power_analysis_formula:
  required_inputs:
    - alpha: 0.05 (Type I error rate)
    - power: 0.80 (1 - Type II error)
    - effect_size: Small (0.2), Medium (0.5), Large (0.8) - Cohen's d
    - tails: One-tailed vs. two-tailed

  tools:
    - G*Power (free software)
    - R package: pwr
    - Online calculators

  typical_results:
    t_test_medium_effect: "n ≈ 64 per group"
    ANOVA_3groups_medium: "n ≈ 52 per group"
    correlation_medium: "n ≈ 85"

survey_research:
  simple_estimate: "n ≥ 384 for 95% CI, ±5% margin"
  stratified: "30-50 per stratum minimum"

regression_analysis:
  green_rule: "n ≥ 50 + 8k (k = number of predictors)"
  harris_rule: "n ≥ 104 + k"

SEM_confirmatory:
  minimum: "n ≥ 200"
  recommended: "10-20 observations per parameter"

exploratory_factor:
  minimum: "n ≥ 100"
  recommended: "5-10 participants per item"

constraints:
  budget: "Cost per participant × n ≤ total budget"
  time: "Data collection time × n ≤ timeline"
  attrition: "Recruit 20-30% more to account for dropout"

adjustment_for_design_effect:
  cluster_sampling: "Multiply SRS sample size by (1 + (m-1)×ICC)"
  # m = cluster size, ICC = intraclass correlation

saturation_guidance:
  phenomenology:
    range: "5-25 participants"
    rationale: "In-depth lived experience, rich data per case"

  grounded_theory:
    range: "20-30 participants"
    stop_when: "No new codes emerge (theoretical saturation)"

  case_study:
    range: "1-4 cases"
    rationale: "Deep contextualized understanding"

  ethnography:
    range: "Field-specific (months to years of immersion)"

  narrative_inquiry:
    range: "1-10 participants"
    rationale: "Story-based, rich narratives"

We will recruit approximately [N] participants because:
1. [Type of qualitative approach] typically requires [range] participants
2. Our population is [homogeneous/heterogeneous], justifying [lower/higher] end
3. We will monitor for saturation after [N-5] interviews
4. Data collection will stop when no new themes emerge in [3 consecutive interviews]

exploratory_sequential:
  phase_1_qual: "12-20 (develop instrument/framework)"
  phase_2_quant: "Power analysis based on phase 1 findings"

explanatory_sequential:
  phase_1_quant: "Power analysis (priority strand)"
  phase_2_qual: "5-15 (explain quantitative results)"

convergent_parallel:
  quantitative: "Meet power requirements (e.g., 200+)"
  qualitative: "Meet saturation (e.g., 15-25)"
  rationale: "Both strands equally important"

joint_display:
  consider: "How will qual and quant data be integrated?"
  ensure: "Sufficient overlap in participant characteristics"

paradigm_decision:
  quantitative:
    goal: "Generalize to population"
    prefer: "Probability sampling"
    size: "Power analysis"

  qualitative:
    goal: "In-depth understanding"
    prefer: "Purposive sampling"
    size: "Saturation"

  mixed_methods:
    goal: "Integration of breadth and depth"
    strategy: "Separate plans for each strand"

purpose_to_strategy:
  generalize_to_population:
    required: "Probability sampling (random)"
    options: ["SRS", "stratified", "cluster"]

  understand_phenomenon_depth:
    preferred: "Purposive sampling"
    options: ["maximum_variation", "typical_case"]

  build_theory_iteratively:
    required: "Theoretical sampling"
    paradigm: "Grounded theory"

  explore_hard_to_reach_group:
    preferred: "Snowball or RDS"

  compare_subgroups:
    required: "Stratified sampling (ensure sufficient n per group)"

access_constraints:
  complete_sampling_frame_available:
    yes: "SRS or stratified possible"
    no: "Consider convenience or purposive"

  geographically_dispersed:
    yes: "Cluster or multistage sampling"
    no: "SRS or systematic"

  nested_structure:
    yes: "Multilevel sampling (e.g., schools → students)"
    account_for: "Design effect in sample size"

  hard_to_identify:
    yes: "Snowball, respondent-driven"

## Sampling Strategy for [Study Title]

### 1. Research Paradigm and Purpose
- **Paradigm**: [Quantitative / Qualitative / Mixed Methods]
- **Purpose**: [Generalize / Understand / Build Theory / Explore]

---

### 2. Sampling Method

**Selected Method**: [e.g., Stratified Random Sampling]

**Rationale**:
- Population is heterogeneous with known subgroups (age, gender)
- Need to ensure representation of all strata
- Sampling frame available from [source]

**Procedure**:
1. Divide population into strata: [list strata]
2. Determine sample size per stratum (proportionate allocation)
3. Use random number generator for selection within each stratum

---

### 3. Sample Size Justification

**Target Sample Size**: [N]

**Calculation Method**:
- **Quantitative**:
  - Power analysis using G*Power
  - α = 0.05, power = 0.80, effect size = [medium/0.5]
  - Result: n = [X] per group
  - Total with 20% attrition buffer: [N]

- **Qualitative**:
  - Phenomenological study requires 5-25 participants
  - Target 15 participants (mid-range for moderate heterogeneity)
  - Monitor for saturation after interview 10

**Supporting Evidence**:
- [Cite relevant methodological literature]
- Similar studies in field used n = [range]

---

### 4. Inclusion/Exclusion Criteria

**Inclusion**:
- [List criteria, e.g., Age 18+, English proficiency, etc.]

**Exclusion**:
- [List criteria]

---

### 5. Recruitment Strategy

**Recruitment Sources**: [e.g., University registry, online forums]

**Recruitment Materials**: [Flyers, emails, social media posts]

**Compensation**: [If applicable, e.g., $20 gift card]

---

### 6. Limitations and Mitigation

**Potential Biases**:
- [e.g., Self-selection bias in online recruitment]

**Mitigation**:
- [e.g., Diversify recruitment channels, compare respondents to non-respondents]

---

### 7. Ethical Considerations

- IRB approval obtained: [Yes/No]
- Informed consent process: [Description]
- Confidentiality measures: [Data storage, de-identification]