Model Evaluation Sample Size Calculator

Introduction to labeled test-set planning for model comparison

Comparing a baseline model with a challenger is not simply a matter of noticing which accuracy is larger on a small validation split. A modest apparent lift can be a real improvement, or it can be ordinary sampling noise. This model evaluation sample size calculator estimates how many labeled examples you should plan before running an accuracy comparison that needs to support a release, procurement, or research decision.

The calculation begins with the current model’s accuracy, the smallest challenger accuracy worth detecting, a significance level, and a desired power. Those choices make the trade-off visible before annotation time, reviewer capacity, or benchmark budget is committed. The result is an approximate count for each model and a combined total for an independent two-group comparison.

Use this estimate as an early design check for a release gate, an experiment plan, a vendor evaluation, or a paper appendix. It is especially useful when the expected accuracy lift is small, because a narrow gap often requires far more labels than intuition suggests. Planning the benchmark first also reduces the temptation to keep sampling until a preferred result appears.

What model-evaluation question this sample size calculator answers

This model evaluation sample size calculator answers a focused planning question: how many labeled observations are needed to have a chosen chance of detecting a specified improvement in ordinary accuracy while controlling the chance of a false positive? It compares a baseline proportion with a higher target proportion using a standard normal approximation for two proportions.

For example, a team might have a current classifier with accuracy 0.80 and decide that 0.85 is the minimum challenger result worth promoting. The calculator estimates the evaluation-set size needed to distinguish those values at the selected alpha and power. The estimate does not guarantee that a particular experiment will succeed. Instead, it describes the scale of experiment designed to have the requested sensitivity if the target accuracy is true.

This tool is most appropriate when each model is evaluated on separately sampled observations, or when that independent-group approximation is acceptable for a rough budget. If both models are scored on exactly the same examples, their outcomes are paired. A paired comparison such as McNemar’s test may then be more efficient and more suitable than this planning approximation.

How to use the model evaluation sample size calculator

How to use this model evaluation sample size calculator begins with choosing the smallest practical lift, not the most optimistic lift. Enter proportions rather than percentages: write 0.80 for 80% and 0.05 for 5%. Submit the form and read the per-model count as a rounded-up planning minimum.

1. Set Baseline Accuracy to a representative accuracy for the current or control model.
2. Set Target Accuracy to the lowest challenger accuracy that would change your decision.
3. Choose Significance Level α, commonly 0.05 for a two-sided comparison.
4. Choose Desired Power (1−β), commonly 0.80 or 0.90.
5. Select Compute, then budget the displayed total plus labels needed for quality control and any separate holdout set.

After the first calculation, run a short sensitivity check. Hold alpha and power fixed, then try a slightly smaller and a slightly larger target lift. This makes clear whether the annotation budget is driven mainly by a realistic performance gap or by a particularly demanding evidence threshold. It also gives stakeholders a concrete way to discuss what level of improvement is genuinely useful.

Choosing baseline accuracy, target accuracy, alpha, and power

These model-evaluation inputs define the claim that the benchmark should support. Baseline accuracy usually comes from a representative prior evaluation, not a favorable development slice. Target accuracy should be the minimum result that would justify deployment, more review, or a change in model strategy. It must be greater than the baseline here because the planned comparison is an improvement question.

Alpha is the tolerated probability of declaring a difference when there is no difference of the kind being tested. A lower alpha asks for stronger evidence and therefore usually increases the required sample. Power is the probability of detecting the planned lift when that lift actually exists. Raising power makes missed improvements less likely, but it also increases the labeling commitment.

Accuracy, alpha, and power are unitless proportions from 0 to 1. Do not enter 80 when you mean 80%; use 0.80. The form rejects zero or invalid alpha and power values because a normal critical value cannot be calculated at those boundaries. In practice, record why each input was chosen so a later reader can distinguish a decision threshold from a convenient guess.

The two-proportion formula behind model evaluation sample size

The model evaluation sample size formula estimates the required count n for each model group. Here, p₁ is baseline accuracy, p₂ is target accuracy, and the pooled planning accuracy is their average. The z values are normal-distribution critical values determined by alpha and power. This is a two-sided alpha calculation, which is why α is divided by two in the first critical value.

The squared difference between target and baseline appears in the denominator. Consequently, moving 0.85 closer to 0.80 makes that denominator much smaller and the planned sample size much larger. The calculator rounds n up to a whole labeled observation for each model, then reports twice that count as the total. The formula is a planning approximation, so it should guide a study design rather than be treated as a substitute for the final statistical analysis.

Worked example: testing an 80% to 85% accuracy lift

This worked example uses the default model-evaluation assumptions: a baseline accuracy of 0.80, a target accuracy of 0.85, alpha of 0.05, and power of 0.80. These settings describe a five-percentage-point absolute accuracy lift. Select Compute to obtain the estimated labeled observations needed per model and the combined total for the independent-groups approximation.

If the resulting label count exceeds the available budget, the useful response is not to ignore the calculation. First ask whether a five-point lift is truly the minimum meaningful change. A larger decision-relevant lift reduces the required count because the models are easier to distinguish. Alternatively, collect labels over a longer period, use a better paired evaluation design, or narrow the claim being tested. Relaxing alpha or power can reduce the count, but it also changes the strength of evidence the team is planning to obtain.

Before approving the study, add a practical buffer for unusable records, adjudication, required demographic or product slices, and any final untouched test set. The mathematical result is an estimate for analyzable observations, not necessarily the number of raw items that must enter an annotation pipeline. A team evaluating several candidates should also decide in advance whether one champion will be compared or whether a multiple-comparison adjustment is needed.

Interpreting the labeled evaluation size result

The model evaluation result reports an approximate number of samples per model and the total across two groups. Treat that number as a planning floor under the stated assumptions. It is not a confidence interval for the eventual observed accuracy, and it does not mean every benchmark of that size will show a statistically significant result. Randomness still affects any individual evaluation.

A quick directional check can validate the entries. A stricter alpha should increase the result. Higher power should also increase it. Making the target further above the baseline should generally reduce it because the models are easier to distinguish. If the opposite happens, check for a reversed baseline and target or for percentages entered in place of proportions.

The Copy Result control captures the current text estimate for a planning note. Record all four input values beside the copied result, because the same numerical sample size is only meaningful in the context of its baseline, detectable lift, alpha, and power. Include the intended data population and date as well, since production traffic and label definitions can change over time.

Limitations and assumptions of accuracy-comparison sample size planning

Limitations of this model evaluation sample size estimate matter whenever a benchmark informs a consequential decision. The approximation assumes independent observations and a simple accuracy outcome. Real evaluation datasets can include repeated users, correlated documents, shifting class mixes, label disagreement, and rare but important failure modes that require a more detailed design. Clusters such as many records from one customer can make an apparently large dataset contain less independent information than its row count implies.

Accuracy can also conceal unequal error costs. For imbalanced classification, fraud detection, medical triage, ranking, retrieval, or generation quality, precision, recall, F1, calibration, AUROC, or a task-specific utility may be more relevant than overall accuracy. In those cases, plan directly around the metric and decision rule that matters rather than treating this calculator as a universal evaluation protocol. A small accuracy gain that worsens a safety-critical subgroup may not be a meaningful improvement.

Finally, do not tune repeatedly on the same final test set. Keep a genuinely held-out evaluation set, define the comparison rule before looking at it, and document slice analysis or multiple-comparison adjustments. Used with those safeguards, this calculator provides a clear first estimate of the labeling commitment required to test a claimed accuracy lift.