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Sampling and Trial Analysis

Coded Factor Levels: Minus One and Plus One Need Their Physical Settings

Factorial codes are coordinates in a design, not machine settings. Translate every coded row using the correct factor-specific units before discussing a trial.

Library dates organize the collection. Actual publication and revision dates are shown separately.

Factorial codes are coordinates in a design, not machine settings. Translate every coded row using the correct factor-specific units before discussing a trial.

The statistical question

In a two-level factorial design, minus one and plus one commonly label the selected low and high levels of each factor. The codes permit a compact model matrix, but their physical meanings differ by factor. A row in standard design order is also not necessarily the planned execution order. Both the code-to-setting map and authorized run sequence must be supplied.

Primary reference: NIST Engineering Statistics Handbook.

An illustrative review example

Consider invented factors A with selected levels 40 and 60 arbitrary units, and B with levels 2 and 6 seconds. The coded row A=+1,B=-1 corresponds to 60 units and 2 seconds, not numerical machine entries of plus one and minus one. The center mapping would be 50 units and 4 seconds if those continuous factors use a linear midpoint convention. These values explain coding and are not proposed operating settings.

Prepare the evidence for discussion

Give each factor a named parameter, unit, low/high definition and approval boundary. Translate the complete matrix into the operator-facing plan through the responsible trial team, and retain the coded version for analysis. Keep nominal alternatives, such as two nozzle identities, separate from continuous midpoint arithmetic. Record execution order and actual values so later analysis can reconstruct what was physically tested rather than assuming every code was followed.

Codes need physical meaning

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

Codes need physical meaning
Question to resolveEvidence to retain
Factor identityActual parameter or category
Code mapLow and high physical values
UnitFactor-specific measurement basis
Run recordAuthorized order and actual settings

Customer Questions

Are coded levels direct control entries?

No. They label selected factor levels and need the factor-specific physical map.

Is standard matrix order necessarily execution order?

It is a design representation; the actual authorized run sequence must be separately identified.

Can nominal alternatives be averaged to form a midpoint?

A nominal category has no numerical midpoint merely because it was coded minus one and plus one.

Primary References

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

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