Dissertation Experiment Analysis

Introduction

This document contains the analysis for the dissertation experiment. The analysis is organized into four main sections:

1. Data Wrangling: Importing, cleaning, and preparing the data
2. Analysis: Core analytical procedures
3. Statistical Tests: Formal statistical testing
4. Visualizations: Data visualization and plotting

Data Wrangling

## Visual angle range for -200 to +200 pixels: 9.06 degrees

Data Summary

Overall Dataset Summary

Participants	Total Trials	Trials per Participant	PSE Min (deg)	PSE Max (deg)	PSE Mean (deg)	PSE SD (deg)
28	21060	752.1	-5.28	1.84	-0.98	1.17

Response Rate Analysis

Data Quality Check

Data Quality Summary

Metric	Value
PSE Mean	-0.98
PSE SD	1.17
3 SD Lower Bound	-4.50
3 SD Upper Bound	2.50
Extreme PSE Participants	1.00
Extreme Response Rate Participants	3.00

Participants with PSE Beyond 3 SD from Mean -4.5 to 2.5

participant	n_trials	mean_pse	LR%
LD_112822	765	-5.28	100

Participants with Extreme Response Rates

participant	n_trials	left_responses	LR%	mean_pse
LD_112822	765	765	100.00	-5.28
RA_040622	765	765	100.00	-0.11
VG_052722	765	738	96.47	-0.07

Final Data Filtering

Data Filtering Summary

Metric	Count
Original Participants	28
PSE Outliers Removed	1
Extreme Response Rates Removed	3
Final Participants	25

Descriptive Statistics

Overall Descriptive Statistics

Sample Size	Mean PSE (deg)	SD PSE (deg)	Mean LR%	SD LR%
25	-0.9	NA	67.14	12.67

## PSE Distribution by Participant

## Left Response Rate Distribution by Participant

Analysis

## Group-Level Left Response Rate by SOA

## Individual-Level Left Response Rate by SOA - Participant MT_042022

## Group-Level Left Response Rate by SOA - Detrended (0-300ms)

## Group-Level Left Response Rate by SOA - Butterworth Filtered (4-18 Hz, 0-300ms)

## 10 Hz Sinusoid Overlay and R^2 Fit (0-300ms)

## R^2 (10 Hz sinusoid fit): 0.027

## RFFT of Filtered Left Response Rate (0-300ms)

## Peak frequencies from group-level FFT:

##        freq       amp
## 1  6.451613 0.6143487
## 2 14.516129 0.2489839

## Top 2 peak frequencies: 6.5 Hz and 14.5 Hz

## Frequency analysis (0-300ms)

## Permutation test (0-300ms, n=1000): p = 0.6880

## Frequency analysis – 0-300ms permutation test

## Critical value (95th % of permuted R^2): 0.187

## Permutation tests for peak frequencies from group-level FFT (0-300ms)

## 
## Peak frequency 6.5 Hz permutation test:
## Observed R^2 (6.5 Hz): 0.780
## Permutation test p-value: 0.0000
## Critical value (95th %): 0.178
## Significant: Yes
## Frequency analysis – 6.5 Hz permutation test

## 
## Peak frequency 14.5 Hz permutation test:
## Observed R^2 (14.5 Hz): 0.129
## Permutation test p-value: 0.1460
## Critical value (95th %): 0.202
## Significant: No
## Frequency analysis – 14.5 Hz permutation test

Individual-Level Frequency Analysis

## Individual-Level 0-300ms RFFT (4–18 Hz filtered residuals)

## Distribution of Power Across 4-18 Hz Frequencies for All Participants (0-300ms)

## Summary of Power by Frequency:
## # A tibble: 9 × 4
##   freq_rounded mean_amp sd_amp n_participants
##          <dbl>    <dbl>  <dbl>          <int>
## 1          4.8    0.165 0.0746             25
## 2          6.5    0.330 0.122              25
## 3          8.1    0.384 0.148              25
## 4          9.7    0.357 0.129              25
## 5         11.3    0.327 0.164              25
## 6         12.9    0.298 0.140              25
## 7         14.5    0.238 0.0985             25
## 8         16.1    0.219 0.122              25
## 9         17.7    0.220 0.120              25
## Bootstrap Analysis of Power Values Across All Frequencies (0-300ms)

## Bootstrap Summary Statistics (95% CI):
## # A tibble: 9 × 5
##   frequency mean_bootstrap sd_bootstrap ci_lower ci_upper
##       <dbl>          <dbl>        <dbl>    <dbl>    <dbl>
## 1       4.8          0.165       0.0148    0.136    0.195
## 2       6.5          0.330       0.0240    0.282    0.378
## 3       8.1          0.384       0.0290    0.327    0.440
## 4       9.7          0.356       0.0248    0.307    0.404
## 5      11.3          0.326       0.0319    0.262    0.386
## 6      12.9          0.298       0.0274    0.243    0.350
## 7      14.5          0.237       0.0192    0.199    0.274
## 8      16.1          0.219       0.0236    0.175    0.267
## 9      17.7          0.220       0.0234    0.177    0.268