Case Study: Multi-Stage Likert‑Scale Transformation for Robust Categorical Analysis

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Background of this multi-stage Likert transformation case study

In this multi-stage Likert transformation case study, perception data from 10‑item, 5‑point Likert scales often suffer from extreme‑response bias and skewed distributions. This methodology‑centered example describes a three‑tiered transformation pipeline that yields psychometrically sound categorical variables ready for chi‑square tests and logistic regression.

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Data & Constructs

• Sample & Context: 320 learners enrolled in online open courses, balanced across age, gender, and prior e‑learning experience.
• Instrument: Ten statements measuring motivations and barriers on a 1 (Strongly Disagree) to 5 (Strongly Agree) scale.
• Subscales:
  • Platform Usability: Q1, Q4, Q7
  • Content Relevance: Q2, Q5, Q8
  • Learning Flexibility: Q3, Q6, Q9
  • Skill Development: Q10 (standalone)

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Transformation Pipeline

⭓ Tier 1 – 5→3‑Point Collapse

• Rule: Responses 4–5 → “Agree” (3); 3 → “Neutral” (2); 1–2 → “Disagree” (1).
• Why: Mitigates extreme‑response bias and improves scale symmetry.
• Validation: Kernel‑density plots before and after collapse confirmed more balanced distributions.

■ Tier 2 – Composite Averaging & Re‑Categorization

• Compute Means: Calculate each subscale’s mean score using rowMeans() in R. Q10 retains its single value.
• Re‑Categorize:
  • Mean > 2.33 → 3 (Agree composite)
  • 1.67–2.33 → 2 (Neutral composite)
  • < 1.67 → 1 (Disagree composite)
• Psychometric Check: Cronbach’s α:
  • Usability α = 0.81
  • Relevance α = 0.79
  • Flexibility α = 0.83

◆ Tier 3 – Final Binary Outcome

• High Intent: All four composites equal 3.
• Moderate/Low Intent: Any composite < 3.
• Purpose: Produces a clear binary variable for categorical analysis.

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Application & Statistical Testing

1. Chi‑Square Tests:
   • Compared High vs. Moderate/Low Intent across gender, age group, and course awareness.
   • Example: χ²(1) = 8.54, p = 0.003 for gender differences.
2. Logistic Regression:
   • Modeled High Intent probability controlling for demographics.
   • Output: OR (95% CI) for prior e‑learning experience = 1.9 (1.3–2.7), p < 0.01.

All analyses were implemented in R (tidyverse, psych, car) and documented in an R Markdown report.

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Discussion

This tiered approach preserves essential variance while satisfying assumptions for categorical methods. Each step’s diagnostics (density plots, reliability statistics, model fit indices) are version‑controlled in Git for full reproducibility.

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Takeaways for Researchers from this multi-stage Likert transformation case

• Document Rules Thoroughly: Use inline comments and diagnostic plots for each transformation.
• Assess Reliability Early: Compute Cronbach’s α before aggregating items.
• Pre‑Register Pipelines: Define collapse rules and cut‑points in your protocol to avoid post‑hoc bias.
• Automate with Code: Encapsulate each tier in reusable functions (e.g., collapse_likert(), compute_composites()) to streamline updates.

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By applying this multi‑stage Likert‑scale transformation, PhD scholars can convert rich attitudinal data into valid categorical outcomes—enhancing both analytic rigor and interpretability.

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Want to explore more PhD-level case studies? Check out our Comprehensive Case Studies on PhD Statistical Analysis guide page.