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Statistical Power and Sample Size for Model Experiments
Statistical power is the probability an experiment detects a specified effect under its assumptions, and sample-size planning estimates how much data are needed for a chosen error rate and detectable effect.
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Model experiments need plans that account for outcome variance, assignment unit, repeated measurements and multiple metrics rather than relying on a universal sample count.
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Power analysis connects the effect an experiment is designed to detect with sample size, outcome variability, significance threshold and statistical power. Power is 1 minus the Type II error probability under a specified alternative. It is not the probability that a result is true. A minimum detectable effect (MDE) is the effect size used in planning; choosing an MDE expresses a decision threshold about the smallest change worth detecting. For two independent equal-sized groups comparing a continuous mean with common standard deviation sigma, a rough normal-approximation sample size per arm is 2*(z_(1-alpha/2)+z_(1-beta))^2*sigma^2/delta^2 for a two-sided test. With alpha 0.05, power 0.80, sigma 10 and delta 2, z values are about 1.96 and 0.84. The calculation is 2*(2.8)^2*100/4, about 392 per group. This is a hypothetical approximation, not a universal prescription; exact tests, unequal allocation, baseline adjustment and finite samples change requirements. Binary outcomes, heavy-tailed metrics, repeated measures, cluster assignment and low traffic require suitable methods. If users are grouped by team or region, correlated outcomes reduce effective information. Multiple metrics or variant comparisons may require multiplicity planning. Experiment duration also depends on traffic patterns, seasonality, label delay and the need to cover full behavioral cycles. Estimate variance and baseline rates from relevant historical data, define primary and guardrail metrics, randomization unit, alpha, power and MDE before launch. Avoid repeatedly checking conventional fixed-horizon p-values and stopping as soon as significance appears unless using a valid sequential method. Report achieved sample size, confidence intervals and uncertainty. Underpowered experiments can miss meaningful effects; very large experiments can detect changes too small to matter. Statistical power supports a plan, but decision value also depends on operational costs, harms and the quality of measurement.
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The Future of Statistical Power and Sample Size for Model Experiments
Experiment planning can improve when teams tie the MDE to a meaningful product decision, use current variance estimates and simulate traffic, clustering and delayed outcomes. Pre-registration of primary outcomes and stopping rules makes results easier to interpret. Analysts should report confidence intervals and practical impact alongside p-values. As model experiments grow more complex, sequential and variance-reduction methods can shorten evaluation when correctly designed. A transparent power calculation helps set expectations for duration and uncertainty before user exposure begins. Record the analysis plan before traffic begins.
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For a hypothetical two-arm experiment with a continuous outcome, standard deviation 10, two-sided alpha 0.05 and 80% power to detect a mean difference of 2, a normal approximation gives roughly 392 independent observations per arm.
A model change is expected to improve a click rate only slightly. The team calculates required sample size before launching and extends the experiment if the eligible traffic rate implies a longer duration.
A cluster-randomized experiment assigns whole teams rather than people. Within-team similarity reduces effective sample size, so the plan accounts for clustering rather than treating every person as independent.
A team tests many model variants and metrics. It adjusts the experiment design or narrows primary outcomes because multiple comparisons and repeated peeking can increase false-positive risk.
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What is Statistical Power and Sample Size for Model Experiments?
Statistical power is the probability an experiment detects a specified effect under its assumptions, and sample-size planning estimates how much data are needed for a chosen error rate and detectable effect. Model experiments need plans that account for outcome variance, assignment unit, repeated measurements and multiple metrics rather than relying on a universal sample count.
In the stated two-arm example, what sample size is approximately required per group?
Using 2*(1.96+0.84)^2*10^2/2^2 gives about 392 observations per arm.
If the target MDE is halved with other assumptions fixed, how does approximate sample size change?
Sample size varies inversely with the square of the effect, so halving it multiplies n by four.
What does 80% power mean under the specified alternative and assumptions?
Power is the probability of detecting the specified effect under the alternative, equal to 1-beta.
What does the MDE represent in planning?
MDE is a planning effect size, not a promise of observed impact.
Why does cluster randomization often require more observations?
Within-cluster correlation reduces effective sample size relative to independent assignments.
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