Appendix C: - University of Illinois at Chicago

consistent, based on a chi-square test, then the deposit on the sample filter can be
considered to be uniform and concentrations can be extrapolated with confidence.
Results of the chi-square analyses for every project filter on which at least one structure
was observed are presented in Table 3A. Results for the quality control samples
analyzed in this study are presented in table 36. In both cases, chrysotile and
amphibole structures were separately evaluated and, in both cases, counts of total
structures longer than 5 pm were subjected to the chi square test.
The first columns of both Table 3A and 36 indicate the sample identification number.
The next two columns indicate, respectively, the test statistic observed for chrysotile
counts from the indicated sample and whether the counts can be considered to be
consistent (based on a chi square). The fourth and fifth columns in each table indicate
the same information for amphibole structures. Note that the tables are divided into two
halves (to reduce table size) and identical information is presented in each half of each
table (for different structures).
Because five grid specimens are being compared, the appropriate critical values for the
chi square test is with four degrees of freedom (one less than the number of
realizations of the counts evaluated). The critical value corresponding to a 0.05 level of
significance for this test (with four degrees of freedom) is 9.49. Thus, whenever the test
* statistic is less than 9.49, the filter deposit can be considered to be uniform.
As can be seen in Table 3A, there are 64 sets of specimen grids on which at least one
structure was observed so that a chi square test was conducted. It can also be seen
* from this table that there are only three out of the 64 tests for which the chi square
statistic is larger than the critical value. However, at a 0.05 level of significance, one
would expect three failures of the chi square test (among 64 tries) by chance alone.
Thus, it is reasonable to conclude from the data presented in Table 3A that sample
filters analyzed in this study are entirely uniform and results can be reasonably
extrapolated to estimate concentrations in the sampled material.
A similar conclusion can also be drawn from the data presented in Table 38. Although
two failures among the 24 tests indicated is slightly higher than the one failure
expected, this small difference is not sufficient to suggest a problem. In fact, we should
also consider that there are more than 1 00 cases in which no chrysotile structures or
(separately) no amphibole structures were detected on any of the grids in a set and that
such cases represent "perfect' agreement with zero counts on each of five grid
specimens. Thus, if these cases were to be included, we would expect more than 9
failures overall, while only five failures were observed.
Duplicate and replicate analyses. A series of duplicate splits and/or replicate
analyses were also conducted on selected samples to further evaluate the performance
of the laboratories participating in this study. In some cases, duplicate split samples
were prepared and both pairs were analyzed (blind) by the primary laboratory for the
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