e1

⛔ Prerequisites (v8.2 — MCP Enforcement)

diverga_check_prerequisites("e1") → must return approved: true If not approved → AskUserQuestion for each missing checkpoint (see .claude/references/checkpoint-templates.md)

Checkpoints During Execution

• 🟠 CP_ANALYSIS_PLAN → diverga_mark_checkpoint("CP_ANALYSIS_PLAN", decision, rationale)

Fallback (MCP unavailable)

Read .research/decision-log.yaml directly to verify prerequisites. Conversation history is last resort.

---

E1-Quantitative Analysis Guide

Agent ID: E1 (formerly 10) Category: E - Publication & Communication (Analysis Methods) VS Level: Full (5-Phase) Tier: Flagship Icon: 📈📊

Overview

Comprehensive guide for both quantitative and qualitative analysis methods appropriate for research design and data characteristics. Applies VS-Research methodology to avoid monotonous analyses like "recommend t-test" or "just do thematic analysis," presenting methodological diversity optimized for research questions across paradigms.

VS-Research 5-Phase Process

Phase 0: Context Collection (MANDATORY)

Must collect before VS application:

Required Context:
  - research_question: "Relationship/difference to analyze"
  - independent_variable: "Type (continuous/categorical), number of levels"
  - dependent_variable: "Type (continuous/categorical), number of levels"
  - design: "Independent/Repeated/Mixed"

Optional Context:
  - control_variables: "Covariate list"
  - sample_size: "Current or expected N"
  - target_journal: "Target journal level"

Phase 1: Modal Analysis Method Identification

Purpose: Explicitly identify the most predictable "obvious" analysis methods

## Phase 1: Modal Analysis Method Identification

⚠️ **Modal Warning**: The following are the most commonly used analyses for this design:

| Modal Method | T-Score | Usage Rate | Limitation |
|--------------|---------|------------|------------|
| [Method1] | 0.92 | 60%+ | [Limitation] |
| [Method2] | 0.88 | 25%+ | [Limitation] |

➡️ Confirming if this is optimal and exploring more suitable alternatives.

Phase 2: Long-Tail Analysis Method Sampling

Purpose: Present alternatives at 3 levels based on T-Score

## Phase 2: Long-Tail Analysis Method Sampling

**Direction A** (T ≈ 0.7): Standard but enhanced analysis
- [Method]: [Description]
- Advantages: Familiar to reviewers, slight improvements
- Suitable for: Conservative journals

**Direction B** (T ≈ 0.45): Modern alternatives
- [Method]: [Description]
- Advantages: Methodological contribution, more accurate inference
- Suitable for: Methodology-oriented journals

**Direction C** (T < 0.3): Innovative approaches
- [Method]: [Description]
- Advantages: Latest methodology, high differentiation
- Suitable for: Top-tier journals

Phase 3: Low-Typicality Selection

Purpose: Select method most appropriate for research question and data

Selection Criteria:

1. Statistical Fit: Assumption satisfaction, data characteristics
2. Research Question Alignment: Optimal for hypothesis testing
3. Methodological Contribution: Differentiation potential
4. Feasibility: Software, expertise

Phase 4: Execution

Purpose: Provide specific guidance for selected analysis method

## Phase 4: Analysis Execution Guide

### Primary Analysis Method

[Specific guidance]

### Assumption Checks

[Procedures and code]

### Effect Size

[Calculation and interpretation]

Phase 5: Suitability Verification

Purpose: Confirm final selection is optimal for research

## Phase 5: Suitability Verification

✅ Modal Avoidance Check:
- [ ] "Was basic t-test/ANOVA sufficient?" → Review complete
- [ ] "Are there more suitable modern alternatives?" → Review complete
- [ ] "Is methodological contribution possible?" → Confirmed

✅ Quality Check:
- [ ] Statistical assumptions satisfied? → YES
- [ ] Accurately answers research question? → YES
- [ ] Defensible in peer review? → YES

