DoE, Factorial & Screening Designer
Generate a coded design matrix for a two-level factorial or a Plackett-Burman screening study, fill in the actual factor levels, then paste your measured responses to read off main effects, two-factor interactions, and model coefficients.
How to use this tool
Plan an experiment that varies several factors at once, then find out which ones actually drive your result. It lays out the runs to perform and, once you add the measurements, ranks each factor's effect.
What to enter
- Design type: a full factorial tests every combination (2–5 factors, best when you want interactions) or a Plackett-Burman screen checks up to 11 factors in 12 runs (main effects only).
- Number of factors: how many variables you are changing (temperature, pH, catalyst…). The tool shows how many runs that needs.
- Measured result per run: after you run the experiment, paste one response number per line in run order. Leave blank to just generate the plan, or click "Fill demo data" to see it work.
Reading the result
First you get the design matrix: the recipe of high/low settings for each run. Once responses are in, the effects analysis lists each factor's main effect: the bigger the magnitude, the more it moves your result. Near-zero effects are candidates to drop.
Worked example
A full factorial with 3 factors lays out 8 runs; paste 8 responses (or click Fill demo data) and the tool ranks which of the three factors carries the largest effect.
Design
Responses
Design matrix
Effects analysis
Methodology
The full factorial enumerates all 2k combinations of two levels (coded −1/+1) in standard Yates order, so every main effect and interaction is estimable. Plackett-Burman uses a 12-run orthogonal array to screen up to 11 factors for main effects only (interactions are confounded). A main effect is the change in mean response when a factor moves from its low to its high level: effect = mean(y at +1) − mean(y at −1); the regression coefficient is half the effect. Two-factor interaction columns are the element-wise products of the two factor columns (full factorial only).
Reading the numbers
- The largest-magnitude effects dominate the response; small ones near zero are candidates to drop. Plot effects on a Pareto or normal-probability chart to judge significance with replication.
- Plackett-Burman is for screening: it finds the vital few factors. Follow up with a factorial or response-surface design on those.
- With no replication there is no pure-error estimate, so treat effect sizes as descriptive, not as p-values.