Abstract
When measuring concentration of chemical compounds, we often haveto deal with a situation when the resulting values are found belowthe detection limit of the determination method. In order tostatistically evaluate such data, the newly developed method ofmaximum likelihood considering multiply left-censored samples isapplied. This paper is motivated by the need to have validinference concerning the equality of the means of two log-normaldistributions that are frequently encountered in environmental andexposure data analysis. As a model distribution of measuredenvironmental and/or biomedical data, log-normal distribution isconsidered. Moreover, using the asymptotic properties of maximumlikelihood estimates, concentrations of chemicals can be compared.A test procedure for comparing the means of two independentlog-normal populations in the presence of multiply censored datais also introduced and evaluated. Asymptotic chi-square test isused in the proposed test procedure. Worked example is given illustrating the use of the methodsprovided utilizing a computer program written in the R language. Asimulation study was performed to examine the power and the sizeof the proposed test procedure introduced in this article.
Highlights
Many environmental data sets are characterized by a small number of high concentrations and a large number of low concentrations and are often right-skewed (Shumway et al, 1989)
When measuring concentration of chemical compounds, we often have to deal with a situation when the resulting values are found below the detection limit of the determination method
Suppose that a sample of n data points is given of which m data points are non-censored, and the remaining mc = n − m observations are left-censored with a single detection limit DL
Summary
Many environmental data sets are characterized by a small number of high concentrations and a large number of low concentrations and are often right-skewed (Shumway et al, 1989). Suppose that a sample of n data points is given of which m data points are non-censored (fully measured), and the remaining mc = n − m observations are left-censored with a single detection limit DL. Harris (1991) considered two parametric and two non-parametric methods for testing the equality of medians of two independent log-normal distributions when some data are left-censored. Stoline (1993) extended results first suggested by Harris (1991) and proposed a procedure for comparing medians of two independent log-normal distributions where some data may be left-censored. The purpose of this paper is to develop a parametric procedure to test the hypothesis of equal means when data are sampled from two independent log-normal distributions utilizing multiply left-censored data sets. A simulation study was performed to inspect the size and the power of the proposed test procedure
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call