---

Typicality Score Reference Table

Quantitative Analysis Method T-Score

T > 0.8 (Modal - Explore Alternatives):
├── Independent t-test
├── One-way ANOVA
├── OLS Regression (simple)
├── Pearson correlation
└── Chi-square test

T 0.5-0.8 (Established - Situational):
├── Factorial ANOVA
├── ANCOVA
├── Multiple regression
├── Hierarchical regression
├── Repeated measures ANOVA
├── Mixed ANOVA
└── Traditional Meta-analysis

T 0.3-0.5 (Modern - Recommended):
├── Hierarchical Linear Modeling (HLM/MLM)
├── Structural Equation Modeling (SEM)
├── Latent Growth Modeling
├── Bayesian regression
├── Mixed-effects models
├── Meta-Analytic SEM (MASEM)
├── Propensity Score Matching
└── Robust methods (bootstrapping)

T < 0.3 (Innovative - For Top-tier):
├── Bayesian methods (full)
├── Causal inference (IV, RDD, DiD)
├── Machine Learning + inference (SHAP, causal forests)
├── Network analysis
├── Computational modeling
└── Novel hybrid methods (Double ML, Targeted learning)

Qualitative Analysis Method T-Score

T > 0.8 (Modal - Explore Alternatives):
├── Generic thematic analysis
├── Basic content analysis
├── Descriptive coding
└── Simple categorization

T 0.5-0.8 (Established - Situational):
├── Braun & Clarke thematic analysis (6-phase)
├── Grounded theory (Strauss & Corbin)
├── Directed content analysis
├── Narrative analysis (thematic)
├── Framework analysis
└── Template analysis

T 0.3-0.5 (Modern - Recommended):
├── Interpretative Phenomenological Analysis (IPA)
├── Constructivist grounded theory (Charmaz)
├── Structural narrative analysis
├── Discourse analysis
├── Reflexive thematic analysis
└── Abductive analysis

T < 0.3 (Innovative - For Top-tier):
├── Critical discourse analysis (CDA)
├── Foucauldian discourse analysis
├── Situational analysis (Clarke)
├── Dialogic/performance narrative analysis
├── Computational text analysis + qualitative interpretation
├── Visual discourse analysis
└── Multimodal analysis

---

Input Requirements

For Quantitative Analysis

Required:
  - research_question: "Relationship/difference to analyze"
  - independent_variable: "Type (continuous/categorical), number of levels"
  - dependent_variable: "Type (continuous/categorical), number of levels"

Optional:
  - control_variables: "Covariate list"
  - design: "Independent/Repeated/Mixed"
  - sample_size: "Current or expected N"
  - target_journal: "Target journal level"

For Qualitative Analysis

Required:
  - research_question: "Phenomenon/experience to explore"
  - data_type: "Interviews/Focus groups/Documents/Visual/Observational"
  - sample_size: "N participants or texts"

Optional:
  - paradigm: "Interpretive/Critical/Constructivist/Positivist"
  - prior_theory: "Deductive approach with existing framework?"
  - software_preference: "NVivo/ATLAS.ti/MAXQDA/Manual"
  - team_coding: "Multiple coders? Y/N"

---

Output Format (VS-Enhanced)

## Statistical Analysis Guide (VS-Enhanced)

---

### Phase 1: Modal Analysis Method Identification

⚠️ **Modal Warning**: The following are most commonly recommended analyses for this design:

| Modal Method | T-Score | Limitation in This Study |
|--------------|---------|--------------------------|
| [Method1] | 0.92 | [Specific limitation] |
| [Method2] | 0.88 | [Specific limitation] |

➡️ Confirming if this is optimal and exploring more suitable alternatives.

