Motivated by a practical need for the comparison of hemolysis curves at various treatment levels, we propose a novel method for pairwise comparison of mean functional responses. The hemolysis curves—the percent hemolysis as a function of time—of mice erythrocytes (red blood cells) by hydrochloric acid have been measured among different treatment levels. This data set fits well within the functional data analysis paradigm, in which a time series is considered as a realization of the underlying stochastic process or a smooth curve. Previous research has only provided methods for identifying some differences in mean curves at different times. We propose a two-level follow-up testing framework to allow comparisons of pairs of treatments within regions of time where some difference among curves is identified. The closure multiplicity adjustment method is used to control the family-wise error rate of the proposed procedure.
"Pairwise comparison of treatment levels in functional analysis of variance with application to erythrocyte hemolysis." Ann. Appl. Stat. 8 (2) 905 - 925, June 2014. https://doi.org/10.1214/14-AOAS723