Multi-Group Gaussian Generator
Generates k independent treatment groups with specified group means μ_j and common within-group variance σ^2.
Statistics & Probability / One-Way ANOVA F-Test
FREE TO EXPLORELABORATORY 31 · STATISTICS & PROBABILITY
One-Way Analysis of Variance (ANOVA), Between/Within Sum of Squares, and F-Test Significance
Decompose total variance in multi-group experimental designs, compute Between-Group Sum of Squares (SSB) and Within-Group Sum of Squares (SSW), evaluate the omnibus F-statistic, and verify the F-ratio scaling law. Explore interactive statistical sampling, probability models, and empirical regression.
SAMPLE · INFER · CONVERGE
Your virtual statistics laboratory.
EXPECTED OMNIBUS F-STATISTIC E[F]—
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
ANOVA tests for differences in means, but is sensitive to variance heterogeneity when group sizes are unequal. The empirical regression of omnibus F-statistics against treatment factor k confirms theoretical variance decomposition with slope m = 1.5000 and R² = 1.000000.
Statistical tools & sampling modules.
Sum of Squares Decomposer
Partitions total sum of squares SST into between-group sum of squares SSB and within-group error sum of squares SSW.
ANOVA Mean Square Table Engine
Computes Mean Square Between MSB = SSB/(k-1) and Mean Square Within MSW = SSW/(N-k).
Omnibus F-Test Resolver
Evaluates the variance ratio F = MSB / MSW and determines exact upper-tail p-values from F(k - 1, N - k).
Eta-Squared Effect Size Meter
Computes proportion of total variance explained by treatment: η² = SSB / SST.
ANOVA F-Ratio Regression Unit
Performs linear regression of expected F-statistic versus treatment factor k to confirm the slope m = 1.500.
FOLLOW THE METHOD
A reason behind every step.
Decompose total variance in multi-group experimental designs, compute Between-Group Sum of Squares (SSB) and Within-Group Sum of Squares (SSW), evaluate the omnibus F-statistic, and verify the F-ratio scaling law. Standardized parameter settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 factor.
01
Configure Multi-Group Experimental Design
Set group count to k = 3 treatments with balanced sample sizes n = 10 per group (total N = 30) on the ANOVA control interface.
02
Synthesize Baseline Observations under H_0
Generate all groups from standard normal N(0, 1) with equal means μ_1 = μ_2 = μ_3 = 0.0. Verify grand mean x̄_grand ≈ 0.0.
03
Perform Orthogonal Variance Decomposition
Compute total sum of squares SST, between-group sum of squares SSB, and within-group sum of squares SSW. Confirm SST = SSB + SSW.
04
Evaluate Omnibus F-Distribution under H_0
Compute F = MSB / MSW across 20,000 runs under the null. Verify that empirical mean F matches E[F] = (N - k)/(N - k - 2) = 27/25 = 1.080.
05
Step Treatment Effect Across Factor k = 1 to 6
Inject systematic treatment shifts across standardized settings k ∈ {1.0, 2.0, 3.0, 4.0, 5.0, 6.0}, recording the omnibus F-statistic.
06
Conduct Linear Regression on ANOVA Scaling
Fit a linear regression model y = mx to coordinate pairs (x = k, y = E[F]). Confirm that empirical slope m = 1.5000 validates non-central F response.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into empirical insight.
Points are your recorded observations. The solid regression line validates One-Way ANOVA F-Test mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
y = 1.5000 · x
| # | Treatment Effect Magnitude Factor k (factor) | Expected Omnibus F-Statistic E[F] (F-Statistic) | Treatment Effect Factor k | Expected Omnibus F-Statistic E[F] | Remove |
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