Currently, the inter-laboratory collaborative studies are often organized for chromosome aberration analysis of the radiation exposed persons, especially for those supposed to be exposed to low-level radiation where large scale data analysis is needed for the dose evaluation, or those involved in radiation accident where there is an immediate need for the biological dose assessment. In such collaborative study, the variability or uniformity of the results obtained by individual scorer is always a matter of important concern. We developed the statistical method for the assessment of  variability of the participants of the collaborative analysis.

(1) Uniformity test for the scoring efficiency in one sample
     Let p₂ be the probability to score aberrations in a cell by scorer K, and p₁ be the probability to score aberrations in a cell by the rest of scorers, N-1, where N is the total number of scorers. The uniformity of the scoring efficiency is tested by the null hypothesis,

p₁=p₂

     The number of aberrations, a, in the number of cells scored, n, follow a binomial distribution,

B(a₂:n₂,p₂) for K

B(a₁:n₁,p₁) for N-1.

    The statistical test for p of the two binomial distributions may be possible by assuming that, under the null hypothesis, a₂ follows the hypergeometric distribution. That is, with a=a₁+a₂ and n=n₁+n₂, the probability density follows the hypergeometric function

p(a₂)=p(a₂:n₂,a,n)=[comb(a; a₂)comb(n-a;n₂-a₂)]/comb(n;n₂)

     Then, the lower tail probability of a₂ is

LP=sum[i-0 to a₂] p(i)

     And the upper tail probability of a₂ is

LP=sum[i=a₂ to n₂] p(i)

2) Uniformity test for the scoring efficiency in multiple samples
    Similarly, for the sample number i (i=1,2,3,…..M), SL as the sum of LP can be obtained, and the probability of SL being below x is expressed by
                                                                                                                        PSL(x)=sum[PL₁(a₁)+LP₂(a₂)+ . . . . +LP_M(a_M)] p₁(a₁)p₂(a₂) . . . . . . .p_M(a_M)

     Similarly, PSU(x) is obtained for the sum of UP being below probability density of x. If the PSL or PSU are below significance level (i.g., 0.005), the scoring of the scorer K is significantly different from that of averaged efficiency of the rest of scorers. If the PSL is blow significance level, the scorer K shows significantly underscore. If the PSU is blow the significance level, the scorer K shows significantly overscore as compared to the average of the rest of scorers.

3) Results and implication for the issue of overdispersion
     The results are summarized in the following Table. In the scoring of unstable chromosome aberrations (dicentrics, rings, fragments) and hence the cells containing those aberrations (X1Cu cells), only three scorers show significant deviation from the group central values. This indicates that the inter-individual (or inter-laboratory) variability in the scoring efficiency is not significantly large.
     In contrast, most of the scorers significantly differ in detecting stable-type aberrations (or Cs cells); they are either over-scoring or under-scoring as compared with the central value of the group. In another word, there is great variability in the frequencies of Cs cells distributed over of central value (over-dispersion). Such inter-individual variability is observed among scorers in the same laboratory.
     The great variability in the scoring efficiency for Cs cells may not be solely due to the slight difference in the scoring criteria of individual scorer. The major reason may stem from the uncertainty of determination that, in the scoring of acquired aberrations, the aberration figures ought to be determined only in one cell that has been selected under the low-power microscopy. To keep unbiased scoring, the cell once selected under low-power microscope should be analyzed anyhow and cannot be rejected unless special reason. Such uncertainty is greater for the conventional Giemsa staining, becomes lesser for G-banding method, and lesser for FISH method.