Math and Computer Science Honors Theses

Principles of Experimental Design

Date of Creation

5-18-2022

Document Type

Departmental Honors Thesis - Restricted Access

Department

Mathematics

First Advisor

Edward J. Soares

Abstract

Experimental design is the process by which research is conducted in an objective manner and maximizes the reliability of conclusions, while minimizing the amount of bias and resources needed to carry out a study. We first demonstrate the importance of sample size determination through study of two forms of statistical inference: confidence intervals and hypothesis tests. We will derive formulas for estimation error and effect size, and examine the relationship between these quantities and sample size. We will also describe multiple comparison methods that control for the build-up of the experiment-wise error rate, as well as methods such as Bonferroni and false-discovery rate correction that reduce the observed significance level. Lastly, we will discuss the experimental conditions for when a permutation test is appropriate to employ, describe how this test is generally conducted, and give some examples of its implementation.

Comments

Reader: Eric Ruggieri

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