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<p>Larval fish photolocomotor behavioral response (PBR) studies are increasingly useful to identify bioactivity profiles and define behavioral phenotypes for pharmaceuticals and environmental contaminants. However, there is a need for improved reproducibility and statistical reliability in the PBR literature, and the standard statistical technique applied in PBR studies, univariate ANOVA, does not account for temporal dependence in the observations, potentially influencing biologically meaningful conclusions. In this work, the functional form of PBR data is utilized, and functional two-way ANOVA (FANOVA) is applied. In addition to addressing the dependence problem, FANOVA allows for both global and regional exploratory and inferential analysis. In this paper, we present a permutation test for two-way FANOVA with four common <i>F</i>-test statistics; the permutation-based approach to generating the approximate sampling distribution of each test statistic under the null FANOVA hypotheses is flexible, statistically sound, and robust to assumption violations. We perform simulation studies for two-way FANOVA, where the size and power of the tests are compared under various combinations of error distributions, treatment covariance structures, and sample sizes. We find that the test statistics perform well with the permutation test. We then demonstrate two-way FANOVA exploratory and inferential analysis for PBR data in a case study.</p>

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Balanced Two-Way Functional ANOVA: A Case Study for Toxicological Photolocomotor Response Studies

  • 期刊论文

  • 发表日期：

    2025年6月13日

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  • Luke Durell,
  • Natalie Mastin,
  • Lea M. Lovin,
  • W. Baylor Steele IV,
  • Bryan W. Brooks,
  • Amanda S. Hering

摘要

Larval fish photolocomotor behavioral response (PBR) studies are increasingly useful to identify bioactivity profiles and define behavioral phenotypes for pharmaceuticals and environmental contaminants. However, there is a need for improved reproducibility and statistical reliability in the PBR literature, and the standard statistical technique applied in PBR studies, univariate ANOVA, does not account for temporal dependence in the observations, potentially influencing biologically meaningful conclusions. In this work, the functional form of PBR data is utilized, and functional two-way ANOVA (FANOVA) is applied. In addition to addressing the dependence problem, FANOVA allows for both global and regional exploratory and inferential analysis. In this paper, we present a permutation test for two-way FANOVA with four common F-test statistics; the permutation-based approach to generating the approximate sampling distribution of each test statistic under the null FANOVA hypotheses is flexible, statistically sound, and robust to assumption violations. We perform simulation studies for two-way FANOVA, where the size and power of the tests are compared under various combinations of error distributions, treatment covariance structures, and sample sizes. We find that the test statistics perform well with the permutation test. We then demonstrate two-way FANOVA exploratory and inferential analysis for PBR data in a case study.