---

### Phase 2: Long-Tail Analysis Method Sampling

**Direction A** (T = 0.72): [Standard Enhanced Method]
- Method: [Specific method]
- Advantages: [Strengths]
- Suitable for: [Target]

**Direction B** (T = 0.48): [Modern Alternative]
- Method: [Specific method]
- Advantages: [Strengths]
- Suitable for: [Target]

**Direction C** (T = 0.28): [Innovative Approach]
- Method: [Specific method]
- Advantages: [Strengths]
- Suitable for: [Target]

---

### Phase 3: Low-Typicality Selection

**Selection**: Direction [B] - [Method name] (T = [X.X])

**Selection Rationale**:
1. [Rationale 1 - Statistical fit]
2. [Rationale 2 - Research question alignment]
3. [Rationale 3 - Feasibility]

---

### Phase 4: Analysis Execution Guide

#### 1. Analysis Overview

| Item | Content |
|------|---------|
| Research Question | [Question] |
| Independent Variable | [Variable name] (Type: [Continuous/Categorical], Levels: [N]) |
| Dependent Variable | [Variable name] (Type: [Continuous/Categorical]) |
| Control Variables | [Variable name] |
| Design | [Independent/Repeated/Mixed] |

#### 2. Recommended Analysis Method

**Primary Analysis**: [Method name]

**Selection Rationale**:
- [Rationale 1]
- [Rationale 2]

**Alternative** (if assumptions violated): [Alternative method]

#### 3. Assumption Check Procedures

##### Normality
- **Test**: Shapiro-Wilk (N < 50) / K-S (N ≥ 50)
- **Visualization**: Q-Q plot, histogram

```r
# R code
shapiro.test(data$DV)
qqnorm(data$DV); qqline(data$DV)

• Interpretation: p > .05 → Normality satisfied
• If violated: [Non-parametric alternative] or bootstrapping

Homogeneity of Variance

• Test: Levene's test

library(car)
leveneTest(DV ~ Group, data = data)

• Interpretation: p > .05 → Homogeneity satisfied
• If violated: Welch's correction / robust SE

[Additional assumptions...]

4. Power Analysis

A Priori Analysis

Parameter	Value
Expected effect size	[d = / η² = / f² = ]
Significance level (α)	.05
Power (1-β)	.80
Required sample size	N = [calculated value]

# G*Power or R pwr package
library(pwr)
pwr.t.test(d = 0.5, sig.level = 0.05, power = 0.80, type = "two.sample")

Sensitivity Analysis

• Minimum detectable effect size with current N: [d = ]

5. Analysis Code

# R code - Primary analysis
library(tidyverse)
library(effectsize)

# 1. Load data
data <- read_csv("data.csv")

# 2. Descriptive statistics
data %>%
  group_by(Group) %>%
  summarise(
    n = n(),
    mean = mean(DV),
    sd = sd(DV)
  )

# 3. Primary analysis
model <- [analysis function]

# 4. Effect size
[effect size calculation code]

# Python code (alternative)
import pandas as pd
import scipy.stats as stats
import pingouin as pg

# [Same analysis in Python]

6. Effect Size Interpretation

Effect Size	Value	Interpretation (Cohen's criteria)	Practical Meaning
[Metric]	[Value]	[Small/Medium/Large]	[Interpretation]

Interpretation Criteria (Cohen, 1988):

Metric	Small	Medium	Large
d	0.2	0.5	0.8
η²	.01	.06	.14
r	.10	.30	.50
f²	.02	.15	.35

7. Multiple Comparisons (if applicable)

Correction Method: [Bonferroni / Tukey / FDR]

• Number of comparisons: [k]
• Corrected α: [α/k or FDR adjusted]

# R code - Multiple comparison correction
p.adjust(p_values, method = "BH")  # Benjamini-Hochberg FDR

8. Results Reporting Format (APA 7th)

[Analysis method] results showed [statistic] was statistically significant[/not significant],
[statistic = X.XX, p = .XXX, effect size = X.XX, 95% CI [X.XX, X.XX]].

Example (selected analysis): "[Method name] results showed that [variable]'s effect on [variable] was statistically significant, [statistic], [effect size], 95% CI [X.XX, X.XX]."

---

Phase 5: Suitability Verification

✅ Modal Avoidance Check:

• Confirmed selection rationale for [selected analysis] over basic analysis
• Reviewed more suitable modern alternatives
• Confirmed methodological contribution potential

✅ Quality Assurance:

• Assumption check procedures included
• Effect size and confidence interval calculations
• APA format results reporting prepared

---

## Qualitative Analysis Methods (NEW in v5.0)

### Thematic Analysis

**Approach**: Braun & Clarke 6-Phase Framework

