Home / Lean Six Sigma / Statistical analysis
Paste your data from Excel and find out whether suppliers, machines, shifts or process settings give different means, which pairs differ, how much each factor weighs and whether the analysis assumptions hold.
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.
R: large standardized residual (|R| > 2). X: unusual X (high leverage).
Each row is a pair. If the interval does not cross zero, the difference is significant (in red).
Mean of each level with its confidence interval. The dashed line is the overall mean.
Fitted mean of the response at each level of each factor (other variables at their mean). The steeper the line, the larger the effect.
Data means for each combination of two factors. Parallel lines: no interaction.
Comparison intervals: two levels whose intervals do not overlap differ. In red, those that do not overlap at least one other.
Box = middle 50% (Q1 to Q3), line = median, × = mean, whiskers to 1.5 × IQR; isolated points are unusual data.
Each measurement by level, with the means connected across levels.
Residual = measurement − fitted mean of its group. They check the assumptions: normality, constant variance and independence.
Normal probability plot
Versus fits
Histogram
Versus order
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 t-test compares two means. With three or more levels (for example, four suppliers), running several t-tests raises the chance of a false alarm: with six pairs at 5% each, the chance of at least one error exceeds 25%. ANOVA tests them all at once and Tukey comparisons control that error.
It is the probability of seeing differences as large as those observed if all means were actually equal. In the supplier example, p < 0.001: the difference is very unlikely to be chance. With p ≥ 0.05 you cannot claim a difference, which does not prove the means are equal.
Tukey compares all pairs and is the default choice. Dunnett compares each level with a control (the current supplier) and is more sensitive when that is all you need. Hsu MCB identifies which level may be the best. Fisher does not correct for many pairs and is only a screening tool.
Choose "Assume equal variances: No". The calculator then uses Welch’s test and Games-Howell comparisons, which do not require equal spreads. Remember that a much more variable level is a quality finding in itself: it will produce more out-of-spec parts even with the right mean.
For ANOVA to be robust to non-normal data, 15 or more per level (20 with 10 to 12 levels), the Assistant criterion used in the report card. To detect a small difference, enter the difference that matters: the card shows the power and how many measurements 80% and 90% power would take.
There is an interaction when the effect of one factor changes with the level of another. In the roughness example, if a higher feed worsened the finish much more at one cutting speed than at another, the lines in the interaction plot would fan out or cross. Parallel lines mean the effects simply add up.
In unbalanced data (levels with different numbers of measurements), the factors are partly confounded. Sequential SS depends on the order in which terms enter; adjusted SS measures each term after all others and is the one used for the F-test. In balanced data both are the same.
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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