Free Speech at UCSB 🗣️

PSTAT 122 Final Project — University of California, Santa Barbara
Author: Isaiah Singer
Date: June 2025

Overview

This project explores how UCSB students perceive the state of free speech on campus and whether the framing of a statement changes their opinions.
By conducting an experiment using a Generalized Randomized Block Design, I analyzed how tone and emphasis affected responses while controlling for class standing (Freshman, Sophomore, Junior, Senior).

The primary goal was to determine if different framings of free speech — respectful exchange, perceived threat, or scholarly growth — influenced how strongly students agreed with each perspective.

Objectives

• Measure UCSB students’ agreement with various framings of free speech.
• Evaluate whether statement tone affects perceived restrictiveness.
• Test statistical significance across groups using ANOVA and permutation methods.
• Assess model assumptions and conduct post-hoc power analysis for insight into sample adequacy.

Tools & Techniques

• R packages: readxl, ggplot2, dplyr, broom, pwr, knitr
• Design: Generalized Randomized Block Design
• Statistical Tests: Two-way ANOVA, Tukey pairwise comparisons, permutation test
• Validation: Normality checks (QQ-plot, Shapiro-Wilk), variance testing, post-hoc power analysis

Data Summary

• Sample size (n): 21 UCSB students
• Treatment groups:
  1. Respectful exchange of ideas
  2. Threat to free speech framing
  3. Scholarly/critical thinking framing
• Block factor: Student class standing (Freshman–Senior)
• Response variable: Rating of agreement (1–10 scale)

Key Findings

• Neither treatment nor block factor showed statistically significant effects (ANOVA p ≈ .99).
• Permutation test confirmed the ANOVA result (p ≈ .992).
• Pairwise comparisons indicated no significant differences between treatments.
• Post-hoc power analysis showed that ~300 participants would be needed to detect a small effect (f ≈ .10, 80% power).
• Normality and variance checks revealed mild skewness and nonlinearity but not enough evidence to reject normality.

Visualization Examples

• Boxplot: Rating distribution across treatments
• Scatterplot: Rating distribution by treatment and class standing
• Histogram & QQ-Plot: ANOVA residual normality check
• Power Curve: Sample size vs. effect size (for 80% power)

Conclusions

• Differences in statement framing did not significantly alter students’ views on free speech.
• The experiment suggests that students at UCSB hold consistent attitudes toward speech restrictiveness, regardless of presentation.
• Small sample size likely limited the study’s power, but findings align with prior research suggesting broad support for free expression.

Reflection

This project demonstrated applied statistical design — from experimental setup to model validation and interpretation — while addressing a socially relevant topic.
It highlights the importance of sample size and assumption testing in real-world research, as well as the complexity of quantifying human attitudes.

Project Files

• scripts/PSTAT122FinalProject.Rmd — Main R Markdown file
• outputs/PSTAT122FinalProject.pdf

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Created by Isaiah Singer — Data Analyst/Scientist | R, Python, SQL | UCSB Statistics & Data Science