Rct Core Design

RCTs answer "does X cause Y?" with minimal assumptions.

import numpy as np
from scipy.stats import norm

# Parameters
alpha = 0.05  # Significance level
power = 0.80  # Statistical power
mde = 0.25  # Minimum detectable effect (SD units)
p = 0.50  # Proportion assigned to treatment

# Calculate critical values
z_alpha = norm.ppf(1 - alpha/2)  # Two-tailed test
z_power = norm.ppf(power)

# Basic sample size
n_base = ((z_alpha + z_power)**2) / (p * (1-p) * mde**2)

# Adjust for clustering if applicable
icc = 0.05  # Intra-cluster correlation
cluster_size = 30  # Average cluster size
design_effect = 1 + (cluster_size - 1) * icc
n_clusters = n_base * design_effect / cluster_size

# Adjust for attrition
attrition_rate = 0.20
n_final = n_base * design_effect / (1 - attrition_rate)

print(f"POWER ANALYSIS FOR RCT")
print(f"Parameters: α={alpha}, power={power}, MDE={mde} SD")
print(f"\nBase sample size: {int(np.ceil(n_base))}")
print(f"Design effect: {design_effect:.2f}")
print(f"Clusters needed: {int(np.ceil(n_clusters))}")
print(f"Final N (with attrition): {int(np.ceil(n_final))}")

return int(np.ceil(n_final)),

</code_template>

</implementation_pattern>

<examples>

<example context="ethical_design" difficulty="intermediate">
<description>Design RCT when direct denial of treatment raises ethical concerns</description>
<code>
```python
@app.cell
def ethical_rct_design():
    # Use phase-in design when denying treatment is ethically problematic
    # All units eventually receive treatment, but timing is randomized

    import pandas as pd
    import numpy as np

    # Context: Limited program slots, everyone gets treatment eventually
    # Solution: Randomize TIMING rather than ACCESS

    n_units = 300
    n_cohorts = 3  # Roll out in 3 waves

    # Assign units to cohorts randomly
    cohorts = np.random.choice(range(n_cohorts), size=n_units)

    # Cohort 1: Immediate (Year 1)
    # Cohort 2: Delayed (Year 2)
    # Cohort 3: Delayed (Year 3)

    df = pd.DataFrame({
        'unit_id': range(n_units),
        'cohort': cohorts,
        'year_treated': cohorts + 1  # Everyone gets treatment
    })

    print("PHASE-IN / STEPPED WEDGE DESIGN")
    print("=" * 50)
    print(df.groupby('cohort').size())

    print("\nEthical advantages:")
    print("- No one permanently denied treatment")
    print("- Addresses capacity constraints")
    print("- Still enables causal inference")

    print("\nAnalysis approach:")
    print("- Compare early vs. late cohorts")
    print("- Use DID or event study framework")
    print("- Longer follow-up for early cohorts")

    return df,