Evaluation of the Sensitivity and Robustness of Modified Chi-Square Ratio Statistic for Cascade Impactor Equivalence Testing Through Monte Carlo Simulations.

The objective of this work was to study the performance of the modified chi-square ratio statistic (mCSRS test) proposed for cascade impactor (CI) profile equivalence testing. The test (T) and reference (R) CI profile datasets were generated from different typical CI profile patterns either with or without inter-site correlation (ISC) through Monte Carlo simulations. The mCSRS test pass rate outcome employing previously published critical values was compared with that of critical values derived from different types of datasets. The influence of number of bootstrap iterations (B) on the consistency of the outcome was assessed within the range of 10-10,000 iterations. Power curves were constructed to study the effect of differences in T and R mean stage deposition, T/R variance ratios, differences between T and R profiles in high/low deposition sites, and sample size on the performance of the mCSRS test. The derived critical values exhibited trends based on R product variability: M1 rank-ordered without ISC (at low variability) and the previously published M8 critical values (at high variability) resulted in lowest pass rate outcomes. The precision of the outcome did not increase considerably beyond B = 2000 (default). The probability of showing equivalence between T and R CI profiles increased with (1) a decrease in mean deposition differences, (2) a decrease in T product variability, and (3) an increase in sample size. The mCSRS outcome is less sensitive to low deposition sites that are prone to analytical variability. In conclusion, the mCSRS test is a sensitive and robust method under most conditions.