Poisson Goodness-of-fit Tests for Radiation-induced Chromosome Aberrations

Abstract

Asymptotic and exact Poisson goodness-to-fit tests have been reviewed with regard to their applicability in analysing distributional properties of data on chromosome aberrations. It has been demonstrated that for typical cytogenetic samples, i.e. when the average number of aberrations per cell is smaller than one, results of asymptotic tests, especially of the most commonly used u-test, differ greatly from results of corresponding exact tests. While the u-statistic can serve as a qualitative index to indicate a tendency towards under- or over-dispersion, exact tests should be used if the assumption of a Poisson distribution is crucial, e.g. in investigating induction mechanisms. If the main interest is to detect a difference between the mean and the variance of a sample it is furthermore important to realize that a much larger sample size is required to detect underdispersion than it is to detect overdispersion.

A note on Poisson goodness-of-fit tests for ionizing radiation induced chromosomal aberration samples

“…The case of y << 1 is usual at low doses in cytogenetic samples, and then the most likely outcome is that the total number of aberrations observed is made up exclusively of cells with only one aberration in it, even for large n. For small counts the true distribution of u is therefore heavily skewed to the right and does not approach the normal distribution for any practically feasible n (Merkle 1981). Graphically, the assumption of normal distribution of D-statistic (the ustatistic is based in this asymptotic approximation) can be appreciated in the Figure 1 for n = 500 and in the Figure 2 for n = 50.…”

“…Another application of the exact D-test was performed by (DuFrain et al 1980) to over-dispersed data of chromosomal aberrations in human lymphocytes exposed to α-particles. (Merkle 1981) applied the exact test to investigate the behavior of several test for the Poisson goodness of fit. A computer program for the exact test was published in (Papworth 1983) based on the test proposed by (Fisher 1950) and the existence of the program was mentioned in (Merkle 1981) as a note added in proof.…”

“…(Merkle 1981) applied the exact test to investigate the behavior of several test for the Poisson goodness of fit. A computer program for the exact test was published in (Papworth 1983) based on the test proposed by (Fisher 1950) and the existence of the program was mentioned in (Merkle 1981) as a note added in proof. The program was written in FORTRAN language to obtain the exact probability values (Papworth 1983).…”

“…The u-test is asymptotic, because it is not based on the exact distribution of a measure (for instance the dispersion index) and it is based on the normal approximation of an exact distribution. Concretely, (Merkle 1981) claimed about the usage of exact test for samples with a small total of counts for the analysis of dicentric chromosomes, in contrast to the approximate tests, like the utest, due to the discrepancy of values. Exact tests and their asymptotic versions about different properties of the Poisson distribution (equidispersion or the probability of the number of zeros given the sample sum) are referred in this work.…”

“…These tests are based on different properties of the Poisson model, as the equi-dispersion (the variance equals to the mean) and the frequency of zeros. The general asymptotic goodness-of-fit test (the classical χ 2 -test) for the Poisson distribution is not used here because it has been proved to be inaccurate for small samples, particularly for the case of chromosomal aberration counts (Rao and Chakravarti 1956;Savage 1970;Merkle 1981). The u-test is asymptotic, because it is not based on the exact distribution of a measure (for instance the dispersion index) and it is based on the normal approximation of an exact distribution.…”