Case Study: “What If” Scenario Analyses for Likert-Scale Data in a Public Health Dissertation

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1. Study Context & Motivation for this Likert scale what if case study

In a Public Health PhD dissertation, 413 healthcare workers rated their perceptions of operational protocols on a 10-item, 5-point Likert scale. After transforming and aggregating responses into 3-point composites, the core analyses used chi-square tests on a derived categorical “high agreement” variable. Stakeholders then asked:

• What if we defined “high agreement” more stringently?
• What if we included the mid-category (“neutral”) as “agreement”?
• What if we analyzed composite scores as numeric rather than categorical?

To inform robust decision-making, the research team ran three “What If” scenario analyses on the Likert pipeline.

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2. Defining the Scenarios for this Likert scale what if case study

1. Stringent Threshold
   • Original: Only composite scores equal to 3 (“Agree”) qualify as “high agreement.”
   • Variation: Require composite = 3 and item-level scores ≥4 before collapsing.
2. Inclusive Threshold
   • Original: Composite = 3 only.
   • Variation: Treat both composite = 2 (“Neutral”) and 3 as “high agreement,” increasing sample size for inferential tests.
3. Continuous Composite Analysis
   • Original: Composite collapsed to categorical {1,2,3}.
   • Variation: Use the raw composite means (ranging 1–3) in an ordinal logistic regression or linear regression, preserving information.

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3. Software & Workflow for this Likert scale what if case study

3.1 Baseline Pipeline Recap

• Data Prep: likert_transform.R collapses 5→3, computes composites, exports likert_masterchart.csv.
• Inferential: inferential_tests.R runs chi-square on high_agreement vs. hospital_type.

3.2 Implementing “What If” Variations

All variations were orchestrated in an expanded likert_whatif.R script:

df <- read.csv("likert_masterchart.csv")

# Scenario 1: Stringent threshold
df$stringent_agree <- with(df, ifelse(composite_protocol == 3 & 
                                       Q1>=4 & Q4>=4 & Q7>=4, 1, 0))

# Scenario 2: Inclusive threshold
df$inclusive_agree <- with(df, ifelse(composite_protocol >= 2, 1, 0))

# Scenario 3: Continuous composite
# Use composite_protocol as numeric predictor

For each scenario, we ran:

• Chi-Square: chisq.test(table(df$<scenario>_agree, df$hospital_type))
• Ordinal Logistic Regression: MASS::polr(factor(composite_protocol) ~ hospital_type + covariates, data=df)
• Linear Regression: lm(composite_protocol ~ hospital_type + covariates, data=df)

Results and diagnostic plots (mosaic plots, residuals, proportional-odds assumption checks) were exported to /whatif_results/.

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4. Key Findings

Scenario	“High Agreement” Rate (Public)	“High Agreement” Rate (Private)	Statistical Outcome
Baseline	42.2 %	60.1 %	χ²(1)=…, p<0.001
Stringent Threshold	28.6 %	48.9 %	χ²(1)=…, p<0.01 (stronger effect size)
Inclusive Threshold	75.5 %	82.3 %	χ²(1)=…, p=0.05 (effect attenuated)
Continuous Composite	N/A (mean scores)	N/A (mean scores)	OR=2.1 (95 % CI 1.4–3.2) in ordinal model; β=0.35, p<0.001 in linear model

• Stringent Threshold magnified group differences, highlighting the robustness of private-hospital staff’s stronger agreement.
• Inclusive Threshold reduced statistical significance, suggesting mid-scale responders dilute the effect.
• Continuous Analysis preserved scale information, yielding consistent effect estimates and enabling adjustment for covariates (e.g., years of service, age).

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5. Implications & Recommendations

• Threshold Selection Matters: Choice of collapsing rule can substantially alter effect sizes and p-values—researchers should pre-register threshold criteria or perform sensitivity checks.
• Mid-Category Insights: Including “neutral” responses may reflect genuine ambivalence rather than partial agreement; consider reporting both versions.
• Utility of Continuous Models: Treating composites as numeric preserves information and allows for covariate adjustment via regression, offering nuanced insights beyond categorical splits.

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6. Takeaways for “What If” Analyses

1. Parameterize Pipelines: Build flexible scripts (likert_whatif.R) that accept threshold parameters for easy reruns.
2. Automate Diagnostics: For each scenario, automate goodness-of-fit and assumption checks (e.g., proportional-odds test for ordinal models).
3. Document All Variations: Maintain a logbook of scenarios tested, their rules, and resulting metrics to support reproducibility and transparency.
4. Visualize Comparisons: Use side-by-side bar charts and overlaid density plots to illustrate how scenario definitions shift distributions.

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This “What If Variations” case study demonstrates how sensitivity analyses on Likert-scale transformations can strengthen the credibility and applicability of findings in a Public Health dissertation.

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