```yaml
thematic_analysis:
  phases:
    phase_1_familiarization:
      activities:
        - "Read and re-read data"
        - "Note initial ideas"
        - "Immerse in content"
      output: "Familiarization notes"

    phase_2_coding:
      activities:
        - "Generate initial codes systematically"
        - "Code interesting features"
        - "Collate data relevant to each code"
      output: "Coded data extracts"
      tools: ["NVivo", "ATLAS.ti", "MAXQDA", "Dedoose"]

    phase_3_searching_themes:
      activities:
        - "Collate codes into potential themes"
        - "Gather data relevant to each theme"
      output: "List of candidate themes"

    phase_4_reviewing_themes:
      activities:
        - "Check themes work with coded extracts"
        - "Generate thematic map"
      output: "Refined themes and thematic map"

    phase_5_defining_naming:
      activities:
        - "Define and refine each theme"
        - "Generate clear definitions"
        - "Name themes"
      output: "Theme definitions and names"

    phase_6_writing:
      activities:
        - "Final analysis"
        - "Select vivid extracts"
        - "Relate to research question and literature"
      output: "Scholarly report"

  quality_criteria:
    - "Theoretical coherence"
    - "Richness of interpretation"
    - "Member checking (optional)"
    - "Audit trail"

  software_comparison:
    nvivo:
      strengths: ["Rich visualization", "Matrix coding", "Framework matrices"]
      best_for: "Large qualitative datasets"

    atlas_ti:
      strengths: ["Hermeneutic unit", "Network views", "Query tools"]
      best_for: "Grounded theory and complex theory building"

    maxqda:
      strengths: ["Mixed methods", "Visual tools", "TeamCloud"]
      best_for: "Mixed methods research"

    dedoose:
      strengths: ["Web-based", "Collaboration", "Mixed methods"]
      best_for: "Team-based coding"

Grounded Theory Analysis

grounded_theory_analysis:
  approaches:
    strauss_corbin:
      paradigm_model:
        - "Causal conditions"
        - "Phenomenon"
        - "Context"
        - "Intervening conditions"
        - "Action/interaction strategies"
        - "Consequences"
      coding_process: "Systematic and structured"

    charmaz_constructivist:
      focus: "Social construction of meaning"
      coding_process: "Flexible and emergent"
      emphasis: "Researcher reflexivity"

    glaser_classic:
      focus: "Theory emergence from data"
      coding_process: "Minimally structured"
      emphasis: "Theoretical sensitivity"

  coding_types:
    open_coding:
      purpose: "Breaking down, examining, comparing, conceptualizing data"
      output: "Concepts and categories"
      techniques:
        - "Line-by-line coding"
        - "Incident-by-incident coding"
        - "Constant comparison"

    axial_coding:
      purpose: "Relating categories to subcategories"
      output: "Paradigm model relationships"
      techniques:
        - "Linking categories"
        - "Identifying conditions-actions-consequences"

    selective_coding:
      purpose: "Integrating and refining theory"
      output: "Core category and theoretical framework"
      techniques:
        - "Storyline development"
        - "Theory integration"

  memo_writing:
    purpose: "Develop theoretical sensitivity and capture analytic thinking"
    types:
      - "Code notes (what code means)"
      - "Theoretical notes (conceptual thinking)"
      - "Operational notes (procedures)"
    frequency: "Continuous throughout coding"

  theoretical_saturation:
    definition: "No new themes/categories emerging from data"
    indicators:
      - "New data fits existing categories"
      - "Categories well-developed"
      - "Relationships between categories clear"

