Home / Lean Six Sigma / Statistical analysis
Find out whether the defect depends on the machine, the shift or the supplier, where the difference lies and whether it is large enough to matter, and test whether counts follow history or chance (Poisson).
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.
Bars = observed; black dash = what would be expected with no association (or with the tested proportions).
Largest to smallest. Red = more occurrences than expected; blue = fewer.
Width = row total; height = % of each column. Thick outline: adjusted residual beyond ±2 (▲ above, ▼ below expected).
Each cell shows how many standard errors the count is above (red) or below (blue) expected; beyond ±2 is significant.
Dot and bar = observed proportion and its exact interval (Clopper-Pearson); dash = test proportion. A bar that misses the dash points to a category off expectation.
Chi-square curve with no association (H0). The shaded area right of the observed value is the P-value.
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.
When both variables are categories counted on the same parts: machine and defect type, shift and scrap, supplier and receiving acceptance. The test says whether the distribution of one changes with the other. In the press example, press 2 on the 1st shift had 76 rejected handles against 61 expected: p = 0.019, there is an association.
The expected count is what the cell would hold with no association: row total × column total ÷ grand total. The contribution, (observed − expected)²/expected, shows how much each cell weighs in the chi-square; the largest tell you where to start investigating.
They show, in standard errors, how far each cell is above or below expectation. Above +2 or below −2 the difference in that cell is significant on its own. It is the most direct way to answer “which machine and which shift?”.
In 2×2 tables with small counts (some expected count below 5), common in receiving inspection with few rejected lots. It computes the exact probability and does not rely on the chi-square approximation. The page shows the two-sided result and both one-sided ones.
The size of the association, from 0 to 1, which does not grow with the amount of data. With thousands of parts nearly everything gives p < 0.05; V separates strong associations (above 0.5) from those that change no decision (below 0.1).
Use “Goodness of fit to proportions”: paste the category, the number observed in the period and the historical proportion (or historical count). The test compares the two distributions and the contribution chart shows which defect type changed.
c and u charts assume defects occur at random (Poisson). If the variance is much larger than the mean, defects cluster in some parts and the chart raises too many alarms. In the panel example, 28 units with 3 defects against 5 expected reject the Poisson hypothesis (p < 0.001).
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.
© 2026 Indus Metrics. Found an error? Write to contato@seudominio.com.