Home / Lean Six Sigma / Basic statistics & tests
Paste your measurements from Excel and see at once the shape of the distribution, the mean and spread with their confidence intervals and whether the data are normal, for each machine, shift or lot. All you need is one column of measurements per group (preferably 30 or more values); specification limits are optional. It is the first step before computing Cpk, building a control chart or comparing groups with ANOVA.
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.
The same numbers as the reports, one group per column, for comparison.
How to read: each column is a group. StDev = typical part-to-part spread; SE Mean = how far the sample mean may be off; Q1–Q3 = range of the middle half of the parts; CI = range where the true value probably lies; P-Value (AD) in red = non-normal data; Unusual data = points beyond the boxplot whiskers.
Box = middle 50%, line = median, × = mean, whiskers to 1.5 × IQR; isolated points are unusual data.
How to read: the vertical axis is the measurement; each box is a group. Boxes at the same height = groups at the same level; a taller box = a more variable group. Red diamonds are unusual values worth checking. Dashed lines = LSL and USL: boxes or whiskers touching them signal risk of out-of-spec parts.
Points on the line = normal data. With one group, the band shows the 95% confidence interval of the fitted percentiles.
How to read: the horizontal axis is the measurement and the vertical one the cumulative percentage of parts (scale stretched at the ends). If a group’s points follow the line of the same color, the data are normal. S-shaped, bent or stepped points = not normal; the text in the corner gives each group’s A² and P-value (red = failed).
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.
A page that brings together, for each data set, the histogram with the normal curve, the boxplot, confidence intervals for the mean and median, the normality test and full descriptive statistics. Use it to understand the data before computing capability, building control charts or comparing groups.
Look at the Anderson-Darling P-value: 0.05 or more, the data can be treated as normal; below 0.05, they cannot. In the camshaft example, Machine 1 has strongly negative kurtosis and a very low p (A² = 4.43), a sign of two mixed populations; Machine 2 also fails (p = 0.029: positive kurtosis, a narrow peak and tails longer than the normal); only Machine 3 passes (p = 0.615).
The mean averages all values; the median is the middle value. For symmetric data they are close. If one side has far-off values (skewness), the mean is pulled and the median better represents the typical part.
They show how far the estimate may be off because only a sample was measured. With 100 parts, the camshaft mean is known to within a few hundredths of a millimeter; with 10 parts, the interval would be about three times wider.
Skewness measures whether one tail is longer (0 for the normal curve). Kurtosis measures whether the distribution is flat (negative) or peaked with heavy tails (positive). Strongly negative kurtosis often points to mixed machines, tools or settings.
To describe the process, 30 or more per group; for capability, 100 or more. With fewer than 20 values the normality test has little power: it rarely rejects even when the data are not normal.
Paste each machine in its own column with the name in the first row, or use the stacked layout with a group column and a value column. Columns may have different lengths. Then use the ANOVA button to test whether the means differ.
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