Experiment Design

Experiment Design

Scientific experiment planning, power analysis, and protocol development.

Design Selection Guide

Power Analysis & Sample Size

pythonCopy code
source /Users/zhangmingda/clawd/.venv/bin/activate
python3 << 'EOF'
from scipy import stats
import numpy as np

# --- Two-sample t-test ---
def sample_size_ttest(effect_size, alpha=0.05, power=0.80):
    """Cohen's d effect sizes: small=0.2, medium=0.5, large=0.8"""
    from scipy.stats import norm
    z_alpha = norm.ppf(1 - alpha/2)
    z_beta = norm.ppf(power)
    n = 2 * ((z_alpha + z_beta) / effect_size) ** 2
    return int(np.ceil(n))

# --- Chi-square test ---
def sample_size_chi2(effect_size, alpha=0.05, power=0.80, df=1):
    """Cohen's w effect sizes: small=0.1, medium=0.3, large=0.5"""
    from scipy.stats import norm, chi2
    z_beta = norm.ppf(power)
    z_alpha = norm.ppf(1 - alpha)
    n = ((z_alpha + z_beta) / effect_size) ** 2
    return int(np.ceil(n))

# --- Correlation ---
def sample_size_correlation(r, alpha=0.05, power=0.80):
    from scipy.stats import norm
    z_alpha = norm.ppf(1 - alpha/2)
    z_beta = norm.ppf(power)
    z_r = 0.5 * np.log((1+r)/(1-r))  # Fisher's z
    n = ((z_alpha + z_beta) / z_r) ** 2 + 3
    return int(np.ceil(n))

# Examples
print(f"t-test (d=0.5): n={sample_size_ttest(0.5)} per group")
print(f"t-test (d=0.3): n={sample_size_ttest(0.3)} per group")
print(f"Chi-square (w=0.3): n={sample_size_chi2(0.3)}")
print(f"Correlation (r=0.3): n={sample_size_correlation(0.3)}")
EOF

Key Design Principles

Controls

• Positive control: Known to produce effect (validates method works)
• Negative control: Known to produce no effect (validates baseline)
• Placebo control: Inert treatment (controls for expectation effects)
• Active control: Existing standard treatment (for superiority/non-inferiority)

Randomization

• Simple: Coin flip / random number
• Block: Ensures equal groups per block
• Stratified: Randomize within strata (age, sex, severity)
• Cluster: Randomize groups, not individuals

Blinding

• Single-blind: Participants don't know assignment
• Double-blind: Participants and researchers don't know
• Triple-blind: Participants, researchers, and analysts don't know

Bias Mitigation

Study Protocol Template

markdownCopy code
# Study Protocol: [Title]

## 1. Background & Rationale
## 2. Objectives & Hypotheses
  - Primary: 
  - Secondary:
## 3. Study Design
  - Type: [RCT / quasi-experiment / observational / ...]
  - Duration:
## 4. Participants
  - Population:
  - Inclusion criteria:
  - Exclusion criteria:
  - Sample size: N = [calculated], power = 0.80, α = 0.05
## 5. Intervention / Exposure
## 6. Outcome Measures
  - Primary:
  - Secondary:
## 7. Randomization & Blinding
## 8. Data Collection Procedures
## 9. Statistical Analysis Plan
  - Primary analysis:
  - Secondary analyses:
  - Handling of missing data:
## 10. Ethical Considerations
  - IRB/Ethics approval:
  - Informed consent:
  - Data privacy:
## 11. Timeline
## 12. Budget

Pre-registration

Recommend pre-registration for confirmatory studies:

• OSF: osf.io (general)
• ClinicalTrials.gov: clinical trials
• PROSPERO: systematic reviews
• AsPredicted: aspredicted.org (quick)

Tips

• Always justify sample size with power analysis
• Pre-register hypotheses and analysis plan
• Plan for 10-20% attrition in sample size calculation
• Document all deviations from protocol
• Consider pilot study for novel methods