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

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

## 10 Hz Sinusoid Overlay and R^2 Fit

## R^2 (10 Hz sinusoid fit): 0.019

## RFFT of Filtered Left Response Rate

## Peak frequencies from group-level FFT:

##        freq       amp
## 1  6.862745 0.4950146
## 2 14.705882 0.3463220
## 3 17.647059 0.2255797

## Top 2 peak frequencies: 6.9 Hz and 14.7 Hz

## Frequency analysis

## Permutation test (full, n=1000): p = 0.6230

## Frequency analysis – Full time series permutation test

## Critical value (95th % of permuted R^2): 0.110

## Permutation tests for peak frequencies from group-level FFT

## 
## Peak frequency 6.9 Hz permutation test:
## Observed R^2 (6.9 Hz): 0.500
## Permutation test p-value: 0.0000
## Critical value (95th %): 0.130
## Significant: Yes
## Frequency analysis – 6.9 Hz permutation test

## 
## Peak frequency 14.7 Hz permutation test:
## Observed R^2 (14.7 Hz): 0.245
## Permutation test p-value: 0.0020
## Critical value (95th %): 0.124
## Significant: Yes
## Frequency analysis – 14.7 Hz permutation test

Individual-Level Frequency Analysis

## Individual-Level Full Time Series RFFT (4–18 Hz filtered residuals)

## Distribution of Power Across 4-18 Hz Frequencies for All Participants

## Summary of Power by Frequency:
## # A tibble: 14 × 4
##    freq_rounded mean_amp sd_amp n_participants
##           <dbl>    <dbl>  <dbl>          <int>
##  1          4.9    0.189 0.100              25
##  2          5.9    0.253 0.122              25
##  3          6.9    0.263 0.124              25
##  4          7.8    0.236 0.105              25
##  5          8.8    0.264 0.137              25
##  6          9.8    0.293 0.114              25
##  7         10.8    0.250 0.139              25
##  8         11.8    0.251 0.108              25
##  9         12.7    0.220 0.126              25
## 10         13.7    0.213 0.105              25
## 11         14.7    0.204 0.108              25
## 12         15.7    0.185 0.137              25
## 13         16.7    0.163 0.0869             25
## 14         17.6    0.142 0.0763             25
## Bootstrap Analysis of Power Values Across All Frequencies

## Bootstrap Summary Statistics (95% CI):
## # A tibble: 14 × 5
##    frequency mean_bootstrap sd_bootstrap ci_lower ci_upper
##        <dbl>          <dbl>        <dbl>    <dbl>    <dbl>
##  1       4.9          0.189       0.0195    0.152    0.228
##  2       5.9          0.253       0.0239    0.206    0.300
##  3       6.9          0.263       0.0242    0.216    0.309
##  4       7.8          0.236       0.0204    0.195    0.275
##  5       8.8          0.264       0.0265    0.214    0.317
##  6       9.8          0.293       0.0220    0.251    0.336
##  7      10.8          0.249       0.0270    0.197    0.302
##  8      11.8          0.250       0.0211    0.209    0.291
##  9      12.7          0.220       0.0247    0.173    0.269
## 10      13.7          0.213       0.0205    0.174    0.254
## 11      14.7          0.204       0.0212    0.164    0.246
## 12      15.7          0.185       0.0265    0.137    0.239
## 13      16.7          0.163       0.0171    0.129    0.197
## 14      17.6          0.142       0.0149    0.114    0.172