Date of Completion

5-5-2023

Degree Type

Honors Thesis

Discipline

Mathematics (MATH)

First Advisor

Robert Rovetti

Abstract

Real world data is inherently noisy and data analysis can be especially complex when noise is compounded in hierarchical and multilevel data structures. Since such data structures can be described using multiple approaches, the way data is collapsed and grouped within these structures can influence its resulting interpretation and analyses. To avoid discrepancies in data collapsing and grouping, multiple statistical approaches have been developed specifically to analyze multilevel data structures. Examples of multilevel statistical models are the two-factor ANOVA and the general linear model with repeated-measures (GLM-RR) which is typically used in the context of looking at change over time. Unlike simple summary-statistics such as t-tests, multilevel models allow for precision in the effect of each level on the observed data. In this study, analyses will be done using both simple statistical models and multilevel models with a dataset from a behavioral decision-making assay that aims to see whether phototactic preference changes over 24 hours in larval zebrafish. The simple and multilevel analyses will be compared through the descriptive analyses and hypothesis testing. The descriptive analyses will provide insight into the practicality of collapsing levels of data in hierarchical data structures and the hypothesis testing will provide comparative insight into the use of both simple and multilevel statistical models.

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