01 · Purpose
Why and when to use it
Consider it when a justified statistical analysis needs a different scale; also consider fitting an appropriate original-scale distribution instead.
Who takes part?
The measurement owner works with people who understand the process and the recorded data. Statistical or measurement-system decisions should involve someone able to check the assumptions and study design.
02 · Application
How to apply it
Start with an agreed measurement purpose, explicit units and trustworthy observations. Identify missing cases and assumptions before calculating.
- Clarify the analysis purpose and inspect data validity and stability.
- Choose a transformation whose domain covers the observations.
- Apply it consistently and record the function and parameters.
- Check model assumptions again on the transformed scale.
- Transform relevant specifications consistently and explain results in original units where appropriate.
03 · Example
A worked measurement example
Original fictional teaching example. Small datasets illustrate the method; they are not proposed as sufficient study sizes. Supplied parameters are assumptions, not estimates from a real process.
| Duration x (minutes) | ln(x) |
|---|---|
| 1 | 0 |
| 2 | 0.693 |
| 4 | 1.386 |
| 8 | 2.079 |
04 · Interpretation
What the result tells you
Equal doubling of duration becomes equal spacing on a log scale. exp(mean(log x)) is the geometric mean, not the original arithmetic mean.
Completion check: A documented scale transformation with a justified analysis and interpretable results.
05 · Judgement
Mistakes and limitations
Logarithms require positive values; do not silently add a constant to accommodate zeros. Transformation does not fix bad measurement, dependence, mixtures or instability.
07 · Reading
Sources and further reading
The tool list follows the accepted LeanTrainingLab overview and its reference to Six Sigma+Lean Toolset, second edition (Lunau, editor; Springer, 2013). The book chapters were not available for direct review during this build. Explanations, examples and worksheets are original teaching material. Further reading supplies professional background; local conventions are stated explicitly.