Factorial Balanced Grid Generator
Generates continuous observations across an a × b factorial grid with cell-specific treatment combinations.
Statistics & Probability / Two-Way Factorial ANOVA
FREE TO EXPLORELABORATORY 32 · STATISTICS & PROBABILITY
Two-Way Factorial Analysis of Variance, Main Treatment Effects, and Interaction Significance
Investigate two-factor experimental designs, partition sum of squares into Factor A, Factor B, and Interaction (A × B) components, evaluate interaction plots for non-parallelism, and verify factorial F-ratio scaling. Explore interactive statistical sampling, probability models, and empirical regression.
SAMPLE · INFER · CONVERGE
Your virtual statistics laboratory.
EXPECTED INTERACTION F-STATISTIC E[F_AB]—
SAMPLING TELEMETRY
Ready to sample with Factor k = 1.0.
Adjust Factor k, then execute statistical trial.
Probabilistic samples are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity empirical probability functions.
Statistical assumptions and distribution limits
In unbalanced designs (unequal cell sizes), sums of squares are non-orthogonal and depend on the choice of Type I, II, or III calculation. The empirical regression of interaction F-statistics against factor k confirms theoretical factorial response with linear slope m = 3.0000 and R² = 1.000000.
Statistical tools & sampling modules.
Three-Way Variance Decomposer
Partitions total sum of squares into SSA, SSB, SSAB (interaction), and SSE (error) components.
Factorial Interaction Plotter
Renders interaction profiles across factor levels to visualize non-parallel crossing lines indicating synergy or antagonism.
Main Effects Significance Unit
Computes F_A = MSA / MSE and F_B = MSB / MSE to test primary treatment factors.
Interaction F-Test Engine
Evaluates the interaction test F_AB = MSAB / MSE to determine whether Factor A effects depend on Factor B levels.
Factorial F-Ratio Regression Unit
Performs linear regression of interaction F-statistics versus factor k to confirm the slope m = 3.000.
FOLLOW THE METHOD
A reason behind every step.
Investigate two-factor experimental designs, partition sum of squares into Factor A, Factor B, and Interaction (A × B) components, evaluate interaction plots for non-parallelism, and verify factorial F-ratio scaling. Standardized parameter settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 factor.
01
Configure 2 × 2 Factorial Experimental Design
Set Factor A levels a = 2 and Factor B levels b = 2 with balanced replication n = 10 per cell (total N = 40) on the factorial console.
02
Synthesize Observations under Additive Null Model
Generate data with purely additive main effects (no interaction: γ_{ij} = 0). Confirm that cell profile lines remain strictly parallel.
03
Decompose Total Sum of Squares
Compute SSA, SSB, SSAB, and SSE. Verify the complete orthogonal variance partition: SST = SSA + SSB + SSAB + SSE.
04
Inject Non-Additive Interaction Synergy
Introduce an interaction effect in cell (2, 2). Observe non-parallel crossing lines on the interaction plot, indicating that Factor A depends on Factor B.
05
Step Interaction Scale Factor Across k = 1 to 6
Increment the interaction parameter across standardized settings k ∈ {1.0, 2.0, 3.0, 4.0, 5.0, 6.0}, recording the interaction F-statistic F_AB.
06
Conduct Linear Regression on Factorial Response
Fit a linear regression model y = mx to coordinate pairs (x = k, y = E[F_AB]). Confirm that empirical slope m = 3.0000 validates interaction scaling.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into empirical insight.
Points are your recorded observations. The solid regression line validates Two-Way Factorial ANOVA mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
y = 3.0000 · x
| # | Factorial Interaction Scale Factor k (factor) | Expected Interaction F-Statistic E[F_AB] (F-Statistic) | Interaction Factor k | Expected Interaction F-Statistic E[F_AB] | Remove |
|---|
No readings yet. Execute a statistical trial and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING