Repeated measures ANOVA results.

Fish photolocomotor behavioral response (PBR) studies have become increasingly prevalent in pharmacological and toxicological research to assess the environmental impact of various chemicals. There is a need for a standard, reliable statistical method to analyze PBR data. The most common method currently used, univariate analysis of variance (ANOVA), does not account for temporal dependence in observations and leads to incomplete or unreliable conclusions. Repeated measures ANOVA, another commonly used method, has drawbacks in its interpretability for PBR study data. Because each observation is collected continuously over time, we instead consider each observation to be a function and apply functional ANOVA (FANOVA) to PBR data. Using the functional approach not only accounts for temporal dependency but also retains the full structure of the data and allows for straightforward interpretation in any subregion of the domain. Unlike the traditional univariate and repeated measures ANOVA, the FANOVA that we propose is nonparametric, requiring minimal assumptions. We demonstrate the disadvantages of univariate and repeated measures ANOVA using simulated data and show how they are overcome by applying FANOVA. We then apply one-way FANOVA to zebrafish data from a PBR study and discuss how those results can be reproduced for future PBR studies.鱼类光运动行为响应（Photolocomotor Behavioral Response, PBR）研究在药理学与毒理学领域愈发普及，其核心用途为评估各类化学品的环境影响。当前亟需一套标准化且可靠的统计方法，用于分析PBR实验数据。目前最常用的单因素方差分析（Analysis of Variance, ANOVA）未考虑观测值的时间依赖性，易得出不完整或不可靠的结论；而另一类常用的重复测量方差分析（Repeated Measures ANOVA），在针对PBR研究数据的可解释性方面存在明显缺陷。由于所有观测值均随时间连续采集，我们将每条观测序列视为一个函数，并将函数型方差分析（Functional ANOVA, FANOVA）应用于PBR数据。该函数型分析方法不仅能够充分考虑时间依赖性，还可完整保留数据的原始结构，且支持对研究域内任意子区域进行直观解读。与传统单因素方差分析及重复测量方差分析不同，我们提出的FANOVA属于非参数方法，仅需极少的前提假设。我们通过模拟数据验证了单因素方差分析与重复测量方差分析的局限性，并展示了应用FANOVA可有效克服上述问题。随后我们将单因素FANOVA应用于一项PBR研究中的斑马鱼实验数据，并探讨了该研究结果可在未来PBR研究中复现的可行路径。