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The goal of simulator is to estimate power that would be achieved in an A/B test, provided historical sample of a metric and assumed effect size.

This simulator is useful in situations when parametric power estimation (for example using t-test) is not possible due to small sample size (when CLT is not applicable) or non-conventional metric, which can't be parametrized by a known probability distribution.

Inspired byhttps://patreonhq.com/a-framework-to-determine-how-much-data-you-need-for-an-experiment-a20fcd2719eb

Simulator can be used at experiment design or analysis stage to estimate sample size requirements or any other elements influencing statistical power of the test.

Simulator is non-parametric, i.e. doesn't have distribution assumptions. Instead, it uses resampling methods on snapshot of historical data to perform the analysis.

Inputs:

• Historical sample of custom metric.
• Sample size.
• Control/target split ratio.
• Significance level of a test - alpha (probability of false positive).
• Minimum detectable uplift.

Output: statistical power.

• Obtain historical snapshot of metric.

• Set required significance level (e.g. 0.05).

• Set minimum effect size.

• Set control/target split ratio

• Iterativelychange sample size in simulator with fixed significance, effect size and ratio to achieve the desired power.

The simulator is based on framework from Patreon, with additional improvements.

Additions contain specific implementations and improvements ofTreated treatment group andPerform statistical procedure parts:

Group treatment is applyingminimum detectable effect to the response metric of untreated group.

Current implementation applies constant uplift (e.g. 10%) to the response metric. In reality, uplift is not constant, but rather random variable with specific mean and dispersion.

In order to simulate this behavior, instead of using flat (constant) uplift - the response metric is bootstrapped at each round of simulation. This addition improves significantly accuracy of the simulator.

Following statistical test is implemented in simulator:

• Two sample, one side permutation test - can be used with arbitrary shaped distributions of metrics, and as upper bound limit for Bayesian A/B tests. Most generic and slowest test.

using PowerSimulatorusing Distributionsusing Statistics# Generate dummy historical sample, drawn from Normal distribution. In practice, should be replaced by snapshot of historical data.hsample=rand(Normal(50.0,20.0),10000)sample_size=2000# Total sample size, control+targetsplit_ratio=0.5# Split ratio control/target group. In this case 50%/50%.effect_size=0.03# Assume 3% effect size.alpha=0.05# Significance level.Controls type I error. Maximum probability of false positive.n_iterations=1000# number of iterations for bootstrap procedure.n_permutations=1000# number of draws for permutation procedure# Call multi-threaded version of simulator.@time outcomes, p_values=simulate_power_threads(hsample, sample_size ,alpha, effect_size, split_ratio, n_iterations, n_permutations)# Calculate power by taking mean of individual outocmes.print("Achieved power:",mean(outcomes))