Content Analysis

content_analysis:
  approaches:
    deductive:
      process: "Theory-driven coding scheme applied to data"
      use_when: "Testing existing theory or frameworks"
      steps:
        - "Develop coding scheme from theory"
        - "Define categories and rules"
        - "Train coders"
        - "Code data"
        - "Calculate reliability"

    inductive:
      process: "Coding scheme emerges from data"
      use_when: "Exploratory research"
      steps:
        - "Immerse in data"
        - "Identify patterns"
        - "Create categories"
        - "Define coding rules"
        - "Code data"

    directed:
      process: "Hybrid - start with theory, allow emergence"
      use_when: "Extending existing theory"

  units_of_analysis:
    analysis_unit:
      definition: "What to count (theme, word, paragraph, entire text)"
      examples: ["Sentence", "Paragraph", "Entire article", "Tweet"]

    coding_unit:
      definition: "Smallest element counted"
      examples: ["Word", "Phrase", "Sentence"]

    context_unit:
      definition: "Boundary for interpreting coding unit"
      examples: ["Paragraph surrounding sentence", "Entire article"]

  reliability_measures:
    krippendorff_alpha:
      use: "Multiple coders, any level of measurement"
      interpretation:
        - "α ≥ 0.80: Acceptable"
        - "α ≥ 0.67: Tentatively acceptable (exploratory)"
      formula: "1 - (Observed disagreement / Expected disagreement)"

    cohen_kappa:
      use: "Two coders, nominal/ordinal data"
      interpretation:
        - "κ < 0.40: Poor"
        - "κ 0.40-0.59: Fair"
        - "κ 0.60-0.74: Good"
        - "κ ≥ 0.75: Excellent"

    percent_agreement:
      use: "Simple reliability estimate (not recommended alone)"
      interpretation: "≥ 80% often used, but doesn't account for chance"

Narrative Analysis

narrative_analysis:
  approaches:
    structural:
      focus: "Organization and structure of narratives"
      frameworks:
        - "Labov's narrative structure (abstract, orientation, complication, evaluation, resolution, coda)"
        - "Burke's dramatistic pentad (act, scene, agent, agency, purpose)"
      analysis_focus: "How story is told"

    thematic:
      focus: "What is told (content)"
      approach: "Identify themes across narratives"
      similarity_to: "Thematic analysis of narrative data"

    dialogic_performance:
      focus: "Interactive context of storytelling"
      emphasis:
        - "Who tells to whom"
        - "When and why"
        - "Co-construction of narrative"

    visual_narrative:
      focus: "Visual storytelling (photos, videos, drawings)"
      methods:
        - "Visual discourse analysis"
        - "Multimodal analysis"

  analytical_elements:
    plot:
      definition: "Sequence of events and how connected"
      questions:
        - "What is the main storyline?"
        - "How are events causally linked?"

    temporality:
      definition: "How time is constructed in narrative"
      aspects:
        - "Chronology vs. flashbacks"
        - "Duration and frequency"
        - "Temporal markers"

    character:
      definition: "Roles and development of actors"
      analysis:
        - "Protagonist/antagonist"
        - "Character agency"
        - "Transformation over time"

    setting:
      definition: "Physical, temporal, social context"
      importance: "How setting shapes narrative"

---

Advanced Quantitative Methods (NEW in v5.0)

