Sample-Size & Cost-of-Testing Planner

How many units to test to reliably detect a difference that matters, how power rises with sample size, and (with costs) the sample size that minimizes total expected cost. Uses exact t-test power. Runs entirely in your browser.

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1. The test

Comparison

Difference to detect (measurement units)

Standard deviation (planning value; paired = SD of the differences)

Significance level, α

Alternative

Target power (%)

2. Cost of testing (optional; leave the last two blank for sample size only)

Fixed cost per study ($)

Cost per unit tested ($)

Cost of missing a real effect ($) (what a real difference this size is worth if the study fails to find it)

Chance the effect is real (%)

When NOT to use this

Means only: it plans t tests on roughly normal data with equal group sizes. Pass/fail proportions, unequal groups, non-parametric, equivalence and non-inferiority tests are outside this version.
It does not plan designed experiments (factorials, blocking, replication); that needs a different tool.
The standard deviation is a planning guess. A pilot-sample SD tends to understate the real one, so look at the sensitivity rows.
Power answers “will I detect a real difference of this size”, not “is that difference important”.
The cost of missing a real effect and the chance it is real are judgments. Treat the cost-minimizing n as a range: the table shows how flat the cost is near it.
Not a substitute for a statistician when the design is complicated (clustered, repeated or sequential data).