Home / Lean Six Sigma / Basic statistics & tests
Is the new supplier better? Did the new method shorten the cycle? Did the poka-yoke cut scrap? Paste the measurements for A and B and see whether the difference is real, whether it matters in practice, whether the sample was large enough and what it is worth per year. You do not need to know which test to use: choose “Compare A × B” and the page decides from the type of data (measurement, pass/fail or count). All you need are the measurements on each side; volume and cost are optional.
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.
How to read: Estimate = the difference (or value) computed from the data; CI = range where the true value probably lies; statistic (t, Z, χ², F) = how far the estimate is from H₀, in units of error; P-value below α = significant difference.
Dot = estimate; bar = confidence interval; red line = H₀; green band = difference that does not matter in practice.
How to read: the axis is the difference B − A (or the estimated statistic). If the interval bar does not cross the red line (H₀), the difference is real; if it lies entirely inside the green band, it is too small to matter. A bar that crosses H₀ and leaves the green band = not enough data to decide.
Difference B − A applied to the annual volume entered.
Dots = each measurement; box = middle 50% and median; diamond with bar = estimate and CI; dashed lines = H₀ or specification.
How to read: each column is a sample and the vertical axis is the measurement. Compare the height of the diamonds (the means) and the length of the bars (the uncertainty): short, well-separated bars indicate a clear difference. Isolated points far from the box are unusual values that can distort the test.
Distribution of each sample’s values, with each mean.
How to read: each bar counts how many values fell in that range; the colors separate the samples and the vertical lines mark the means. Bell-like humps, with no double peaks or long tails, confirm the t-test is appropriate; if the shape is very skewed, prefer the nonparametric test.
Chance of detecting each true difference with the current sample (solid) and with the sample that gives 80% at the difference that matters (dashed).
How to read: the horizontal axis is the size of the true difference and the vertical one the chance that the test notices it. Good means the solid curve is above 80% at the difference that matters. If it is below, a “no difference” result does not prove equality: the sample is too small to see that difference.
How the test statistic is distributed if H₀ is true; the red area is the P-value.
How to read: the curve shows the values the test statistic usually takes when there is no difference at all. The line marks the value from your data. If it falls in the middle of the curve, the result is common and may be chance; if it falls in the tail, with a small red area (below α), it is unlikely to be chance.
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Use the "Compare A × B" mode: paste the measurements for A and B and say which is better (higher or lower). The page picks the test, shows the difference B − A with its confidence interval and tells you whether it is real, large enough to matter and whether the sample was big enough. In the cycle-time example, the new method is about 2.2 s faster and the whole interval lies beyond 1 s, so the improvement is real and relevant.
That a difference as large as the one observed would be rare (under 5% chance) if A and B were the same. It does not say whether the difference is large: with huge samples, tiny differences become significant. That is why the page also shows the confidence interval and the band of the difference that matters.
When the same part, lot or operator appears in both conditions, such as the same part measured on two gauges or the same lot before and after a treatment. Pairing removes part-to-part variation and often detects differences the 2-sample test misses. Different parts in A and B: use the 2-sample test.
Only if the whole confidence interval fits inside the green band of the difference that matters. If the interval is wide, the result is inconclusive: the sample was too small. The power curve shows the chance the test had of seeing the difference and how many more samples are needed for 80%.
To compare two proportions defective (before × after, shift × shift), use 2 proportions: the page runs the Z test and Fisher’s exact test, which holds even with few defects. For counts of defects per part, failures per month or stops per shift, use the Poisson rates.
To compare the spread (stability) of two processes without assuming normal data. The F and chi-square tests are exact only for normal data and can be badly off with heavy tails. A process B with the same mean but a smaller standard deviation is also an improvement: fewer parts out of specification.
Because each look is a new chance of a false alarm. Looking 5 times at 5%, the real chance of “finding” a difference that does not exist reaches about 14%. Set the sample size beforehand, or enter how many times you looked: the page shows the real α and the corrected p threshold for each look.
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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