Home / Lean Six Sigma / Basic statistics & tests
Before comparing supplier A with B, a new method with the old one, or before with after, find out how many parts to measure so a difference that matters is not missed, and what it costs. You enter the smallest difference that would change the decision and an estimate of the process spread (from history or a pilot); the page returns the sample per group, the power achieved and cheaper or safer scenarios.
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
Same layout as the power and sample size report: hypotheses, assumed values and the results table.
Chance of detecting each size of difference, for the calculated sample size and for half and twice it. The dot is your choice.
How to read: the horizontal axis is the true difference between the groups; the vertical one is the chance that the test detects it. Each curve is a sample size. Follow the curve up to the 80% line: differences to the right of that point will almost always be detected; to the left, they may go unnoticed.
How power grows with the sample for the chosen difference: beyond a point, each extra part adds little.
How to read: the horizontal axis is the number of parts per group and the vertical one the power. The curve rises fast at first and then flattens: the marked dot is your choice. If it sits on the flat part, cutting a few parts barely changes the power; on the steep part, every part counts.
Sample needed for each difference at 80%, 90% and 95% power (log scale). Half the difference needs about four times the sample.
How to read: the horizontal axis is the difference you want to detect; the vertical one is how many parts per group are needed (log scale: each grid line multiplies by 10). The three lines are 80%, 90% and 95% power. The smaller the difference, the higher the curve climbs: asking for too much precision can get expensive.
Distribution of the test statistic if there is no difference (H0) and if the chosen difference exists (H1). Red: false alarm α; green: power; amber: β, the chance of missing it.
How to read: there are two curves: the left one is what the test would show if there were no difference; the right one, if the chosen difference existed. The vertical line is the decision threshold. The further apart the curves (larger sample or larger difference), the larger the green area (power) and the smaller the amber one (risk of missing it).
How to read: each row is an alternative scenario (another power, difference or size). Compare the sample column (and cost, if entered) to see how much each extra requirement costs in parts.
Take this page’s results to another calculator with the fields already filled in.
The calculation report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. The full report also includes the charts and interpretations, in color. In the print dialog, choose Save as PDF.
Choose 2-sample t, enter the smallest mean difference that matters (for example 0.5 mm), the process standard deviation (0.4 mm) and the desired power (80%). The page gives the number of parts per supplier: in the example, 12 parts from each, with an actual power of 83%.
It is the chance that the test flags a difference that really exists. With 50% power, a well-run study misses half of the real differences; with 80% or 90%, you rarely miss a difference of the chosen size.
Use historical data from the same process, the within σ from a control chart, or a pilot study of 10 to 30 parts (paste them into "Estimate the standard deviation from data"). To plan with a margin, use the upper limit of the confidence interval.
The precision of a mean improves with the square root of the number of parts. To see a difference half as large, the error of the mean must halve, and that takes four times as much data.
Only when, before collecting, you decided that just one direction matters (for example, the improvement is only worth it if it reduces defects). It needs fewer parts but cannot see changes in the opposite direction.
A standard test tries to prove there is a difference; failing to find one does not prove the products are the same. An equivalence test tries to prove the difference lies within acceptable limits, which is the right approach to validate a change of supplier or method.
Choose 2-level factorial, enter the factors, model terms, effect to detect and standard deviation. The page calculates the replicates and total runs; center points help test curvature and add degrees of freedom to the error.
Important notice: Indus Metrics tools produce estimates and pre-sizing results from the data you enter and from published engineering methods. They do not replace design, calculations or reports signed by a licensed professional engineer (PE), nor verification against the applicable codes, standards and regulations, such as OSHA rules and the ASME codes. Material and fuel properties vary: check manufacturer data or your own process analyses before deciding. By using this site you agree to the Terms of Use.
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