GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 316 of 500
Plan a factorial experiment: the coded runs for a full or half-fraction factorial design, with centre points and replicates — the starting point of any designed food-process trial.
Try sample values — fills the form with the worked example below.
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Factorial runs
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Total runs
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Runs per replicate
Equation: Full factorial runs = 2ᵏ; half-fraction runs = 2ᵏ⁻¹. Total runs = (factorial runs + centre points) × replicates. Each factor is coded −1 (low) and +1 (high); centre points are coded 0.
Method: Factorial design per Box, Hunter and Hunter, Statistics for Experimenters, and Montgomery, Design and Analysis of Experiments. The design matrix is built from the standard Yates order (factor 1 alternates fastest).
Assumptions: the factors are independent and each has two levels (plus the centre); the response is measured the same way at every run.
Limitations: a half fraction confounds main effects with interactions — it screens factors but cannot estimate every interaction. The builder plans the design; it does not analyse the results (use Tools 306, 307 or 312 for that).
Rounding: run counts are whole numbers; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Factorial design per Box, Hunter and Hunter, Statistics for Experimenters, and Montgomery, Design and Analysis of Experiments. The design matrix is built from the standard Yates order (factor 1 alternates fastest).
Assumptions: the factors are independent and each has two levels (plus the centre); the response is measured the same way at every run.
Limitations: a half fraction confounds main effects with interactions — it screens factors but cannot estimate every interaction. The builder plans the design; it does not analyse the results (use Tools 306, 307 or 312 for that).
Rounding: run counts are whole numbers; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: 2 factors, full factorial, 4 centre points, 1 replicate: factorial runs 4, total runs 8.
Enter values above to see results.
Add centre points when you want to check for curvature — without them a two-level design cannot see it. Tool 316 of 500 — GIFSQ
