Plan and visualize multi-factor experimental designs
Design Configuration
Replicates increase precision and allow error estimation
Power Analysis (Optional)
Small: 0.2, Medium: 0.5, Large: 0.8
Design Summary
Effects Structure
Power Analysis
Design Matrix
Randomized Run Order
Randomize the order of experimental runs to protect against time-related confounding:
Help
What is Factorial Design?
A factorial design studies the effects of two or more factors simultaneously by testing all possible combinations of factor levels. This allows you to:
Estimate main effects of each factor
Detect interactions between factors
Be more efficient than one-factor-at-a-time experiments
Design Types
Full Factorial (2^k): Tests all combinations. For k factors with 2 levels each, requires 2^k runs. Provides complete information about all main effects and interactions.
Fractional Factorial: Tests a carefully chosen subset of combinations. Reduces runs but confounds some effects. Use when resources are limited and you can assume some interactions are negligible.
Main Effects vs Interactions
Main Effect: The average effect of changing one factor across all levels of other factors
Two-way Interaction: When the effect of one factor depends on the level of another factor
Three-way Interaction: When a two-way interaction depends on the level of a third factor (often negligible)
Example Applications
2×2 Design: Testing two drugs (yes/no) × two doses (low/high)
2×3 Design: Temperature (2 levels) × Catalyst (3 types)
2×2×2 Design: Drug × Dose × Gender in clinical trial
Industrial: Temperature × Pressure × Time for manufacturing optimization