D016013:Likelihood Functions; D057230:Limit of Detection; D015233:Models, Statistical; D016273:Occupational Exposure / Q000032:analysis*; D012016:Reference Values; D018401:Sample Size
keywords: maximum likelihood estimates; non-central t distribution; pivotal test; powers; signed likelihood ratio test