Bayesian Analysis

bayesian_analysis:
  core_concept: "Update beliefs with data using Bayes' theorem"

  packages:
    r_packages:
      brms:
        description: "Bayesian Regression Models using Stan"
        strengths: ["Flexible syntax", "Multilevel models", "Great documentation"]
        example: |
          library(brms)
          fit <- brm(y ~ x + (1|group), data = data,
                     family = gaussian(),
                     prior = c(prior(normal(0, 10), class = b)))

      rstanarm:
        description: "Applied Regression Modeling via Stan"
        strengths: ["Easy syntax", "Pre-compiled models", "Fast"]

    python_packages:
      pymc:
        description: "Probabilistic programming in Python"
        strengths: ["Flexible", "Large community", "Integration with ArviZ"]
        example: |
          import pymc as pm
          with pm.Model() as model:
              beta = pm.Normal('beta', mu=0, sigma=10)
              sigma = pm.HalfNormal('sigma', sigma=1)
              y_obs = pm.Normal('y_obs', mu=beta*x, sigma=sigma, observed=y)
              trace = pm.sample(2000)

  use_cases:
    prior_incorporation:
      description: "Incorporate existing knowledge as priors"
      example: "Meta-analysis results as priors for new study"

    small_samples:
      description: "Better uncertainty quantification with limited data"
      advantage: "Regularization prevents overfitting"

    complex_hierarchical:
      description: "Natural fit for multilevel/hierarchical models"
      advantage: "Partial pooling and shrinkage"

  advantages:
    - "Quantifies uncertainty via posterior distributions"
    - "Incorporates prior knowledge formally"
    - "No p-values or significance testing"
    - "Intuitive probability statements (e.g., '95% probability effect > 0')"

  reporting:
    elements:
      - "Prior specification and justification"
      - "Posterior distributions (median, 95% credible intervals)"
      - "Convergence diagnostics (Rhat, ESS)"
      - "Posterior predictive checks"

Machine Learning for Inference

machine_learning:
  paradigm_shift: "Prediction-focused, but can support causal inference"

  techniques:
    random_forest:
      use_for: "Variable importance, non-linear relationships"
      interpretation: ["Feature importance via Gini/permutation", "Partial dependence plots"]
      packages: ["randomForest (R)", "scikit-learn (Python)"]

    support_vector_machines:
      use_for: "Classification with complex boundaries"
      kernels: ["Linear", "Polynomial", "RBF"]
      packages: ["e1071 (R)", "scikit-learn (Python)"]

    neural_networks:
      use_for: "Complex non-linear patterns, image/text data"
      architectures: ["Feedforward", "CNN", "RNN/LSTM"]
      packages: ["keras/tensorflow", "pytorch"]

    gradient_boosting:
      use_for: "High-performance prediction, structured data"
      implementations: ["XGBoost", "LightGBM", "CatBoost"]
      advantage: "State-of-the-art performance on tabular data"

  validation_strategies:
    cross_validation:
      k_fold:
        description: "Split data into k folds, rotate train/test"
        typical_k: "5 or 10"

      stratified:
        description: "Preserve class proportions in each fold"
        use_when: "Imbalanced outcome variable"

      leave_one_out:
        description: "Use n-1 observations to predict 1"
        use_when: "Very small sample sizes"

    holdout:
      description: "Single train/test split (e.g., 80/20)"
      use_when: "Large datasets"

    bootstrap:
      description: "Resample with replacement"
      use_for: "Uncertainty estimation, small samples"

  interpretation_tools:
    shap_values:
      description: "Shapley Additive Explanations"
      advantage: "Game-theoretic, consistent feature attribution"
      packages: ["shap (Python)", "fastshap (R)"]
      use: "Explain individual predictions and global patterns"

    feature_importance:
      methods:
        - "Permutation importance (model-agnostic)"
        - "Gini importance (tree-based)"
        - "Coefficient magnitude (linear models)"

    partial_dependence:
      description: "Marginal effect of feature on prediction"
      packages: ["pdp (R/Python)", "iml (R)"]

    lime:
      description: "Local Interpretable Model-agnostic Explanations"
      use: "Explain individual predictions via local linear approximation"

  causal_ml:
    double_machine_learning:
      description: "Use ML for nuisance parameters, preserve inference"
      packages: ["DoubleML (Python/R)"]