causalis.shared.rct_design.mde.calculate_mdecalculate_mde
Calculate the Minimum Detectable Effect (MDE) for conversion or continuous data_contracts.
Parameters
- sample_sizeint or tuple of int
Total sample size or a tuple of (control_size, treatment_size). If a single integer is provided, the sample will be split according to the ratio parameter.
- baseline_ratefloat, optional
Baseline conversion rate (for conversion data_contracts) or baseline mean (for continuous data_contracts). Required for conversion data_contracts.
- variancefloat or tuple of float, optional
Variance of the data_contracts. For conversion data_contracts, this is calculated from the baseline rate if not provided. For continuous data_contracts, this parameter is required. Can be a single float (assumed same for both groups) or a tuple of (control_variance, treatment_variance).
- alphafloat, default 0.05
Significance level (Type I error rate).
- powerfloat, default 0.8
Statistical power (1 - Type II error rate).
- data_typestr, default ‘conversion’
Type of data_contracts. Either ‘conversion’ for binary/conversion data_contracts or ‘continuous’ for continuous data_contracts.
- ratiofloat, default 0.5
Ratio of the sample allocated to the control group if sample_size is a single integer.
Returns
A dictionary containing: - ‘mde’: The minimum detectable effect (absolute) - ‘mde_relative’: The minimum detectable effect as a percentage of the baseline (relative) - ‘parameters’: The parameters used for the calculation
Examples
Calculate MDE for conversion data_contracts with 1000 total sample size and 10% baseline conversion rate
Calculate MDE for continuous data_contracts with 500 samples in each group and variance of 4
Notes
For conversion data_contracts, the MDE is calculated using the formula: MDE = (z_α/2 + z_β) * sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2))
For continuous data_contracts, the MDE is calculated using the formula: MDE = (z_α/2 + z_β) * sqrt((σ1²/n1) + (σ2²/n2))
where:
z_α/2 is the critical value for significance level α
z_β is the critical value for power
p1 and p2 are the conversion rates in the control and treatment groups
σ1² and σ2² are the variances in the control and treatment groups
n1 and n2 are the sample sizes in the control and treatment groups
Canonical target
causalis.shared.rct_design.mde.calculate_mde
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