Kurtosis Reports: Check Whether the Software Subtracts Three

The statistical question

Kurtosis and excess kurtosis differ by subtracting three from the conventional kurtosis measure. Their normal-distribution reference values are therefore three and zero respectively. Sample implementations can also apply finite-sample adjustments. A comparison needs both the definition and estimator convention. Kurtosis concerns tail behavior and does not by itself establish a process failure or explain its cause.

Primary reference: NIST Engineering Statistics Handbook.

An illustrative review example

Imagine the same fictional file is analyzed twice. One output labels kurtosis as 4.2, and another labels excess kurtosis as 1.2. Subtracting three reconciles those values without changing any observed readings. If a third program gives a slightly different result, check its sample correction rather than assuming a changed data set. These are invented reporting numbers, not claimed measurements from a production process.

Prepare the evidence for discussion

Preserve software version, estimator definition, adjustment convention, sample size and data filter alongside the output. Review the actual tail readings and collection conditions before drawing an engineering conclusion. When comparing repeated supplier reports, include a common glossary rather than copying unexplained chart labels. A reliable discussion separates a definition mismatch, a computation difference and an actual change in the observations.

A definition can shift the output by three

This blank worksheet is for your own project. It contains no H M machine trial result.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• Primary reference: NIST Engineering Statistics Handbook