Quantitative Reasoning with Data

This project was an academic group project under the GEA1000: Quantitative Reasoning with Data module

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Part A: Journal Article Evaluation

Study Overview

• Aim: Investigate association between cognitive function and traumatic upper-limb injuries.
• Variables:
  • Independent: Traumatic upper-limb injury (measured via pain level, hand function, etc.).
  • Dependent: Cognitive function (measured via RAVLT and SCWT tests).
• Key Finding:

  "Individuals with traumatic upper-limb injury had greater cognitive deficits in short-term memory than uninjured individuals."

Methodology

• Subjects:
  • Observational Group: 104 patients from Guangdong Work Injury Rehabilitation Hospital.
  • Control Group: 104 uninjured individuals from the local community.
• Target Population: Individuals with traumatic upper-limb injuries.

Critical Analysis

• Confounders Controlled: Age, sensory damage, medical history, mental status.
• Uncontrolled Confounder: Sleep quality before testing.
• Hypothesis Testing:
  • Null (H₀): No association between injury and cognitive function.
  • Alternate (H₁): Association exists.
  • Conclusion: Insufficient evidence to reject H₀ (no significant difference in executive function).

Strengths & Limitations

Strengths	Limitations
Rigorous exclusion criteria.	Limited cognitive assessment methods (RAVLT/SCWT only).
Acknowledged potential confounders.	No pre-injury cognitive function data.

Generalizability

• Findings apply only to patients from Guangdong due to geographic and sampling constraints.

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Part B: Spotify Data Analysis

Dataset Overview

• Size: 1,343 songs (2000–2020).
• Variables:
  • Categorical: Genre, Explicit, Key.
  • Numerical: Danceability, Energy, Tempo, Popularity.

Key Analyses

1. Tempo Categorization

   • Fast (120–168 BPM) was most common (42%).
   • Mode: Correctly identified as the category with highest proportion.

2. Valence Classification

   • Happy (valence ≥ 0.5): 51.6% of songs.
   • Basic Rule: rate(Happy) varied by mode (e.g., 49.4% for minor vs. 52.6% for major).

3. Danceability vs. Tempo

   • Moderate tempo (76–108 BPM) showed highest danceability.
   • Outliers: Extremely slow/fast tempos had limited data.

4. Explicit Content & Happiness

   • Association: Not Happy songs had slightly higher explicit content (51.1% vs. 48.9%).

5. Acousticness vs. Energy

   • Overall: Strong negative correlation (r = -0.713).
   • Genre Variations:
     • Strongest in Metal (r = -0.915).
     • Weakest in Reggae (r = -0.307).

6. Hypothesis Test: Rock Song Length

   • Claim: Average length = 255,000 ms (4m15s).
   • Result: Rejected H₀ (p < 0.001); actual mean = 228,678 ms.

Additional Analysis

• Confounder Check: Mode (major/minor) confounds Danceability vs. Tempo association.

Limitations

1. Sampling Bias: First 1,000 songs per sub-genre may not represent all music.
2. Non-Probability Sampling: Songs beyond the first 1,000 had no chance of selection.

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Visualizations

• Boxplot: Danceability across tempo categories.
• Scatterplot: Acousticness vs. energy (with genre stratification).

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🔍 Key Insights

• Ecological Fallacy Example: Overall negative Acousticness-Energy correlation masked weak associations in specific genres (e.g., Regional Mexican Music).
• Data Constraints: Small sample sizes for extreme tempo categories reduced reliability.

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Project Timeline

Week	Task
4	Data released.
5–10	Analysis period.
10/11	Report submission.
11/12	Presentations.
Reading Week	Peer evaluations.